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• 101.
KTH. Halmstad University, Sweden.
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.). Elekta Instrument AB, Sweden.
A modified fuzzy C means algorithm for shading correction in craniofacial CBCT images2017Ingår i: IFMBE Proceedings, Springer, 2017, s. 531-538Konferensbidrag (Refereegranskat)

CBCT images suffer from acute shading artifacts primarily due to scatter. Numerous image-domain correction algorithms have been proposed in the literature that use patient-specific planning CT images to estimate shading contributions in CBCT images. However, in the context of radiosurgery applications such as gamma knife, planning images are often acquired through MRI which impedes the use of polynomial fitting approaches for shading correction. We present a new shading correction approach that is independent of planning CT images. Our algorithm is based on the assumption that true CBCT images follow a uniform volumetric intensity distribution per material, and scatter perturbs this uniform texture by contributing cupping and shading artifacts in the image domain. The framework is a combination of fuzzy C-means coupled with a neighborhood regularization term and Otsu’s method. Experimental results on artificially simulated craniofacial CBCT images are provided to demonstrate the effectiveness of our algorithm. Spatial non-uniformity is reduced from 16% to 7% in soft tissue and from 44% to 8% in bone regions. With shading- correction, thresholding based segmentation accuracy for bone pixels is improved from 85% to 91% when compared to thresholding without shading-correction. The proposed algorithm is thus practical and qualifies as a p lug and p lay extension into any CBCT reconstruction software for shading correction.

• 102.
Alpen Adria Univ Klagenfurt, Klagenfurt, Austria..
Univ Paris 13, Villetaneuse, France.. Univ Washington, Seattle, WA 98195 USA.. Alpen Adria Univ Klagenfurt, Klagenfurt, Austria.. KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
POP-STACK SORTING AND ITS IMAGE: PERMUTATIONS WITH OVERLAPPING RUNS2019Ingår i: Acta Mathematica Universitatis Comenianae, ISSN 0862-9544, E-ISSN 0231-6986, Vol. 88, nr 3, s. 395-402Artikel i tidskrift (Refereegranskat)

Pop-stack sorting is an important variation for sorting permutations via a stack. A single iteration of pop-stack sorting is the transformation T : S-n -> S-n that reverses all the maximal descending sequences of letters in a permutation. We investigate structural and enumerative aspects of pop-stacked permutations - the permutations that belong to the image of S-n under T. This work is part of a project aiming to provide the full combinatorial analysis of sorting with a pop-stack, as it was successfully done for sorting with a stack (though, even in this case, some famous problems are still open). The first results already show that pop-stack sorting has a very rich combinatorial structure, and leads to surprising phenomena.

• 103.
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
Mating Non-Renormalizable Quadratic Polynomials2009Ingår i: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 287, nr 1, s. 1-40Artikel i tidskrift (Refereegranskat)

In this paper we prove the existence and uniqueness of matings of the basilica with any quadratic polynomial which lies outside of the 1/2-limb of M, is non-renormalizable, and does not have any non-repelling periodic orbits.

• 104. Avgustinovich, S. V.
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
On intersection problem for perfect binary codes2006Ingår i: Designs, Codes and Cryptography, ISSN 0925-1022, E-ISSN 1573-7586, Vol. 39, nr 3, s. 317-322Artikel i tidskrift (Refereegranskat)

The main result is that to any even integer q in the interval 0 <= q <= 2(n+1-2) (log(n+1)), there are two perfect codes C-1 and C-2 of length n = 2(m) -1, m >= 4, such that vertical bar C-1 boolean AND C-2 vertical bar = q.

• 105. Avgustinovich, S. V.
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
On partitions of an n-cube into nonequivalent perfect codes2007Ingår i: Problems of Information Transmission, ISSN 0032-9460, E-ISSN 1608-3253, Vol. 43, nr 4, s. 310-315Artikel i tidskrift (Refereegranskat)

We prove that for all n = 2(k)-1, k >= 5. there exists a partition of the set of all binary vectors of length n into pairwise nonequivalent perfect binary codes of length n with distance 3.

• 106. Avgustinovich, S. V.
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
On the structure of symmetry groups of Vasil'ev codes2005Ingår i: Problems of Information Transmission, ISSN 0032-9460, E-ISSN 1608-3253, Vol. 41, nr 2, s. 105-112Artikel i tidskrift (Refereegranskat)

The structure of symmetry groups of Vasil'ev codes is studied. It is proved that the symmetry group of an arbitrary perfect binary non-full-rank Vasil'ev code of length n is always nontrivial; for codes of rank n - log(n + 1) + 1, an attainable upper bound on the order of the symmetry group is obtained.

