The three-state toric homogeneous Markov chain model has Markov degree two

We prove that the three-state toric homogenous Markov chain model has Markov degree two. In algebraic terminology this means, that a certain class of toric ideals are generated by quadratic binomials. This was conjectured by Haws, Martin del Campo, Takemura and Yoshida, who proved that they are generated by binomials of degree six or less.Comment: Updated language and notation. 13page

Tverberg's theorem and graph coloring

The topological Tverberg theorem has been generalized in several directions by setting extra restrictions on the Tverberg partitions. Restricted Tverberg partitions, defined by the idea that certain points cannot be in the same part, are encoded with graphs. When two points are adjacent in the graph, they are not in the same part. If the restrictions are too harsh, then the topological Tverberg theorem fails. The colored Tverberg theorem corresponds to graphs constructed as disjoint unions of small complete graphs. Hell studied the case of paths and cycles. In graph theory these partitions are usually viewed as graph colorings. As explored by Aharoni, Haxell, Meshulam and others there are fundamental connections between several notions of graph colorings and topological combinatorics. For ordinary graph colorings it is enough to require that the number of colors q satisfy q>Delta, where Delta is the maximal degree of the graph. It was proven by the first author using equivariant topology that if q>\Delta^2 then the topological Tverberg theorem still works. It is conjectured that q>K\Delta is also enough for some constant K, and in this paper we prove a fixed-parameter version of that conjecture. The required topological connectivity results are proven with shellability, which also strengthens some previous partial results where the topological connectivity was proven with the nerve lemma.Comment: To appear in Discrete and Computational Geometry, 13 pages, 1 figure. Updated languag

Polytopes from Subgraph Statistics

Polytopes from subgraph statistics are important in applications and conjectures and theorems in extremal graph theory can be stated as properties of them. We have studied them with a view towards applications by inscribing large explicit polytopes and semi-algebraic sets when the facet descriptions are intractable. The semi-algebraic sets called curvy zonotopes are introduced and studied using graph limits. From both volume calculations and algebraic descriptions we find several interesting conjectures.Comment: Full article, 21 pages, 8 figures. Minor expository update

Algebraic Statistics

This thesis on algebraic statistics contains five papers. In paper I we define ideals of graph homomorphisms. These ideals generalize many of the toric ideals defined in terms of graphs that are important in algebraic statistics and commutative algebra.   In paper II we study polytopes from subgraph statistics. Polytopes from subgraph statistics are important for statistical models for large graphs and many problems in extremal graph theory can be stated in terms of them. We find easily described semi-algebraic sets that are contained in these polytopes, and using them we compute dimensions and get volume bounds for the polytopes.  In paper III we study the topological Tverberg theorem and its generalizations. We develop a toolbox for complexes from graphs using vertex decomposability to bound the connectivity.  In paper IV we prove a conjecture by Haws, Martin del Campo, Takemura and Yoshida. It states that the three-state toric homogenous Markov chain model has Markov degree two. In algebraic terminology this means that a certain class of toric ideals are generated by quadratic binomials.  In paper V we produce cellular resolutions for a large class of edge ideals and their powers. Using algebraic discrete Morse theory it is then possible to make many of these resolutions minimal, for example explicit minimal resolutions for powers of edge ideals of paths are constructed this way.Denna avhandling om algebraisk statistik innehåller fem artiklar. I artikel I definieras ideal av grafhomomorfier. Dessa ideal generaliserar ett flertal konstruktioner av ideal från grafer som är viktiga i algebraisk statistik samt kommutativ algebra. I artikel II behandlas polytoper från delgrafsstatistik. Dessa är viktiga för att förstå statistiska modeller som beskriver stora grafer och många problem om ytterlighetsgrafer kan formuleras med dem. Bland verktygen som används är att beskriva semi-algebraiska mängder i polytoperna och genom detta bestämma deras dimension samt begränsa volymen. I artikel III behandlas den topologiska tverbergssatsen med generaliseringar. Grafkomplexen förstås genom att begränsa sammanhängandegraden medelst hörnnedbrytbarhet. I artikel IV bevisas att ideal tillhörande markovkedjor med tre tillstånd är genererade i grad två, vilket förmodats av Haws, Martin del Campo, Takemura och Yoshida. I artikel V skapas cellulära upplösningar för en stor klass av kantideal samt deras potenser. Med algebraisk diskret morseteori görs dessa upplösningar minimala för kantideal från stigar.

Occurrence of sharks, rays and rabbit fish in the Greater North Sea – and catches in Swedish fisheries

