Some Basic Facts About Linear Spaces and Fields

The regime complex for crisis finance in the euro area included the European Council, Council of the European Union, and Eurogroup in addition to the three institutions of the troika. As the member states acted largely, though not exclusively, through the council system, these bodies stood at the center of the institutional mix. This chapter reviews the institutions as a prelude to examining the dilemmas that confronted them over the course of the crises. It presents a brief review of some of the basic facts about their origins, membership, and organization. Each section then delves more deeply into these institutions’ governance and principles to understand their capabilities and strategic challenges. As a consequence of different mandates and design, the European Commission, European Central Bank, and International Monetary Fund diverged with respect to their approach to financing, adjustment, conditionality, and debt sustainability. This divergence set the stage for institutional conflict in the country programs.

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Probability and Random Processes

10.1093/oso/9780198821939.003.0002 ◽

2018 ◽

Author(s):

Stefan Thurner ◽

Rudolf Hanel ◽

Peter Klimekl

Keyword(s):

Random Processes ◽

Distribution Functions ◽

Basic Logic ◽

Heavy Tailed Distributions ◽

Random Components ◽

Classical Distribution ◽

Heavy Tailed ◽

Basic Facts ◽

Stochastic Events ◽

Stochastic Event

Phenomena, systems, and processes are rarely purely deterministic, but contain stochastic,probabilistic, or random components. For that reason, a probabilistic descriptionof most phenomena is necessary. Probability theory provides us with the tools for thistask. Here, we provide a crash course on the most important notions of probabilityand random processes, such as odds, probability, expectation, variance, and so on. Wedescribe the most elementary stochastic event—the trial—and develop the notion of urnmodels. We discuss basic facts about random variables and the elementary operationsthat can be performed on them. We learn how to compose simple stochastic processesfrom elementary stochastic events, and discuss random processes as temporal sequencesof trials, such as Bernoulli and Markov processes. We touch upon the basic logic ofBayesian reasoning. We discuss a number of classical distribution functions, includingpower laws and other fat- or heavy-tailed distributions.

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Processing subject focus across two Spanish varieties

Probus ◽

10.1515/probus-2019-0004 ◽

2020 ◽

Vol 32 (1) ◽

pp. 93-127

Author(s):

Bradley Hoot ◽

Tania Leal

Keyword(s):

Language Processing ◽

Sentence Processing ◽

Word Order ◽

Judgment Task ◽

Spanish Speakers ◽

Experimental Results ◽

Final Position ◽

Reading Task ◽

New Information ◽

Basic Facts

AbstractLinguists have keenly studied the realization of focus – the part of the sentence introducing new information – because it involves the interaction of different linguistic modules. Syntacticians have argued that Spanish uses word order for information-structural purposes, marking focused constituents via rightmost movement. However, recent studies have challenged this claim. To contribute sentence-processing evidence, we conducted a self-paced reading task and a judgment task with Mexican and Catalonian Spanish speakers. We found that movement to final position can signal focus in Spanish, in contrast to the aforementioned work. We contextualize our results within the literature, identifying three basic facts that theories of Spanish focus and theories of language processing should explain, and advance a fourth: that mismatches in information-structural expectations can induce processing delays. Finally, we propose that some differences in the existing experimental results may stem from methodological differences.

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