Non-vanishing boundary effects and quasi-first order phase transitions in high dimensional Ising models

In order to gain a better understanding of the Ising model in higher dimensions we have made a comparative study of how the boundary, open versus cyclic, of a d-dimensional simple lattice, for d=1,...,5, affects the behaviour of the specific heat C and its microcanonical relative, the entropy derivative -dS/dU. In dimensions 4 and 5 the boundary has a strong effect on the critical region of the model and for cyclic boundaries in dimension 5 we find that the model displays a quasi first order phase transition with a bimodal energy distribution. The latent heat decreases with increasing systems size but for all system sizes used in earlier papers the effect is clearly visible once a wide enough range of values for K is considered. Relations to recent rigorous results for high dimensional percolation and previous debates on simulation of Ising models and gauge fields are discussed.Comment: 12 pages, 27 figure

A remark on Hamiltonian cycles

AbstractEvery 2-connected graph G with δ ⩾ (v + κ)3 is hamiltonian where v denotes the order, δ the minimum degree and κ the point connectivity of G

Circuits through specified edges

AbstractWe prove a theorem implying the conjecture of Woodall [14] that, given any k independent edges in a (k+1)-connected graph, there is a circuit containing all of them. This implies the truth of a conjecture of Berge [1, p.214] and provides strong evidence to a conjecture of Lovász [8]

Completing some Partial Latin Squares

AbstractWe show that any partial 3 r× 3 r Latin square whose filled cells lie in two disjoint r×r sub-squares can be completed. We do this by proving the more general result that any partial 3 r by 3 r Latin square, with filled cells in the top left 2r× 2 r square, for which there is a pairing of the columns so that in each row there is a filled cell in at most one of each matched pair of columns, can be completed if and only if there is some way to fill the cells of the top left 2 r× 2 r square

Cycle Double Covers and Semi-Kotzig Frame

Let $H$ be a cubic graph admitting a 3-edge-coloring $c: E(H)\to \mathbb Z_3$ such that the edges colored by 0 and $\mu\in\{1,2\}$ induce a Hamilton circuit of $H$ and the edges colored by 1 and 2 induce a 2-factor $F$. The graph $H$ is semi-Kotzig if switching colors of edges in any even subgraph of $F$ yields a new 3-edge-coloring of $H$ having the same property as $c$. A spanning subgraph $H$ of a cubic graph $G$ is called a {\em semi-Kotzig frame} if the contracted graph $G/H$ is even and every non-circuit component of $H$ is a subdivision of a semi-Kotzig graph. In this paper, we show that a cubic graph $G$ has a circuit double cover if it has a semi-Kotzig frame with at most one non-circuit component. Our result generalizes some results of Goddyn (1988), and H\"{a}ggkvist and Markstr\"{o}m [J. Combin. Theory Ser. B (2006)]

Sex som självskadebeteende bland unga : En kvalitativ studie om unga som uttrycker sitt lidande genom att skada sig själva