• 107. Ayyer, Arvind
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
Some genelalized juggling processes (extended abstract)2015Ingår i: DMTCS proc. FPSAC'15, Nancy, France, 2015, s. 925-936Konferensbidrag (Refereegranskat)

We consider generalizations of juggling Markov chains introduced by Ayyer, Bouttier, Corteel and Nunzi. We first study multispecies generalizations of all the finite models therein, namely the MJMC, the add-drop and the annihilation models. We then consider the case of several jugglers exchanging balls. In all cases, we give explicit product formulas for the stationary probability and closed-form expressions for the normalization factor if known.

• 108. Ayyer, Arvind
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
An inhomogeneous multispecies TASEP on a ring2014Ingår i: Advances in Applied Mathematics, ISSN 0196-8858, E-ISSN 1090-2074, Vol. 57, s. 21-43Artikel i tidskrift (Refereegranskat)

We reinterpret and generalize conjectures of Lam and Williams as statements about the stationary distribution of a multispecies exclusion process on the ring. The central objects in our study are the multiline queues of Ferrari and Martin. We make some progress on some of the conjectures in different directions. First, we prove Lam and Williams' conjectures in two special cases by generalizing the rates of the Ferrari-Martin transitions. Secondly, we define a new process on multiline queues, which have a certain minimality property. This gives another proof for one of the special cases; namely arbitrary jump rates for three species.

• 109. Ayyer, Arvind
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
Correlations in the multispecies tasep and a conjecture by Lam2017Ingår i: Transactions of the American Mathematical Society, ISSN 0002-9947, E-ISSN 1088-6850, Vol. 369, nr 2, s. 1097-1125Artikel i tidskrift (Refereegranskat)

We study correlations in the multispecies TASEP on a ring. Results on the correlation of two adjacent points prove two conjectures by Thomas Lam on (a) the limiting direction of a reduced random walk in (A) over tilde (n-1) and (b) the asymptotic shape of a random integer partition with no hooks of length n, a so called n-core. We further investigate two-point correlations far apart and three-point nearest neighbour correlations and prove explicit formulas in almost all cases. These results can be seen as a finite strengthening of correlations in the TASEP speed process by Amir, Angel and Valko. We also give conjectures for certain higher order nearest neighbour correlations. We find an unexplained independence property (provably for two points, conjecturally for more points) between points that are closer in position than in value that deserves more study.

• 110.
Indian Inst Sci, Dept Math, Bangalore, Karnataka, India..
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
Reverse juggling processes2019Ingår i: Random structures & algorithms (Print), ISSN 1042-9832, E-ISSN 1098-2418, Vol. 55, nr 1, s. 56-72Artikel i tidskrift (Refereegranskat)

Knutson introduced two families of reverse juggling Markov chains (single and multispecies) motivated by the study of random semi-infinite matrices over Fq. We present natural generalizations of both chains by placing generic weights that still lead to simple combinatorial expressions for the stationary distribution. For permutations, this is a seemingly new multivariate generalization of the inversion polynomial.

• 111.
Mainz University, Department of Mathematics.
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.). KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
Dynamical Symmetries in Supersymmetric Matrix2008Ingår i: Documenta Mathematica, ISSN 1431-0635, E-ISSN 1431-0643, Vol. 13, s. 103-116Artikel i tidskrift (Refereegranskat)

We reveal a dynamical SU(2) symmetry in the asymptotic description of supersymmetric matrix models. We also consider a recursive approach for determining the ground state, and point out some additional properties of the model(s).

• 112. Bachelet, Delphine
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
Occurrence of Anti-Drug Antibodies against Interferon-Beta and Natalizumab in Multiple Sclerosis: A Collaborative Cohort Analysis2016Ingår i: PLoS ONE, ISSN 1932-6203, E-ISSN 1932-6203, Vol. 11, nr 11, artikel-id e0162752Artikel i tidskrift (Refereegranskat)

