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  • 1. Buljan, Matej
    et al.
    Nordqvist, Jonas
    Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA).
    Martins, Rafael Messias
    Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för datavetenskap och medieteknik (DM).
    An investigation on the impact of sampling techniques for t-SNEManuskript (preprint) (Övrigt vetenskapligt)
    Abstract [en]

    The main topic of this article concerns t-SNE, a dimensionality reduction technique that has gained much popularity for its increased capability of creating low-dimensional embeddings that preserve well-separated clusters from high-dimensional spaces. Despite its strengths, the runnning times for t-SNE are usually high and do not scale well with the size of datasets, which4limits its applicability to scenarios that involve, for example, Big Data and interactive visualization. Downsampling the dataset into more manageable sizes is a possible straightforward workaround, but it is not clear from the literature how much the quality of the embedding suffers from the downsampling, and whether simple random sampling is indeed the best possible solution. In this paper, we report on a thorough series of experiments performed to draw conclusions about the quality of embeddings from running t-SNE on samples of data using different sampling techniques: simple random sampling, random walk sampling, and the so-calledhubnesssampling. Throughout our testing, a specific variant of random walk sampling distinguished itself as a better alternative to simple random sampling.

  • 2.
    Chandler, Rebecca E.
    et al.
    Uppsala Monitoring Centre (UMC).
    Juhlin, Kristina
    Uppsala Monitoring Centre (UMC).
    Fransson, Jonas
    Uppsala Monitoring Centre (UMC).
    Caster, Ola
    Uppsala Monitoring Centre (UMC) ; Stockholm University.
    Edwards, Ralph I.
    Uppsala Monitoring Centre (UMC).
    Norén, Niklas G.
    Uppsala Monitoring Centre (UMC).
    Current Safety Concerns with Human Papillomavirus Vaccine: A Cluster Analysis of Reports in VigiBase®2017Ingår i: Drug Safety, ISSN 0114-5916, E-ISSN 1179-1942, Vol. 40, nr 1, s. 81-90Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    INTRODUCTION: A number of safety signals-complex regional pain syndrome (CRPS), postural orthostatic tachycardia syndrome (POTS), and chronic fatigue syndrome (CFS)-have emerged with human papillomavirus (HPV) vaccines, which share a similar pattern of symptomatology. Previous signal evaluations and epidemiological studies have largely relied on traditional methodologies and signals have been considered individually.

    OBJECTIVE: The aim of this study was to explore global reporting patterns for HPV vaccine for subgroups of reports with similar adverse event (AE) profiles.

    METHODS: All individual case safety reports (reports) for HPV vaccines in VigiBase(®) until 1 January 2015 were identified. A statistical cluster analysis algorithm was used to identify natural groupings based on AE profiles in a data-driven exploratory analysis. Clinical assessment of the clusters was performed to identify clusters relevant to current safety concerns.

    RESULTS: Overall, 54 clusters containing at least five reports were identified. The four largest clusters included 71 % of the analysed HPV reports and described AEs included in the product label. Four smaller clusters were identified to include case reports relevant to ongoing safety concerns (total of 694 cases). In all four of these clusters, the most commonly reported AE terms were headache and dizziness and fatigue or syncope; three of these four AE terms were reported in >50 % of the reports included in the clusters. These clusters had a higher proportion of serious cases compared with HPV reports overall (44-89 % in the clusters compared with 24 %). Furthermore, only a minority of reports included in these clusters included AE terms of diagnoses to explain these symptoms. Using proportional reporting ratios, the combination of headache and dizziness with either fatigue or syncope was found to be more commonly reported in HPV vaccine reports compared with non-HPV vaccine reports for females aged 9-25 years. This disproportionality remained when results were stratified by age and when those countries reporting the signals of CRPS (Japan) and POTS (Denmark) were excluded.

    CONCLUSIONS: Cluster analysis reveals additional reports of AEs following HPV vaccination that are serious in nature and describe symptoms that overlap those reported in cases from the recent safety signals (POTS, CRPS, and CFS), but which do not report explicit diagnoses. While the causal association between HPV vaccination and these AEs remains uncertain, more extensive analyses of spontaneous reports can better identify the relevant case series for thorough signal evaluation.