Syftet med den här studien är att beskriva hur vi kan känna igen unga som använder sex som självskadebeteende. Studien görs för att man inom social- och hälsovården bättre ska kunna förstå, bemöta samt hjälpa dessa unga i deras tillfrisknande. Respondenten vill även ta reda på om det är möjligt att börja må bra igen och få ett gott liv efter att man har skadat sig själv genom sex. Centrala frågeställningar är: vad kännetecknar unga som skadar sig själva genom riskfyllda och skadliga sexuella handlingar eller andra former av självskadebeteende samt hur går tillfrisknandet till? Respondenten har valt en kvalitativ narrativ metod, samt använt sig av innehållsanalys för att analysera resultatet. Som teoretisk utgångspunkt valde respondenten Antonovskys modell KASAM och Erikssons (1994) Den lidande människan. Resultatet visar att om man blir utsatt för sexuella övergrepp leder detta till trauman som drabbar den utsatte på bred front och sätter spår för livet. Att bli utsatt för sexuella övergrepp tar sig fysiska, psykiska samt synliga uttryck. Beteendet är svårt att bryta. Resultaten i studien pekar mot att det är möjligt att få ett bra liv efter att beteendet upphört. För att möjliggöra detta krävs professionell hjälp för att kunna ändra beteendet och få ett gott liv. Utvecklingsarbete: Syftet med utvecklingsarbetet är att via en webbportals informationssida lättförståeligt och lättillgängligt informera om vad sex som självskadebeteende är. Det görs för att sprida kunskap bland unga så att de förstår att det finns hjälp att få. Arbetet görs som en fördjupning av respondentens examensarbete Sex som självskadebeteende bland unga (Häggkvist. 2014). Centrala frågeställningar är: Vad är sex som självskadebeteende? och Hur söker man hjälp? Som teoretiska utgångspunkter använder respondenten KASAM enligt Antonovsky (1987) och Den lidande människan enligt Eriksson (1994). Slutprodukten av detta utvecklingsarbete är en informationssida på webbportalen www.Decibel.fi som riktar sig till unga i åldern 13-25 år. Informationssidan läggs upp under våren 2015, webbportalen www.Decibel.fi ansvarar för layouten.The aim of this study is to describe how to recognise adolescents using sex as a means of inflicting self-harm. The reason for conducting the study is to provide a means for people working within social and health care to better understand and treat these individuals, helping them to recover. Furthermore the respondent aims at determining whether it is possible to start feeling well again and to receive a good life after destructively harming oneself through the use of sex. The essential questions are: 1) What is characteristic of adolescents inflicting self-harm through the use of hazardous and harmful sexual acts, or other forms of self- destructive behaviour, as well as 2) how to recover from this. The respondent has chosen a qualitative narrative method combined with a content analysis to analyse the results. As theoretical frameworks Antonovsky’s model of Sense of Coherence as well as Eriksson’s (1994) The Suffering Human Being are used. The results show that the consequences of being made victim of sexual abuse are wideranging traumas that leave a deep mark for live. Being made victim of sexual abuse manifests physically, psychologically and visually. The behaviour pattern is difficult to break. In addition, the results point towards the possibility of receiving a good life after the behaviour has ceased. To enable this professional help is required. Development project: The aim of this development project is to create an easily accessible and easily understood information page about self-destructive behaviour at a web portal. The reason for this is to spread knowledge about the topic among young people, and also to let them know that there is help to obtain. This study is a continuation of the respondent’s essay Sex As Self-destructive Behaviour Amongst Adolescents (Häggkvist, 2014). The questions at issue are “What is sex as self-destructive behaviour?” and “How does one seek help?” The present study is based on the theories of SOC formulated by Antonovsky (1987) and The Suffering Human Being by Eriksson (1994). The outcome of this in-depth article is an information page on the web portal www.Decibel.fi, which targets young people between the ages 13 to 25. The information page will be on the Internet in spring 2015. The web portal www.Decibel.fi will be responsible for the layout

Förstudie för utvärdering av jaktberikning på Parken Zoo

The aim with this study is to prepare for a larger study, by gathering information about hunting enrichment, discuss which enrichment Parken Zoo in Eskilstuna have that are suitable to use in the larger study and report which observation methods that are used in other articles. In the larger study, the focus will lie on evaluation methods and measurable results. They have, during several years at Parken Zoo in Eskilstuna, developed different types of hunting enrichments for their carnivores, because hunting is a natural behavior that is hard to accommodate in captivity. The bigger project will integrate other zoos so that they can do a study on a larger group of animals, and because a lot of other studies in the same field only capture the results of few individuals. In this literature study you will read about the goals of enrichment, research that have been done on enrichment for felids and review several specific articles about hunting enrichment for felids

Intercalates and Discrepancy in Random Latin Squares

An intercalate in a Latin square is a $2\times2$ Latin subsquare. Let $N$ be the number of intercalates in a uniformly random $n\times n$ Latin square. We prove that asymptotically almost surely $N\ge\left(1-o\left(1\right)\right)\,n^{2}/4$, and that $\mathbb{E}N\le\left(1+o\left(1\right)\right)\,n^{2}/2$ (therefore asymptotically almost surely $N\le fn^{2}$ for any $f\to\infty$). This significantly improves the previous best lower and upper bounds. We also give an upper tail bound for the number of intercalates in two fixed rows of a random Latin square. In addition, we discuss a problem of Linial and Luria on low-discrepancy Latin squares

A Proof of a Conjecture of Ohba

We prove a conjecture of Ohba which says that every graph $G$ on at most $2\chi(G)+1$ vertices satisfies $\chi_\ell(G)=\chi(G)$.Comment: 21 page