Affect in mathematics education: an introduction

The article presents an introduction to the concept of affect in mathematics education research

Polyteam Semantics

Team semantics is the mathematical framework of modern logics of dependence and independence in which formulae are interpreted by sets of assignments (teams) instead of single assignments as in first-order logic. In order to deepen the fruitful interplay between team semantics and database dependency theory, we define "Polyteam Semantics" in which formulae are evaluated over a family of teams. We begin by defining a novel polyteam variant of dependence atoms and give a finite axiomatisation for the associated implication problem. We also characterise the expressive power of poly-dependence logic by properties of polyteams that are downward closed and definable in existential second-order logic (ESO). The analogous result is shown to hold for poly-independence logic and all ESO-definable properties.Peer reviewe

The hippocampus reevaluated in unconscious learning and memory: at a tipping point?

Classic findings from the neuropsychological literature invariably indicated that performances on tests of memory that can be accomplished without conscious awareness were largely spared in amnesia, while those that required conscious retrieval (e.g., via recognition or recall) of information learned in the very same sessions was devastatingly impaired. Based on reports of such dissociations, it was proposed that one of the fundamental distinctions between memory systems is whether or not they support conscious access to remembered content. Only recently have we come to realize that the putative systemic division of labor between conscious and unconscious memory is not so clean. A primary goal of this review is to examine recent evidence that has been advanced against the view that the hippocampus is selectively critical for conscious memory. Along the way, consideration is given to criticisms that have been levied against these findings, potential explanations for differences in the reported results are proposed, and methodological pitfalls in investigations of unconscious memory are discussed. Ultimately, it is concluded that a tipping point has been reached, and that while conscious recollection depends critically on hippocampal integrity, the reach of the hippocampus extends to unconscious aspects of memory performance when relational memory processing and representation are required

Parametrised Complexity of Model Checking and Satisfiability in Propositional Dependence Logic

In this paper, we initiate a systematic study of the parametrised complexity in the field of Dependence Logics which finds its origin in the Dependence Logic of V\"a\"an\"anen from 2007. We study a propositional variant of this logic (PDL) and investigate a variety of parametrisations with respect to the central decision problems. The model checking problem (MC) of PDL is NP-complete. The subject of this research is to identify a list of parametrisations (formula-size, treewidth, treedepth, team-size, number of variables) under which MC becomes fixed-parameter tractable. Furthermore, we show that the number of disjunctions or the arity of dependence atoms (dep-arity) as a parameter both yield a paraNP-completeness result. Then, we consider the satisfiability problem (SAT) showing a different picture: under team-size, or dep-arity SAT is paraNP-complete whereas under all other mentioned parameters the problem is in FPT. Finally, we introduce a variant of the satisfiability problem, asking for teams of a given size, and show for this problem an almost complete picture.Comment: Update includes refined result

Facets of Distribution Identities in Probabilistic Team Semantics

We study probabilistic team semantics which is a semantical framework allowing the study of logical and probabilistic dependencies simultaneously. We examine and classify the expressive power of logical formalisms arising by different probabilistic atoms such as conditional independence and different variants of marginal distribution equivalences. We also relate the framework to the first-order theory of the reals and apply our methods to the open question on the complexity of the implication problem of conditional independence.Peer reviewe

Suomen vapaustaistelu maailmasodan tapahtumasarjan vaiheena

Artikkelissa tarkastellaan niitä vaiheita, jotka johtivat aikanaan Suomen itsenäistymiseen. Tarkastelussa on mukana kansainvälisen tilanteen lisäksi Suomessa vallalla olleet mielipiteet ja aktivistiliikkeet. Erityinen huomio kiinnitetään Saksan suhtautumiseen Suomeen Euroopan eri tapahtumien aikana. Lopuksi kirjoittaja toteaa: "Saksalaiset joukot tulivat loppujen lopuksi myötävaikuttamaan Suomen vapauttamiseen, joskin aivan toisenlaisissa olosuhteissa kuin mitä Wetterhof ja muut aktivistit olivat kuvitelleet.

Sotamarsalkanarvo Ruotsi-Suomessa ja itsenäisen Suomen ensimmäinen sotamarsalkka Kaarle Kustaa Mannerheim

Artikkelissa selvitetään aluksi yleisellä tasolla historiallisesta näkökulmasta sotamarsalkanarvon ja sen tunnusmerkkien alkuperää varhaisemmalta keskiajalta alkaen. Kirjoittaja toteaa, että Ruotsissa sotamarsalkanarvo otettiin käyttöön 1500-luvun jälkipuoliskolla. Kyseisen arvon myöntämistä Ruotsin eri hallitsijoiden aikana selvitetään seikkaperäisesti. Mannerheimin henkilöhistoriaa ja hänen johtamistoimintaansa vapaussodassa kuvataan yksityiskohtaisten vapaussodan tapahtumiin liittyvien esimerkkien valossa.Artikkelissa käsitellään myös Mannerheimin merkitystä tärkeissä sotilaspoliittisissa kysymyksissä, joista keskeisin käsitteli artikkelin mukaan Saksan apua. Lopuksi kirjoittaja toteaa "Kenraali Kaarle Kustaa Mannerheimin nimittämistä sotamarsalkaksi vapaussotamme päättymisen 15-vuotismuistojuhlien yhteydessä voidaan pitää pienenä konkreettisena todisteena siitä, että aikalaisillekin alkaa jo yleisemmin selvitä hänen historiallisten mittasuhteidensa suuruus. Suuremmalle johtajalle tätä arvoa tuskin on annettu Pohjoismaissa.

Complexity Thresholds in Inclusion Logic

Logics with team semantics provide alternative means for logical characterization of complexity classes. Both dependence and independence logic are known to capture non-deterministic polynomial time, and the frontiers of tractability in these logics are relatively well understood. Inclusion logic is similar to these team-based logical formalisms with the exception that it corresponds to deterministic polynomial time in ordered models. In this article we examine connections between syntactical fragments of inclusion logic and different complexity classes in terms of two computational problems: maximal subteam membership and the model checking problem for a fixed inclusion logic formula. We show that very simple quantifier-free formulae with one or two inclusion atoms generate instances of these problems that are complete for (non-deterministic) logarithmic space and polynomial time. Furthermore, we present a fragment of inclusion logic that captures non-deterministic logarithmic space in ordered models

Baltic Ecological Recycling Agriculture and Society (BERAS project) - a case of Juva milk system

The aim of the study was to determine the potential, impact and prerequisites of localization and enhanced recycling in a rural food system, illustrated by the case of Juva milk. An interdisciplinary scenario based on the increase of local, organic milk to 50 % of milk comsumption was created and the sustainability was compared, on the basis of the statistics and data collected from the actors, with the present milk system

Reasoning about embedded dependencies using inclusion dependencies

The implication problem for the class of embedded dependencies is undecidable. However, this does not imply lackness of a proof procedure as exemplified by the chase algorithm. In this paper we present a complete axiomatization of embedded dependencies that is based on the chase and uses inclusion dependencies and implicit existential quantification in the intermediate steps of deductions