  • 3.
    Lindahl, Karl-Olof
    et al.
    Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA).
    Nordqvist, Jonas
    Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA).
    Geometric location of periodic points of 2-ramified power series2018Ingår i: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 465, nr 2, s. 762-794Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper we study the geometric location of periodic points of power series defined over fields of prime characteristic p. More specifically, we find a lower bound for the absolute value of all periodic points in the open unit disk of minimal period pn of 2-ramified power series. We prove that this bound is optimal for a large class of power series. Our main technical result is a computation of the first significant terms of the pnth iterate of 2-ramified power series. As a by-product we obtain a self-contained proof of the characterization of 2-ramified power series.

  • 4.
    Lindenberg, Björn
    et al.
    Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA).
    Nordqvist, Jonas
    Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA).
    Lindahl, Karl-Olof
    Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA).
    Distributional Reinforcement Learning with EnsemblesManuskript (preprint) (Övrigt vetenskapligt)
    Abstract [en]

    It is well-known that ensemble methods often provide enhanced performance in reinforcement learning. In this paper we explore this concept further by using group-aided training within the distributional reinforcement learning paradigm. Specifically, we propose an extension to categorical reinforcement learning, where distributional learning targets are implicitly based on the total information gathered by an ensemble. We empirically show that this may lead to much more robust initial learning, a stronger individual performance level and good efficiency on a per-sample basis.

  • 5.
    Lundberg, Jonas
    et al.
    DISA.
    Nordqvist, Jonas
    Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA). DISA.
    Laitinen, Mikko
    University of Eastern Finland, Finland.
    Towards a language independent Twitter bot detector2019Ingår i: Proceedings of 4th Conference of The Association Digital Humanities in the Nordic Countries: Copenhagen, March 6-8 2019 / [ed] Navarretta Costanza et al., Copenhagen: Digital Humanities in the Nordic countries , 2019Konferensbidrag (Refereegranskat)
    Abstract [en]

    This article describes our work in developing an application that recognizes automatically generated tweets. The objective of this machine learning application is to increase data accuracy in sociolinguistic studies that utilize Twitter by reducing skewed sampling and inaccuracies in linguistic data. Most previous machine learning attempts to exclude bot material have been language dependent since they make use of monolingual Twitter text in their training phase. In this paper, we present a language independent approach which classifies each single tweet to be either autogenerated (AGT) or human-generated (HGT). We define an AGT as a tweet where all or parts of the natural language content is generated automatically by a bot or other type of program. In other words, while AGT/HGT refer to an individual message, the term bot refers to non-personal and automated accounts that post content to online social networks. Our approach classifies a tweet using only metadata that comes with every tweet, and we utilize those metadata parameters that are both language and country independent. The empirical part shows good success rates. Using a bilingual training set of Finnish and Swedish tweets, we correctly classified about 98.2% of all tweets in a test set using a third language (English).

  • 6.
    Nordqvist, Jonas
    Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA).
    Characterization of 2-ramified power series2017Ingår i: Journal of Number Theory, ISSN 0022-314X, E-ISSN 1096-1658, Vol. 174, s. 258-273Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper we study lower ramification numbers of power series tangent to the identity that are defined over fields of positive characteristics p. Let g be such a series, then g has a fixed point at the origin and the corresponding lower ramification numbers of g are then, up to a constant, the degree of the first non-linear term of p-power iterates of g. The result is a complete characterization of power series g having ramification numbers of the form 2 ( 1 + p + 
 + p n ) . Furthermore, in proving said characterization we explicitly compute the first significant terms of g at its pth iterate.

  • 7.
    Nordqvist, Jonas
    Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA).
    Ramification numbers and periodic points in arithmetic dynamical systems2018Licentiatavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    The field of discrete dynamical systems is a rich and active field of research within mathematics, with applications ranging from biology to computer science, finance, engineering and various others. In this thesis properties of certain discrete dynamical systems are studied together with number theoretic properties of the functions defining these systems. The dynamical systems studied in this thesis are defined by iteration of power series g with a fixed point at the origin, tangent to the identity, and defined over fields of prime characteristic p. We are interested in the geometric location of the periodic points in the open unit disk. Recent results have shown that there is a connection between the lower ramification numbers of g and the geometric location of the periodic points in the open unit disk. The lower ramification numbers of g can be described as the multiplicity of zero as a fixed point of p-power iterates of g.