Immunogenicity of biopharmaceutical products in multiple sclerosis is a frequent side effect which has a multifactorial etiology. Here we study associations between anti-drug antibody (ADA) occurrence and demographic and clinical factors. Retrospective data from routine ADA test laboratories in Sweden, Denmark, Austria and Germany (Dusseldorf group) and from one research study in Germany (Munich group) were gathered to build a collaborative multi-cohort dataset within the framework of the ABIRISK project. A subset of 5638 interferon-beta (IFN beta)-treated and 3440 natalizumab-treated patients having data on at least the first two years of treatment were eligible for interval-censored time-to-event analysis. In multivariate Cox regression, IFN beta-1a subcutaneous and IFN beta-1b subcutaneous treated patients were at higher risk of ADA occurrence compared to IFN beta-1a intramuscular-treated patients (pooled HR = 6.4, 95% CI 4.9-8.4 and pooled HR = 8.7, 95% CI 6.6-11.4 respectively). Patients older than 50 years at start of IFN beta therapy developed ADA more frequently than adult patients younger than 30 (pooled HR = 1.8, 95% CI 1.4-2.3). Men developed ADA more frequently than women (pooled HR = 1.3, 95% CI 1.1-1.6). Interestingly we observed that in Sweden and Germany, patients who started IFN beta in April were at higher risk of developing ADA (HR = 1.6, 95% CI 1.1-2.4 and HR = 2.4, 95% CI 1.5-3.9 respectively). This result is not confirmed in the other cohorts and warrants further investigations. Concerning natalizumab, patients older than 45 years had a higher ADA rate (pooled HR = 1.4, 95% CI 1.0-1.8) and women developed ADA more frequently than men (pooled HR = 1.4, 95% CI 1.0-2.0). We confirmed previously reported differences in immunogenicity of the different types of IFN beta. Differences in ADA occurrence by sex and age are reported here for the first time. These findings should be further investigated taking into account other exposures and biomarkers.

• 113. Backelin, Jörgen
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
Parity splits by triple point distances in X-trees2006Ingår i: Annals of Combinatorics, ISSN 0218-0006, E-ISSN 0219-3094, Vol. 10, nr 1, s. 1-18Artikel i tidskrift (Refereegranskat)

At the conference Dress defined parity split maps by triple point distance and asked for a characterisation of such maps coming from binary phylogenetic X-trees. This article gives an answer to that question. The characterisation for X-trees can be easily described as follows: If all restrictions of a split map to sets of five or fewer elements is a parity split map for an X-tree, then so is the entire map. To ensure that the parity split map comes from an X-tree which is binary and phylogenetic, we add two more technical conditions also based on studying at most five points at a time.

• 114. Baker, Matthew
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
Bitangents of tropical plane quartic curves2016Ingår i: Mathematische Zeitschrift, ISSN 0025-5874, E-ISSN 1432-1823, Vol. 282, nr 3-4, s. 1017-1031Artikel i tidskrift (Refereegranskat)

We study smooth tropical plane quartic curves and show that they satisfy certain properties analogous to (but also different from) smooth plane quartics in algebraic geometry. For example, we show that every such curve admits either infinitely many or exactly 7 bitangent lines. We also prove that a smooth tropical plane quartic curve cannot be hyperelliptic.

• 115. Baladi, Viviane
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
Whitney-Holder continuity of the SRB measure for transversal families of smooth unimodal maps2015Ingår i: Inventiones Mathematicae, ISSN 0020-9910, E-ISSN 1432-1297, Vol. 201, nr 3, s. 773-844Artikel i tidskrift (Refereegranskat)

We consider families of nondegenerate unimodal maps. We study the absolutely continuous invariant probability (SRB) measure of , as a function of on the set of Collet-Eckmann (CE) parameters: Upper bounds: Assuming existence of a transversal CE parameter, we find a positive measure set of CE parameters , and, for each , a set of polynomially recurrent parameters containing as a Lebesgue density point, and constants , , so that, for every -Holder function , In addition, for all , the renormalisation period of satisfies , and there are uniform bounds on the rates of mixing of for all with . If , the set contains almost all CE parameters. Lower bounds: Assuming existence of a transversal mixing Misiurewicz-Thurston parameter , we find a set of CE parameters accumulating at , a constant , and a function , so that C vertical bar t - t(0)vertical bar(1/2) >= vertical bar integral A(0)d mu(t) - integral A(0)d mu(t0) vertical bar >= C-1 vertical bar t - t(0)vertical bar(1/2), for all t is an element of Delta(MT)'.

• 116.
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
Cauchy Integrals Method in the Study of Perturbations of Operators2016Självständigt arbete på avancerad nivå (masterexamen), 20 poäng / 30 hpStudentuppsats (Examensarbete)

Vi visar att analytiska funktioner på öppna enhetsskivan som uppfyller Höldervillkoret av ordning r, där r ligger på intervallet (0,1), är operator Hölder av ordning r på mängden av alla linjära kontraktioner på ett Hilbert rum. Vidare så är det känt att analytiska Lipschitzfunktioner på enhetsskivan inte behöver vara operator-Lipschitz. Vi visar att om vi lägger till ett visst integralvillkor så är dessa funktioner operator-Lipschitz. Vi visar de två resultaten med redskap från operatorteori som inkluderar Spektralsatsen och dilationer av kontraktioner.

