The research at hand aims to define effectiveness of algorithmic trading, comparing with different benchmarks represented by several types of indexes. How big returns can be gotten by algorithmic trading, taking into account the costs of informational and trading infrastructure needed for robot trading implementation? To get the result, it’s necessary to compare two opposite trading strategies: 1) Algorithmic trading (implemented by high-frequency trading robot (based on statistic arbitrage strategy) and trend-following trading robot (based on the indicator Exponential Moving Average with the Variable Factor of Smoothing)) 2) Index investing strategy (classical index strategies “buy and hold”, implemented by four different types of indexes: Capitalization weight index, Fundamental indexing, Equal-weighted indexing, Risk-based indexation/minimal variance). According to the results, it was found that at the current phase of markets’ development, it is theoretically possible for algorithmic trading (and especially high-frequency strategies) to exceed the returns of index strategy, but we should note two important factors: 1) Taking into account all of the costs of organization of high-frequency trading (brokerage and stock exchanges commissions, trade-related infrastructure maintenance, etc.), the difference in returns (with superiority of high-frequency strategy) will be much less . 2) Given the fact that “markets’ efficiency” is growing every year (see more about it further in thesis), and the returns of high-frequency strategies tends to decrease with time (see more about it further in thesis), it is quite logical to assume that it will be necessary to invest more and more in trading infrastructure to “fix” the returns of high-frequency trading strategies on a higher level, than the results of index investing strategies.

In this thesis we investigate the geometric and algorithmic aspects of the random-cluster model, a correlated bond percolation model of great importance in the field of mathematics and statistical mechanics. We focus on the computational and statistical efficiency of the single-bond or heat-bath Markov chain for the random-cluster model and develop algorithmic techniques that allow for an improvement from a previously known polynomial to a poly-logarithmic runtime scaling of updates for general graphs. The interplay between the (critical) cluster structure of the random-cluster model and algorithmic, as well as statistical, efficiencies is considered, leading to new exact identities. A complementary analysis of certain fragility properties of the Fortuin-Kasteleyn clusters provides new insights into fragmentation phenomena, culminating in a revised scaling relation for a related fragmentation power law exponent, previously only shown for the marginal bond percolation case. By utilising the established structural results, a dynamic fragmentation process is studied that allows for an extraction of characteristics of the equilibrium cluster structure by a careful analysis of the limiting fragments, as well as the entire evolution of the fragmentation process. Besides focussing on structural and computational aspects, in this dissertation we also analyse the efficiency of the coupling from the past perfect sampling algorithm for the random-cluster model via large-scale numerical simulations. Two key results are the particular, close to optimal, efficiency in the off-critical setting and the intriguing observation of its superiority compared to the alternative Chayes-Machta-Swendsen-Wang approach in three dimensions. Governed by a random runtime, the efficiency of the coupling from the past algorithm depends crucially on the fluctuations of the runtime. In this connection a compelling appearance of universal Gumbel fluctuations in the distribution of the runtime of the coupling from the past algorithm is established, both at and off criticality. Fluctuations at a tricritical point and at a discontinuous phase transition are shown to deviate from this Gumbel law. The above findings in two and three dimensions are supported by a rigorous analysis of certain aspects of the algorithm in one dimension, including a proof of the limiting Gumbel law.