    Part of this thesis concerns characterizing power series having certain sequences of ramification numbers. The other part concerns utilizing these results in order to describe the geometric location of the periodic points in terms of their distance to the origin. More precisely, we characterize all 2-ramified power series, i.e. power series having ramification numbers of the form 2(1 + p + … + pn). Moreover, we also obtain a lower bound of the absolute value of the periodic points in the open unit disk of such series.

  • 8.
    Nordqvist, Jonas
    Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA).
    Residue fixed point index and wildly ramified power series2020Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [sv]

    Denna avhandling behandlar diskreta dynamiska system. Dessa är system där dynamiken modelleras med en itererad funktion. Tillämpningarna för diskreta dynamiska systems återfinns bland annat i biologi, pseudo-slumptalsgenerering och statistisk mekanik för att nämna några exempel. I denna avhandling är vi intresserade av dynamiska system som beskrivs av iterationer av en potensserie f med en fixpunkt i origo, där den tangerar identitetsavbildningen. Särskilt är vi intresserade av potensserier vars koefficienter kommer från en kropp med positiv karaktäristik p. Vi är intresserade av de så kallade underförgreningstalen till f. Underförgreningstalen till en potensserie f kan kortfattat beskrivas som multipliciteten av origo betraktad som en fixpunkt till iterationer av f. Denna avhandling innehåller fyra artiklar som behandlar detta ämne.

    I artikel I studerar vi så kallade 2-förgrenade potensserier och karaktäriserar dessa i termer av dess första signifikanta termer. Detta utvecklas sedan i artikel II, där vi beskriver absolutbeloppet av de periodiska punkterna för 2-förgrenade potensserier. Detta medför också att vi erhåller ett fristående bevis för huvudresultatet i artikel I.

     

    I artikel III, studerar vi potensserier med en fixpunkt i origo med liten multiplicitet, d.v.s. potensserier där multipliciteten för origo som en fixpunkt är mindre än karaktäristiken för koefficientkroppen. Vi erhåller en karaktärisering av dessa i termer av dess första signifikanta termer, samt även formulerat som ickeförsvinnandet av den så kallade iterativa residyn. Vi erhåller även en formel för att beräkna det holomorfa indexet för en fixpunkt i fallet då multiplikatorn av fixpunkten är 1. Vidare utvecklar vi resultaten från artikel II genom att erhålla resultat om de periodiska punkternas geometriska placering i den öppna enhetsskivan för konvergenta potensserier med en fixpunkt med liten multiplicitet.

    I artikel IV studerar vi potensserier där origo är en fixpunkt med multiplicitet som är större än karaktäristiken i koefficientkroppen. Vi introducerar även en invariant i positiv karaktäristik nära besläktad med det holomorfa indexet. Vi erhåller en karaktärisering av sådana potensserier när dessa har de minsta möjliga underförgreningstalen, i termer av ickeförsvinnandet av denna invariant. Vi erhåller också resultat gällande antalet parametrar som behövs för att klassificera dessa potensserier under formella koordinatbyten.

  • 9.
    Nordqvist, Jonas
    Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA).
    Wildly ramified power series with large multiplcityManuskript (preprint) (Övrigt vetenskapligt)
    Abstract [en]

    In this paper we consider wildly ramified power series, \emph{i.e.}, power series defined over a field of positive characteristic, fixing the origin, where it is tangent to the identity. In this setting we introduce a new invariant under change of coordinates  called the \emph{second residue fixed point index}, and provide a closed formula for it. As the name suggests this invariant is closely related to the residue fixed point index, and they coincide in the case that the power series have small multiplicity. Finally, we characterize power series with large multiplicity having the smallest possible multiplicity at the origin under iteration, in terms of this new invariant.

  • 10.
    Nordqvist, Jonas
    et al.
    Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA).
    Rivera-Letelier, Juan
    University of Rochester, USA.
    Residue fixed point index and wildly ramified power seriesManuskript (preprint) (Övrigt vetenskapligt)
    Abstract [en]

    In this paper, we study power series having a fixed point of multiplier~$1$. First, we give a closed formula for the residue fixed point index, in terms of the first coefficients of the power series. Then, we use this formula to study wildly ramified power series in positive characteristic. Among power series having a multiple fixed point of small multiplicity, we characterize those having the smallest possible lower ramification numbers in terms of the residue fixed point index. Furthermore, we show that these power series form a generic set, and, in the case of convergent power series, we also give an optimal lower bound for the distance to other periodic points.

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