This report was written in response to a request from the Swedish Agency for Marine and Water Management to update an earlier technical note from SLU Aqua “Occurrence of skates and rays in northern European waters and catches in Swedish fisheries in the Skagerrak/Kattegat and the eastern North Sea”. The aim was to provide a comprehensive overview of elasmobranchs present in Swedish waters and to what extent these species are caught in Swedish fisheries. To describe the occurrence and spatial distribution of sharks, rays and rabbit fish we used fisheries-independent survey data from 1967–2020, as well as data from the national on-board observer program and official landing data. During this time a total of 21 species of sharks, rays and rabbit fish were reported from the Skagerrak, Kattegat and the Sound. Seven of the species were common in both the fishery independent and the commercial data supporting that they are native to Swedish waters. These species included three shark species; velvet belly (Etmopterus spinax), lesser spotted dogfish (Scyliorhinus canicula) and spurdog (Squalus acanthias); three species of rays; starry ray (Amblyraja radiata), thornback ray (Raja clavata), and sailray (Rajella lintea); and the rabbit fish (Chimaera monstrosa). The round ray (Rajella fyllae) was also relatively common in survey catches from the deeper parts of the Skagerrak. All common species were present year round, but spurdog also showed a seasonal trend, being more common along the Norwegian coast and in offshore part of the Skagerrak in the first quarter, and closer to the Swedish coast in the third and fourth quarter. There are no longer any targeted fisheries for elasmobranchs by Swedish vessels but by-catches occur, predominantly in demersal trawl fisheries in the deeper parts (> 200 m) of Skagerrak and the Norwegian trench where a majority the observed hauls had by-catch of one or more species. Usage of a sorting device (grid) in the Nephrops and Pandalus trawl fisheries appear to reduce the amount of by-catches. Historical and anecdotal information suggest that by-catch of spurdog in gillnets could be significant, but as landing were prohibited in 2010, no data is available since then. Starry ray and spurdog represents > 75 % of the estimated total catch weight of shark and rays combined. More than 90 % of elasmobranchs was discarded, which is not surprising given that landing of spurdog, starry ray, common skate and thornback ray are prohibited in 3a. Sailray is the only species landed to some extent (few tonnes per year) by Swedish vessels during the last five years. Swedish landings of sailray mainly come from the Pandalus fishery and from demersal trawl fishing without grids in the deeper parts of Skagerrak

Polytopes from Subgraph Statistics

We study polytopes that are convex hulls of vectors of subgraph densities. Many graph theoretical questions can be expressed in terms of these polytopes, and statisticians use them to understand exponential random graph models. Relations among their Ehrhart polynomials are described, their duals are applied to certify that polynomials are non-negative, and we find some of their faces. For the general picture we inscribe cyclic polytopes in them and calculate volumes. From the volume calculations we conjecture that a variation of the Selberg integral indexed by Schur polynomials has a combinatorial formula. We inscribe polynomially parametrized sets, called curvy zonotopes, in the polytopes and show that they approximate the polytopes arbitrarily close

Fishing through time: population dynamics of plaice (<i>Pleuronectes platessa</i>) in the Kattegat–Skagerrak over a century

AbstractOver the past century, advances in technology and historical events such as climate change have resulted in significant changes in the exploitation pattern, population sizes and the potential yield of fish stocks. These variations provide contrast in the data that improves our knowledge on population dynamics and our ability to develop management strategies for long‐term sustainable exploitation. In this study, we use a standardized scientific trawl survey to obtain a historical time series (1901–2007) of relative abundance, recruitment and size structure for plaice in the Kattegat–Skagerrak. Our work extends the available time series by more than 80 years so that the evaluation of trends is more informative than is possible from the current assessment. We show that the current adult biomass is approximately 40% of the maximum observed at the beginning of the century and during the 1960s. The average maximum individual length has been reduced by 10 cm over the studied time period. An analysis of trends in mean length indicates that fishing mortality was variable during the first half of the century and has increased steadily over the past 20 years. Recruitment has been the highest on record during recent years, suggesting that the alleged link between coastal environmental degradation and juvenile survival is of low importance. The overall findings of our work will provide managers with a historical perspective on the population dynamics of the stock, which will support the long‐term management of plaice in the Kattegat–Skagerrak

The European Reference Genome Atlas: piloting a decentralised approach to equitable biodiversity genomics.

ABSTRACT: A global genome database of all of Earth’s species diversity could be a treasure trove of scientific discoveries. However, regardless of the major advances in genome sequencing technologies, only a tiny fraction of species have genomic information available. To contribute to a more complete planetary genomic database, scientists and institutions across the world have united under the Earth BioGenome Project (EBP), which plans to sequence and assemble high-quality reference genomes for all ∼1.5 million recognized eukaryotic species through a stepwise phased approach. As the initiative transitions into Phase II, where 150,000 species are to be sequenced in just four years, worldwide participation in the project will be fundamental to success. As the European node of the EBP, the European Reference Genome Atlas (ERGA) seeks to implement a new decentralised, accessible, equitable and inclusive model for producing high-quality reference genomes, which will inform EBP as it scales. To embark on this mission, ERGA launched a Pilot Project to establish a network across Europe to develop and test the first infrastructure of its kind for the coordinated and distributed reference genome production on 98 European eukaryotic species from sample providers across 33 European countries. Here we outline the process and challenges faced during the development of a pilot infrastructure for the production of reference genome resources, and explore the effectiveness of this approach in terms of high-quality reference genome production, considering also equity and inclusion. The outcomes and lessons learned during this pilot provide a solid foundation for ERGA while offering key learnings to other transnational and national genomic resource projects.info:eu-repo/semantics/publishedVersio

Fonden Jag och Min Hund : Examensarbete i Informationsdesign

Följande rapport behandlar hur välgörenhetsorganisationer arbetarför att konkurrera med varandra när det handlar om att attraheragivare. Mina undersökningar har visat att det inte längre räckermed att stå på stan och sjunga eller gå runt med en bössa för atttjäna ihop till ett gott ändamål. Nu för tiden är givare väldigtkräsna och kräver något tillbaka och det tidigt. Mitt arbete ärfokuserat på välgörenhet som gagnar barn och ungdomar.Granskningarna är fokuserade på audiellt material. Somkomplement till mina efterforskningar har jag gjort ett praktisktarbete där jag producerat ett releasematerial för radio till FondenJag och Min Hund, en fiktiv fond med målet att främja ett liv medservicehund. Anslaget från fonden är tänkt att gå till barn ochungdomar under 25. En servicehund kan hjälpa en person som ärsjuk i exempelvis diabetes, epilepsi eller som har ettfunktionshinder. Mitt arbete och mina avvägningar under detpraktiska arbetet har baserats på de analyser jag gjort under detteoretiska arbetet