Vi löser även ett problem som är relaterat till teorin om dilationer som uppstod på en matematisk frågor- och svarhemsida. Mer specifikt visar vi att för ett visst polynom som antar operatorvärden så är von Neumanns olikhet falsk.

• 117.
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori. KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.). Elekta, Box 7593, 103 93 Stockholm, Sweden. KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori. KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
Data-driven nonsmooth optimizationManuskript (preprint) (Övrigt vetenskapligt)
• 118. Bank, Efrat
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
PRIME POLYNOMIALS IN SHORT INTERVALS AND IN ARITHMETIC PROGRESSIONS2015Ingår i: Duke mathematical journal, ISSN 0012-7094, E-ISSN 1547-7398, Vol. 164, nr 2, s. 277-295Artikel i tidskrift (Refereegranskat)

In this paper we establish function field versions of two classical conjectures on prime numbers. The first says that the number of primes in intervals (x,x x(is an element of)] is about x(is an element of)/logx. The second says that the number of primes p < x in the arithmetic progression p equivalent to a (mod d), for d < x(1-delta), is about pi(x)/phi(d), where phi is the Euler totient function. More precisely, for short intervals we prove: Let k be a fixed integer Then pi(q)(I(f,is an element of)) similar to #I(f,is an element of)/k, q -> infinity holds uniformly for all prime powers q, degree k monic polynomials is an element of F-a[t] and is an element of(0)(f, q) <= is an element of, where is an element of(0) is either 1/k, or 2/k if p vertical bar k(k-1), or 3/k if further p = 2 and deg f ' <= 1. Here I (f, is an element of) = {g is an element of F-q[t] vertical bar deg( f - g) <= is an element of deg f }, and pi(q)(I(f, is an element of)) denotes the number of prime polynomials in I (f, 6). We show that this estimation fails in the neglected cases. For arithmetic progressions we prove: let k be a fixed integer. Then pi(q)(k; D,f) similar to pi(q)(k)/phi(D), q -> infinity, holds uniformly for all relatively prime polynomials D, f is an element of F-q[t] satisfying parallel to D parallel to <= q(k)(1-(delta 0)) where delta(0) is either 3/k or 4/k if p = 2 and (f /D)' is a constant. Here pi(q)(k) is the number of degree k prime polynomials and pi(a)(k; D, f) is the number of such polynomials in the arithmetic progression P equivalent to f (mod D). We also generalize these results to arbitrary factorization types.

• 119. Baranov, Anton
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
Boundary properties of Green functions in the plane2008Ingår i: Duke mathematical journal, ISSN 0012-7094, E-ISSN 1547-7398, Vol. 145, nr 1, s. 1-24Artikel i tidskrift (Refereegranskat)

We study the boundary properties of the Green function of bounded simply connected domains in the plane. Essentially, this amounts to studying the conformal mapping taking the unit disk onto the domain in question. Our technique is inspired by a 1995 article of Jones and Makarov [11]. The main tools are an integral identity as well as a uniform Sobolev embedding theorem. The latter is in a sense dual to the exponential integrability of Marcinkiewicz-Zygmund integrals. We also develop a Grunsky identity, which contains the information of the classical Grunsky inequality. This Grunsky identity is the case where p = 2 of a more general Grunsky identily for L-p-spaces.

• 120. Bates, Dan
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
Computing intersection numbers of Chern classesManuskript (preprint) (Övrigt vetenskapligt)

Let Z $\subset$ Pr be a smooth variety of dimension n and let c0, . . . , cn be the Chern classes of Z. We present an algorithm to compute the degree of any monomial in {c0, . . . , cn}. The method is based on intersection theory and may be implemented as a numeric, symbolic, or as a numeric/symbolic hybrid algorithm.

• 121. Bates, Daniel J.
Besana, Gian, MarioCollege of Computing and Digital Media - DePaul University, 1 E. Jackson - Chicago.Di Rocco, SandraKTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).Wampler, Charles W.
Interactions of classical and numerical algebraic geometry2009Proceedings (redaktörskap) (Refereegranskat)
• 122. Bauer, T.
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
On the postulation of lines and a fat line2019Ingår i: Journal of symbolic computation, ISSN 0747-7171, E-ISSN 1095-855X, Vol. 91, s. 3-16Artikel i tidskrift (Refereegranskat)

In the present note we show that the union of r general lines and one fat line in P3 imposes independent conditions on forms of sufficiently high degree d, where the bound is independent of the number of lines. This extends former results of Hartshorne and Hirschowitz on unions of general lines, and of Aladpoosh on unions of general lines and one double line.

