Bounded Counter Languages

We show that deterministic finite automata equipped with $k$ two-way heads are equivalent to deterministic machines with a single two-way input head and $k-1$ linearly bounded counters if the accepted language is strictly bounded, i.e., a subset of $a_1^*a_2^*... a_m^*$ for a fixed sequence of symbols $a_1, a_2,..., a_m$. Then we investigate linear speed-up for counter machines. Lower and upper time bounds for concrete recognition problems are shown, implying that in general linear speed-up does not hold for counter machines. For bounded languages we develop a technique for speeding up computations by any constant factor at the expense of adding a fixed number of counters

Procjena duljine traga pukotine razlomljene stijenske mase pomoću algoritma SVM (algoritma stroja potpornih vektora)

Jointed rock masses modeling needs the geometrical parameters of joints such as orientation, spacing, trace length, shape, and location. The rock joint trace length is one of the most critical design parameters in rock engineering and geotechnics. It controls the stability of the rock slope and tunnels in jointed rock masses by affecting rock mass strength. This parameter is usually determined through a joint survey in the field. Among the parameters, trace length is challenging because a complete joint plane within rock mass cannot be observed directly. The development of predictive models to determine rock joint length seems to be essential in rock engineering. This research made an effort to introduce a support vector machine (SVM) model to estimate rock joint trace length. The SVM is an advanced intelligence method used to solve the problem characterized by a small sample, non-linearity, and high dimension with a good generalization performance. In this study, three data sets from the sedimentary, igneous, and metamorphic rocks were organized, which location of joints on the scanline, aperture, spacing, orientation (D/DD), roughness, Schmidt rebound of the joint’s wall, type of termination, trace lengths in both sides of the scanline and joint sets were measured. The results of SVM prediction demonstrate that predicted and measured results are in good agreement. The SVM model-based results were compared with those obtained from field surveys. The proposed SVM model-based model was very efficient in predicting rock joint trace length values. The actual trace length could be estimated; thus, the expensive, difficult, time-consuming, and destructive joint surveys related to obscured joints could be avoided.Za modeliranje razlomljenih stijenskih masa potrebni su geometrijski parametri pukotina kao što su orijentacija, razmak, duljina pukotine, oblik i lokacija. Duljina pukotine stijene jedan je od najkritičnijih projektnih parametara u inženjerstvu stijena i geotehnici. Ona kontrolira stabilnost nagiba stijene i tunela u razlomljenim stijenskim masama te utjecaj na čvrstoću stijenske mase. Obično se utvrđuje terenskim istraživanjima. Istraživanje duljine pukotine zahtjevno je, jer se cjelovita duljina unutar stijenske mase ne može promatrati izravno. Razvoj modela za predviđanje duljine traga pukotine iznimno je važan u inženjerstvu stijena. U okviru ovoga istraživanja predstavljen je algoritam SVM (engl. support vector machine, hrv. stroj potpornih vektora) za procjenu duljine pukotine. Riječ je o naprednoj metodi koja se koristi za rješavanje problema maloga uzorka, nelinearnosti i višestrukih dimenzija, s dobrim svojstvima generalizacije problema. Priređena su tri skupa podataka iz taložnih, magmatskih i metamorfnih stijena, koji uključuju položaj pukotina na liniji uzorkovanja, te njihov otvor, razmak, orijentaciju, hrapavost, Schmidtov odbojni test na stijenke pukotine, tip završetka, duljine traga na obje strane linije uzorkovanja i skupove pukotina. Rezultati predloženoga algoritma pokazuju podudarnost predviđenih i izmjerenih rezultata dobivenih terenskim istraživanjima. Rezultati pokazuju da je predloženi algoritam vrlo učinkovit u predviđanju vrijednosti duljine traga pukotine stijenske mase. Njegovim korištenjem može se dobro procijeniti stvarna duljina traga pukotine te izbjeći skupa, teška, dugotrajna i agresivna istraživanja razlomljenih stijenskih masa

Essays on Probabilistic Machine Learning for Economics

This thesis consists of three essays that explore the use of probabilistic machine learning techniques in combination with information-theoretic concepts to answer economic questions. Over the past years, economists have started applying machine learning methods to a wide range of topics. Probabilistic methods in the context of unsupervised learning represent one particular modelling approach at the intersection of computer science and statistics. While widely used in applied statistics, these models, however, do not necessarily provide relevant and interpretable outputs from an economist's perspective. In this thesis, I appeal to information-theoretic methods to summarise the probabilistic information inferred from such models and construct economically meaningful measures.Nikolas Kuhlen gratefully acknowledges the financial support of The Alan Turing Institute under research award No. TU/C/000030

Dimensions of Timescales in Neuromorphic Computing Systems

This article is a public deliverable of the EU project "Memory technologies with multi-scale time constants for neuromorphic architectures" (MeMScales, https://memscales.eu, Call ICT-06-2019 Unconventional Nanoelectronics, project number 871371). This arXiv version is a verbatim copy of the deliverable report, with administrative information stripped. It collects a wide and varied assortment of phenomena, models, research themes and algorithmic techniques that are connected with timescale phenomena in the fields of computational neuroscience, mathematics, machine learning and computer science, with a bias toward aspects that are relevant for neuromorphic engineering. It turns out that this theme is very rich indeed and spreads out in many directions which defy a unified treatment. We collected several dozens of sub-themes, each of which has been investigated in specialized settings (in the neurosciences, mathematics, computer science and machine learning) and has been documented in its own body of literature. The more we dived into this diversity, the more it became clear that our first effort to compose a survey must remain sketchy and partial. We conclude with a list of insights distilled from this survey which give general guidelines for the design of future neuromorphic systems

The Nexus between Artificial Intelligence and Economics

This book is organized as follows. Section 2 introduces the notion of the Singularity, a stage in development in which technological progress and economic growth increase at a near-infinite rate. Section 3 describes what artificial intelligence is and how it has been applied. Section 4 considers artificial happiness and the likelihood that artificial intelligence might increase human happiness. Section 5 discusses some prominent related concepts and issues. Section 6 describes the use of artificial agents in economic modeling, and section 7 considers some ways in which economic analysis can offer some hints about what the advent of artificial intelligence might bring. Chapter 8 presents some thoughts about the current state of AI and its future prospects.