Recognizable tree series with discounting

We consider weighted tree automata with discounting over commutative semirings. For their behaviors we establish a Kleene theorem and an MSO-logic characterization. We introduce also weighted Muller tree automata with discounting over the max-plus and the min-plus semirings, and we show their expressive equivalence with two fragments of weighted MSO-sentences

Weighted Automata and Logics on Hierarchical Structures and Graphs

Formal language theory, originally developed to model and study our natural spoken languages, is nowadays also put to use in many other fields. These include, but are not limited to, the definition and visualization of programming languages and the examination and verification of algorithms and systems. Formal languages are instrumental in proving the correct behavior of automated systems, e.g., to avoid that a flight guidance system navigates two airplanes too close to each other. This vast field of applications is built upon a very well investigated and coherent theoretical basis. It is the goal of this dissertation to add to this theoretical foundation and to explore ways to make formal languages and their models more expressive. More specifically, we are interested in models that are able to model quantitative features of the behavior of systems. To this end, we define and characterize weighted automata over structures with hierarchical information and over graphs. In particular, we study infinite nested words, operator precedence languages, and finite and infinite graphs. We show Büchi-like results connecting weighted automata and weighted monadic second order (MSO) logic for the respective classes of weighted languages over these structures. As special cases, we obtain Büchi-type equivalence results known from the recent literature for weighted automata and weighted logics on words, trees, pictures, and nested words. Establishing such a general result for graphs has been an open problem for weighted logics for some time. We conjecture that our techniques can be applied to derive similar equivalence results in other contexts like traces, texts, and distributed systems

Multi-weighted Automata Models and Quantitative Logics

Recently, multi-priced timed automata have received much attention for real-time systems. These automata extend priced timed automata by featuring several price parameters. This permits to compute objectives like the optimal ratio between rewards and costs. Arising from the model of timed automata, the multi-weighted setting has also attracted much notice for classical nondeterministic automata. The present thesis develops multi-weighted MSO-logics on finite, infinite and timed words which are expressively equivalent to multi-weighted automata, and studies decision problems for them. In addition, a Nivat-like theorem for weighted timed automata is proved; this theorem establishes a connection between quantitative and qualitative behaviors of timed automata. Moreover, a logical characterization of timed pushdown automata is given

Approximation in Description Logics: How Weighted Tree Automata Can Help to Define the Required Concept Comparison Measures in FL₀

Recently introduced approaches for relaxed query answering, approximately defining concepts, and approximately solving unification problems in Description Logics have in common that they are based on the use of concept comparison measures together with a threshold construction. In this paper, we will briefly review these approaches, and then show how weighted automata working on infinite trees can be used to construct computable concept comparison measures for FL₀ that are equivalence invariant w.r.t. general TBoxes. This is a first step towards employing such measures in the mentioned approximation approaches.Accepted to LATA 201

Evaluation of the development of a new drug: VIR-7831 case study

Biotechnology is one of the most promising industries, billion of dollars are expended in Research & Development every year to discover, develop, and commercialise biopharmaceutical products for treating several diseases. Understanding how those investments will generate cash flows in the future is difficult, but at the same time it is essential to understand the real value of a biotechnology company. The aim of this project is to estimate the present value of the future commercialisation of an underdevelopment drug. In the beginning of 2020, the humanity stepped in to deal with a new virus, SARS-COV-2, that caused a worldwide pandemic crisis. Due to the actuality of the topic, it was decided to elaborate a practical case study by evaluating VIR7831, a COVID-19 antibody that VIR Biotechnology is currently developing.A Biotecnologia é uma das mais promissoras indústrias, cerca de biliões são despendidos para a investigação e desenvolvimento, todos os anos, no âmbito da descoberta, produção e comercialização de produtos biofármacos, de forma a tratar inúmeras doenças. Entender como essas investigações, poderão originar dinheiro no futuro é difícil, mas ao mesmo tempo, é essencial compreender o verdadeiro valor de uma companhia biotecnológica. O intuito deste projeto é o de estimar o valor presente, da futura comercialização de um fármaco em subdesenvolvimento. No início de 2020, a humanidade viu-se confrontada com um novo vírus, SARS-COV-2, proporcionando uma crise pandémica mundial. Face à atualidade do tópico, foi decidido elaborar um caso prático, avaliando VIR-7831, um anticorpo ao Covid-19, que a Biotécnologia VIR se encontra a desenvolver

In defense of compilation: A response to Davis' form and content in model-based reasoning

In a recent paper entitled 'Form and Content in Model Based Reasoning', Randy Davis argues that model based reasoning research aimed at compiling task specific rules from underlying device models is mislabeled, misguided, and diversionary. Some of Davis' claims are examined and his basic conclusions are challenged about the value of compilation research to the model based reasoning community. In particular, Davis' claim is refuted that model based reasoning is exempt from the efficiency benefits provided by knowledge compilation techniques. In addition, several misconceptions are clarified about the role of representational form in compilation. It is concluded that techniques have the potential to make a substantial contribution to solving tractability problems in model based reasoning

Venture Cycles: Theory and Evidence

We demonstrate how endogenous information acquisition in venture capital markets creates investment cycles when competing financiers undertake their screening decisions in an uncoordinated way, thereby highlighting the role of intertemporal screening externalities induced by competition among venture capitalists as a structural source of instability. We show that uncoordinated screening behavior of competing financiers is an independent source of fluctuations inducing venture investment cycles. We also empirically document the existence of cyclical features in a number of industries such as biotechnology, electronics, financial services, healthcare, medical services and consumer products.screening, venture capital, investment cycles

Weighted automata and multi-valued logics over arbitrary bounded lattices

AbstractWe show that L-weighted automata, L-rational series, and L-valued monadic second order logic have the same expressive power, for any bounded lattice L and for finite and infinite words. We also prove that aperiodicity, star-freeness, and L-valued first-order and LTL-definability coincide. This extends classical results of Kleene, Büchi–Elgot–Trakhtenbrot, and others to arbitrary bounded lattices, without any distributivity assumption that is fundamental in the theory of weighted automata over semirings. In fact, we obtain these results for large classes of strong bimonoids which properly contain all bounded lattices

The Black-Scholes formula and volatility smile.

This paper investigates the development and applications of the Black-Scholes formula. This well-known formula is a continuous time model used primarily to price European style options. However in recent decades, observations in financial market data have brought into question some of the basic assumptions that the model relies on. Of particular interest is the prevalence of the volatility smile in asset option prices. This is a violation of one of the key assumptions under this model, and as a result alternatives to and modifications of Black-Scholes have been suggested, some continuous and some discrete. This paper researches one such modification, proposed by Derman and Kani (1994), in which observed market data is used to create a discrete time implied asset price tree that correctly reflects changing volatilities, risk-neutral probabilities, and observed option prices. The results are then used to price a less conventional derivative arrangement