• 123. Bauer, Thomas
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
A primer on Seshadri constants2009Ingår i: INTERACTIONS OF CLASSICAL AND NUMERICAL ALGEBRAIC GEOMETRY  , Providence, RI: American Mathematical Society (AMS), 2009, Vol. 496, s. 33-70Konferensbidrag (Refereegranskat)

Seshadri constants express the so called local positivity of a line bundle on a projective variety. They were introduced in [Dem92] by Demailly. The original hope of using them towards a proof of the Fujita conjecture was too optimistic, but it soon became clear that they are interesting invariants quite in their own right. Lazarsfeld's book [PAG] contains a whole chapter devoted to local positivity and serves as a very enjoyable introduction to Seshadri constants. Since this book has appeared, the subject witnessed quite a bit of development. It is the aim of these notes to give an account of recent progress as well as to discuss many open questions and provide some examples. The idea of writing these notes occurred during the workshop on Seshadri constants held in Essen 12-15 February 2008.

• 124.
Fachbereich Mathematik und Informatik, Philipps-Universität, Hans-Meerwein-Strasse, Lahnberge, 35032, MARBURG, GERMANY.
Di Rocco, SandraKTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).Harbourne, BrianDepartment of Mathematics, University of Nebraska-Lincoln, NE 68588, LINCOLN, UNITED STATES.Szemberg, TomaszDepartment of Mathematics, Krakow Pedagogical Academy, ul. Podchorazych 2, 30-084, KRAKOW, POLAND.
Mini-Workshop: Linear Series on Algebraic Varieties2010Proceedings (redaktörskap) (Övrigt vetenskapligt)

Linear series have long played a central role in algebraic geometry. In recent years, starting with seminal papers by Demailly and Ein-Lazarsfeld, local properties of linear series – in particular local positivity, as measured by Seshadri constants – have come into focus. Interestingly, in their multi-point version they are closely related to the famous Nagata conjecture on plane curves. While a number of important basic results are available by now, there are still a large number of open questions and even completely open lines of research.

• 125.
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
Formal plethories2014Ingår i: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 254, s. 497-569Artikel i tidskrift (Refereegranskat)

Unstable operations in a generalized cohomology theory E give rise to a functor from the category of algebras over E* to itself which is a colimit of representable functors and a comonoid with respect to composition of such functors. In this paper I set up a framework for studying the algebra of such functors, which I call formal plethories, in the case where E* is a Prüfer ring. I show that the "logarithmic" functors of primitives and indecomposables give linear approximations of formal plethories by bimonoids in the 2-monoidal category of bimodules over a ring.

• 126.
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
Graph properties of DAG associahedra and related polytopes2018Självständigt arbete på avancerad nivå (masterexamen), 20 poäng / 30 hpStudentuppsats (Examensarbete)

En riktad acyklisk graf kan betraktas som en representant för relationer av betingat oberoende mellan stokastiska variabler. Ett grundläggande problem inom kausal inferens är, givet att vi får data från en sannolikhetsfördelning som uppfyller en mängd relationer av betingat oberoende, att hitta den underliggande graf som representerar dessa relationer. Den giriga SP-algoritmen strävar efter att hitta den underliggande grafen genom att traversera kanter på en polytop kallad DAG-associahedern. Därav spelar kantstrukturen hos DAG-associahedern en stor roll för vår förståelse för den giriga SP-algoritmens komplexitet. I den här uppsatsen studerar vi grafegenskaper hos kantgrafer av DAG-associahedern, relaterade polytoper och deras viktiga delgrafer. Exempel på grafe-genskaper som vi studerar är diameter, radie och center. Våra diameterresultat för DAG-associahedern ger upphov till en ny kausal inferensalgoritm med förbättrade teoretiska på-litlighetsgarantier och komplexitetsbegränsningar jämfört med den giriga SP-algoritmen.

