84 research outputs found
A note on the component structure in random intersection graphs with tunable clustering
We study the component structure in random intersection graphs with tunable
clustering, and show that the average degree works as a threshold for a phase
transition for the size of the largest component. That is, if the expected
degree is less than one, the size of the largest component is a.a.s. of
logarithmic order, but if the average degree is greater than one, a.a.s. a
single large component of linear order emerges, and the size of the second
largest component is at most of logarithmic order.Comment: 8 pages, Published at
http://www.combinatorics.org/Volume_15/PDF/v15i1n10.pdf by the Electronic
Journal of Combinatorics (http://www.combinatorics.org
Normaltillriktning av typsnittet Resultat : JÀmförelse av tvÄ metoders resultat
Typsnitt tillverkade för bĂ„de skĂ€rm och tryck Ă€r allt vanligare och speciellt webblĂ€sare stĂ€ller tekniska krav pĂ„ typsnitten. De flesta webblĂ€sare förstĂ„r sig inte pĂ„ fontens kerning information utan slopar det och litar pĂ„ normaltillriktningen. I mitt arbete undersöker jag hurudan inverkan de tvĂ„ sĂ€tten att göra normaltillriktningen, för hand eller med auto-spacing funktionen, har pĂ„ typsnittets fĂ€rg. Som utgĂ„ngspunkt anvĂ€nder jag mig av tvĂ„ versioner av typsnittet âResultatâ som jag sedan jĂ€mför med varandra. Resultat Ă€r ett sans-serif typsnitt som jag sjĂ€lv skapat. MĂ„let med arbetet Ă€r att ge klarhet om vilkendera metoden producerar en jĂ€mnare fĂ€rg, att utforska typiska drag i normaltillriktningen som orsakas av auto-spacing samt att förstĂ„ vilka för- och nackdelar bĂ„da metoderna har. Eftersom arbetet inte Ă€r en teoretisk studie baserar den sig pĂ„ den erfarenhet jag fĂ„tt frĂ„n att skapa mitt egna typsnitt. Normaltillriktningen baserar sig pĂ„ redan existerande metoder som presenteras i arbetet. I undersökningen kom det fram att normaltillriktning för hand producerar en jĂ€mnare fĂ€rg. Auto-spacing gav ett hyfsat resultat men kantmarginalerna för bokstĂ€ver med oregelbundna former visade sig vara konstiga vilket ledde till en ojĂ€mn fĂ€rg. Att göra normaltillriktningen för hand gav ett bĂ€ttre resultat men tog avsevĂ€rt lĂ€ngre jĂ€mfört med auto-spacing. Avslutningsvis reflekterar jag kring hela processen och hur jag kan anvĂ€nda denna kunskap i framtida typsnitt.Typefaces designed for both screen and print are becoming more common and especially web browsers add technical limitations to the typefaces. Most web browser doesnât understand the kerning information in a font and defaults to the letter-spacing. In my thesis Iâll focus on how the two ways of doing the letter-spacing, by hand or by using the autospacing function, affect the color of the typeface. As a starting point Iâve used two versions of the typeface âResultatâ which I compare against each other. Resultat is a sansserif typeface that Iâve made myself. The goal with this thesis is to show which method produces a more even color, examine typical characteristics in letter-spacing caused by auto-spacing and to understand what pros and cons each method has. This isnât a theoretical study and will be based on the experience I got from designing my own typeface. The letter-spacing will be based on already existing methods which will be presented in the thesis. During the research I discovered that letter-spacing by hand produces a much more even color. Auto-spacing gave an ok result, although the sidebearings of letters with irregular shapes had some issues resulting in an uneven color. Letter-spacing by hand produced a much better result but took a considerable amount of time compared to autospacing. Finally I reflect on the whole process and think about how I will use this knowledge in future typefaces
A dynamic network in a dynamic population: asymptotic properties
We derive asymptotic properties for a stochastic dynamic network model in a
stochastic dynamic population. In the model, nodes give birth to new nodes
until they die, each node being equipped with a social index given at birth.
During the life of a node it creates edges to other nodes, nodes with high
social index at higher rate, and edges disappear randomly in time. For this
model we derive criterion for when a giant connected component exists after the
process has evolved for a long period of time, assuming the node population
grows to infinity. We also obtain an explicit expression for the degree
correlation (of neighbouring nodes) which shows that is always
positive irrespective of parameter values in one of the two treated submodels,
and may be either positive or negative in the other model, depending on the
parameters
A Discussion of Discrimination and Fairness in Insurance Pricing
Indirect discrimination is an issue of major concern in algorithmic models.
This is particularly the case in insurance pricing where protected policyholder
characteristics are not allowed to be used for insurance pricing. Simply
disregarding protected policyholder information is not an appropriate solution
because this still allows for the possibility of inferring the protected
characteristics from the non-protected ones. This leads to so-called proxy or
indirect discrimination. Though proxy discrimination is qualitatively different
from the group fairness concepts in machine learning, these group fairness
concepts are proposed to 'smooth out' the impact of protected characteristics
in the calculation of insurance prices. The purpose of this note is to share
some thoughts about group fairness concepts in the light of insurance pricing
and to discuss their implications. We present a statistical model that is free
of proxy discrimination, thus, unproblematic from an insurance pricing point of
view. However, we find that the canonical price in this statistical model does
not satisfy any of the three most popular group fairness axioms. This seems
puzzling and we welcome feedback on our example and on the usefulness of these
group fairness axioms for non-discriminatory insurance pricing.Comment: 14 page
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