Algorithms that are being used in sensitive contexts such as deciding to give a job offer or giving inmates parole should be accurate as well as being non-discriminatory. The latter is important especially due to emerging concerns about automatic decision making being unfair to individuals belonging to certain groups. The machine learning literature has seen a rapid evolution in research on this topic. In this thesis, we study various problems in sequential decision making motivated by challenges in algorithmic fairness. As part of this thesis, we modify the fundamental framework of prediction with expert advice. We assume a learning agent is making decisions using the advice provided by a set of experts while this set can shrink. In other words, experts can become unavailable due to scenarios such as emerging anti-discriminatory laws prohibiting the learner from using experts detected to be unfair. We provide efficient algorithms for this setup, as well as a detailed analysis of the optimality of them. Later we explore a problem concerned with providing any-time fairness guarantees using the well-known exponential weights algorithm, which leads to an open question about a lower bound on the cumulative loss of exponential weights algorithm. Finally, we introduce a novel fairness notion for supervised learning tasks motivated by the concept of envy-freeness. We show how this notion might bypass certain issues of existing fairness notions such as equalized odds. We provide solutions for a simplified version of this problem and insights to deal with further challenges that arise by adopting this notion. / Graduate

In the design of material handling systems with complex and unpredictable dynamics, conventional search and optimization approaches that are based only on performance measures offer little guarantee of robustness. Using evidence from research into complex systems, the use of behavior-based optimization is proposed, which takes advantage of observed relationships between complexity and optimality with respect to both performance and robustness. Based on theoretical complexity measures, particularly algorithmic complexity, several simple complexity measures are created. The relationships between these measures and both performance and robustness are examined, using a model of a directly connected material handling system as a backdrop. The fundamental causes of the relationships and their applicability in the proposed behavior-based optimization approach are discussed. / Ph. D.

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... myriad carbon, myriad silicon ... is inspired by the ubiquitous presence of carbon and silicon, elements fundamental to both nature and technology. These elements, interwoven into our daily lives, are manifest in the natural world around us, in the technology we use, and within ourselves. This piece delves into the intersection of the natural and technological realms, fostering a dialogue that extends beyond grand narratives. It focuses on the everyday interactions between nature’s organic creations and human-made technology. The music reflects this interplay, fluidly transitioning between organic and mechanical sounds, thus embodying the dualistic nature of our environment. However, the essence of the piece goes beyond a simple dichotomy of nature versus technology, exploring the subtleties of contemporary composition. The piece unfolds as a process, revealing layers of complexity and subtlety, without making any definitive statements.

Det sociala mediet Instagram är en applikation där människor världen runt kan dela med sig av resor, måltider och den nya familjemedlemmens ankomst. Genom att kommentera, gilla, arkivera och utforska kan användaren hålla sig uppdaterad dygnet runt. När Instagram i mars 2016 meddelade att de skulle införa algoritmer, vilka profilerar och kartlägger användare, ändrades rangordningen på inläggen i användarnas flöde. Vem som nu får se vad, när och hur styrs av dessa osynliga matematiska formler. Studien syftar till att undersöka hur svenska Instagramanvändare i åldern 15-40 år upplever dessa personliga algoritmer och huruvida dessa har en inverkan på hur de använder sig av applikationen. Då Instagram är tätt förknippat med att visa upp sig själv ser jag det även intressant att undersöka vilken roll algoritmerna har för individernas syn på sig själva. Genom mixed methods kommer både en enkät och kvalitativa intervjuer att utföras för att få en genomgripande förståelse för fenomenet på flera plan. Den kvantitativa delen ämnar att skapa en mer generell uppfattning hur individerna upplever algoritmerna och hur deras användning ser ut. Detta medan den kvalitativa delen är till för att fördjupa förståelsen för relationen mellan individerna och algoritmerna. Med hjälp av teorier rörande synlighet, algoritmer och identitet är målet att få en djupare förståelse för detta tämligen nya fenomen. Analysens resultat visar att medvetenheten är måttlig och kunskapen om algoritmerna är relativt begränsad. Det finns en tydlig skillnad mellan de som har skapat egna teorier om hur algoritmerna fungerar och de som är helt omedvetna. Vidare var det tydligt att algoritmerna hade en inverkan - både medvetet och omedvetet - på individerna vad gällde olika strategier för att bättre synas och få likes. Slutligen visade det sig att de personliga algoritmerna spelar en jämförelsevis stor roll för individernas syn på sig själva i termer av validitet och reflektion.