• 127.
Univ Grenoble Alpes, CNRS, Inst Fourier, F-38000 Grenoble, France..
Univ Durham, Dept Math Sci, Durham DH1 3LE, England.. KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.). Royal Inst Technol KTH, Dept Math, Linstedtsvagen 25, SE-10044 Stockholm, Sweden..
AIRY POINT PROCESS AT THE LIQUID-GAS BOUNDARY2018Ingår i: Annals of Probability, ISSN 0091-1798, E-ISSN 2168-894X, Vol. 46, nr 5, s. 2973-3013Artikel i tidskrift (Refereegranskat)

Domino tilings of the two-periodic Aztec diamond feature all of the three possible types of phases of random tiling models. These phases are determined by the decay of correlations between dominoes and are generally known as solid, liquid and gas. The liquid-solid boundary is easy to define microscopically and is known in many models to be described by the Airy process in the limit of a large random tiling. The liquid-gas boundary has no obvious microscopic description. Using the height function, we define a random measure in the two-periodic Aztec diamond designed to detect the long range correlations visible at the liquid-gas boundary. We prove that this random measure converges to the extended Airy point process. This indicates that, in a sense, the liquid-gas boundary should also be described by the Airy process.

• 128. Bell, Steven
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
Szegö coordinates, quadrature domains, and double quadrature domains2011Ingår i: Computational methods in Function Theory, ISSN 1617-9447, E-ISSN 2195-3724, Vol. 11, nr 1, s. 25-44Artikel i tidskrift (Refereegranskat)

We define Szegö coordinates on a finitely connected smoothly bounded planar domain which effect a holomorphic change of coordinates on the domain that can be as close to the identity as desired and which convert the domain to a quadrature domain with respect to boundary arc length. When these Szegö coordinates coincide with Bergman coordinates, the result is a double quadrature domain with respect to both area and arc length. We enumerate a host of interesting and useful properties that such double quadrature domains possess, and we show that such domains are in fact dense in the realm of bounded C-smooth finitely connected domains.

• 129.
Dipartimento di Matematica, Università di Roma Tor Vergata.
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.). Dipartimento di Matematica Pura e Applicata, Università di Padova. Dipartimento di Informatica, Università di Verona.
Closure and Convexity Results for Closed Relativistic Strings2010Ingår i: Complex Analysis and Operator Theory, ISSN 1661-8254, Vol. 4, nr 3, s. 473-496Artikel i tidskrift (Refereegranskat)

We study various properties of closed relativistic strings. In particular, we characterize their closure under uniform convergence, extending a previous result by Y. Brenier on graph-like unbounded strings, and we discuss some related examples. Then we study the collapsing profile of uniformly convex planar strings which start with zero initial velocity, and we obtain a result analogous to the well-known theorem of Gage and Hamilton for the curvature flow of plane curves. We conclude the paper with the discussion of an example of weak Lipschitz evolution starting from the square in the plane.

• 130. Benedetto, R. L.
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
Periods of rational maps modulo primes2013Ingår i: Mathematische Annalen, ISSN 0025-5831, E-ISSN 1432-1807, Vol. 355, nr 2, s. 637-660Artikel i tidskrift (Refereegranskat)

Let K be a number field, let be a rational map of degree at least 2, and let . We show that if alpha is not in the forward orbit of beta, then there is a positive proportion of primes of K such that is not in the forward orbit of . Moreover, we show that a similar result holds for several maps and several points. We also present heuristic and numerical evidence that a higher dimensional analog of this result is unlikely to be true if we replace alpha by a hypersurface, such as the ramification locus of a morphism .

• 131. Benedetto, Robert L.
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
A case of the dynamical Mordell-Lang conjecture2012Ingår i: Mathematische Annalen, ISSN 0025-5831, E-ISSN 1432-1807, Vol. 352, nr 1, s. 1-26Artikel i tidskrift (Refereegranskat)

We prove a special case of a dynamical analogue of the classical Mordell- Lang conjecture. Specifically, let phi be a rational function with no periodic critical points other than those that are totally invariant, and consider the diagonal action of phi on (P(1))(g). If the coefficients of phi are algebraic, we show that the orbit of a point outside the union of the proper preperiodic subvarieties of (P(1))(g) has only finite intersection with any curve contained in (P(1))(g). We also show that our result holds for indecomposable polynomials phi with coefficients in C. Our proof uses results from p-adic dynamics together with an integrality argument. The extension to polynomials defined over C uses the method of specialization coupled with some new results of Medvedev and Scanlon for describing the periodic plane curves under the action of (phi, phi) on A(2).

• 132. Benedetto, Robert L.
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
A gap principle for dynamics2010Ingår i: Compositio Mathematica, ISSN 0010-437X, E-ISSN 1570-5846, Vol. 146, nr 4, s. 1056-1072Artikel i tidskrift (Refereegranskat)

Let f(1), ... , f(g) is an element of C(z) be rational functions, let Phi = (f(1), ... ,f(g)) denote their coordinate-wise action on (P-1)(g), let V subset of (P-1)(g) be a proper subvariety, and let P be a point in (P-1)(g)(C). We show that if S = {n >= 0 : Phi(n)(P) is an element of V(C)} does not contain any infinite arithmetic progressions, then S must be a very sparse set of integers. In particular, for any k and any sufficiently large N, the number of n <= N such that Phi(n)(P) is an element of V(C) is less than log(k)N, where log(k) denotes the kth iterate of the log function. This result can be interpreted as an analogue of the gap principle of Davenport-koth and Mumford.

• 133.
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
Jones, Peter W.Department of Mathematics, Yale University.Smirnov, StanislavSection de mathématiques, Université de Genéve.Winckler, BjörnKTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
Perspectives in analysis: Essays in honor of Lennart Carleson’s 75th birthday. Proceedings of the conference held at the Royal Institute of Technology, Stockholm, May 26–28, 2003.2005Proceedings (redaktörskap) (Refereegranskat)
• 134.
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
Kneading sequences for double standard maps2009Ingår i: Fundamenta Mathematicae, ISSN 0016-2736, E-ISSN 1730-6329, Vol. 206, s. 61-75Artikel i tidskrift (Refereegranskat)

We investigate the symbolic dynamics for the double standard maps of the circle onto itself, given by f(a,b) (x) = 2x + a + (b/pi) sin(2 pi x) (mod 1), where b = 1 and a is a real parameter, 0 <= a < 1

• 135.
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
Random perturbations and statistical properties of Henon-like maps2006Ingår i: Annales de l'Institut Henri Poincare. Analyse non linéar, ISSN 0294-1449, E-ISSN 1873-1430, Vol. 23, nr 5, s. 713-752Artikel i tidskrift (Refereegranskat)

For a large class of non-uniformly hyperbolic diffeomorphisms, we prove stochastic stability under small random noise: the unique stationary probability measure of the Markov chain converges to the Sinai-Ruelle-Bowen measure of the unperturbed attractor when the noise level tends to zero.

• 136. Beneš, C.
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.). Uppsala University, Sweden.
Scaling limit of the loop-erased random walk Green’s function2015Ingår i: Probability theory and related fields, ISSN 0178-8051, E-ISSN 1432-2064Artikel i tidskrift (Refereegranskat)

We consider loop-erased random walk (LERW) running between two boundary points of a square grid approximation of a planar simply connected domain. The LERW Green’s function is the probability that the LERW passes through a given edge in the domain. We prove that this probability, multiplied by the inverse mesh size to the power 3/4, converges in the lattice size scaling limit to (a constant times) an explicit conformally covariant quantity which coincides with the (Formula presented.) Green’s function. The proof does not use SLE techniques and is based on a combinatorial identity which reduces the problem to obtaining sharp asymptotics for two quantities: the loop measure of random walk loops of odd winding number about a branch point near the marked edge and a “spinor” observable for random walk started from one of the vertices of the marked edge.

• 137.
Matematiska vetenskaper, Chalmers och Göteborgs universitet..
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.). Institutionen för naturvetenskapernas och matematikens didaktik, Umeå universitet.
Success-factors in transition to university mathematics2017Ingår i: International journal of mathematical education in science and technology, ISSN 0020-739X, E-ISSN 1464-5211Artikel i tidskrift (Refereegranskat)

This study examines different factors' relative importance for students' performance in the transition to university mathematics. Students' characteristics (motivation, actions and beliefs) were measured when entering the university and at the end of the first year. Principal component analysis revealed four important constructs: Self-efficacy, Motivation type, Study habits and Views of mathematics. Subsequently, orthogonal partial least squares (OPLS) analysis was used for measuring the constructs' ability to predict students' university mathematics grades. No individual constructs measured at the time of entrance predicted more than 5% of the variation. On the other hand, jointly they predicted 14%, which is almost in pair with upper secondary grades predicting 17%. Constructs measured at the end of the first year were stronger predictors, jointly predicting 37% of the variation in university grades, with Self-efficacy (21%) and Motivation (12%) being the two strongest individual predictors. In general, Study habits were not important for predicting university achievement. However, for students with low upper secondary grades, the textbook and interaction with peers, rather than internet-based resources, contributed positively to achievement. The association between Views of mathematics and performance was weak for all groups and non-existing for students with low grades.

• 138. Benguria, Rafael D.
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
The sharp constant in the Hardy-Sobolev-Maz'ya inequality in the three dimensional upper half-space2008Ingår i: Mathematical Research Letters, ISSN 1073-2780, E-ISSN 1945-001X, Vol. 15, nr 4, s. 613-622Artikel i tidskrift (Refereegranskat)

It is shown that the sharp constant in the Hardy-Sobolev-Maz'ya inequality on the upper half space H-3 subset of R-3 is given by the Sobolev constant. This is achieved by a duality argument relating the problem to a Hardy-Littlewood-Sobolev type inequality whose sharp constant is determined as well.

• 139. Berg, S.
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
Ehrhart tensor polynomials2018Ingår i: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 539, s. 72-93Artikel i tidskrift (Refereegranskat)

The notion of Ehrhart tensor polynomials, a natural generalization of the Ehrhart polynomial of a lattice polytope, was recently introduced by Ludwig and Silverstein. We initiate a study of their coefficients. In the vector and matrix cases, we give Pick-type formulas in terms of triangulations of a lattice polygon. As our main tool, we introduce hr-tensor polynomials, extending the notion of the Ehrhart h⁎-polynomial, and, for matrices, investigate their coefficients for positive semidefiniteness. In contrast to the usual h⁎-polynomial, the coefficients are in general not monotone with respect to inclusion. Nevertheless, we are able to prove positive semidefiniteness in dimension two. Based on computational results, we conjecture positive semidefiniteness of the coefficients in higher dimensions. Furthermore, we generalize Hibi's palindromic theorem for reflexive polytopes to hr-tensor polynomials and discuss possible future research directions.

• 140.
KTH, Skolan för teknikvetenskap (SCI), Tillämpad fysik, Kvant- och biofotonik.
KTH, Skolan för teknikvetenskap (SCI), Tillämpad fysik, Kvant- och biofotonik. Royal Inst Technol KTH, Dept Appl Phys, Albanova Univ Ctr, Expt Biomol Phys, SE-10691 Stockholm, Sweden.. KTH, Skolan för teknikvetenskap (SCI), Tillämpad fysik, Kvant- och biofotonik. Royal Inst Technol KTH, Dept Appl Phys, Albanova Univ Ctr, Expt Biomol Phys, SE-10691 Stockholm, Sweden.. Karolinska Inst, Dept Med Solna, Karolinska Univ Hosp Solna, Clin Pharmacol, L7 03, SE-17176 Stockholm, Sweden.. KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.). Karolinska Inst, Dept Oncol Pathol, Karolinska Univ Hosp, K7,Z1 00, S-17176 Stockholm, Sweden.. Karolinska Inst, Dept Oncol Pathol, Karolinska Univ Hosp, K7,Z1 00, S-17176 Stockholm, Sweden.. Karolinska Inst, Dept Oncol Pathol, Karolinska Univ Hosp, K7,Z1 00, S-17176 Stockholm, Sweden.;Acad Univ Hosp, Dept Obstet & Gynaecol, SE-75185 Uppsala, Sweden.;Uppsala Univ, Inst Women & Child Hlth, SE-75185 Uppsala, Sweden.. KTH, Skolan för teknikvetenskap (SCI), Tillämpad fysik, Kvant- och biofotonik.
Super-resolution microscopy can identify specific protein distribution patterns in platelets incubated with cancer cells2019Ingår i: Nanoscale, ISSN 2040-3364, E-ISSN 2040-3372, Vol. 11, nr 20, s. 10023-10033Artikel i tidskrift (Refereegranskat)

Protein contents in platelets are frequently changed upon tumor development and metastasis. However, how cancer cells can influence protein-selective redistribution and release within platelets, thereby promoting tumor development, remains largely elusive. With fluorescence-based super-resolution stimulated emission depletion (STED) imaging we reveal how specific proteins, implicated in tumor progression and metastasis, re-distribute within platelets, when subject to soluble activators (thrombin, adenosine diphosphate and thromboxane A2), and when incubated with cancer (MCF-7, MDA-MB-231, EFO21) or non-cancer cells (184A1, MCF10A). Upon cancer cell incubation, the cell-adhesion protein P-selectin was found to re-distribute into circular nano-structures, consistent with accumulation into the membrane of protein-storing alpha-granules within the platelets. These changes were to a significantly lesser extent, if at all, found in platelets incubated with normal cells, or in platelets subject to soluble platelet activators. From these patterns, we developed a classification procedure, whereby platelets exposed to cancer cells, to non-cancer cells, soluble activators, as well as non-activated platelets all could be identified in an automatic, objective manner. We demonstrate that STED imaging, in contrast to electron and confocal microscopy, has the necessary spatial resolution and labelling efficiency to identify protein distribution patterns in platelets and can resolve how they specifically change upon different activations. Combined with image analyses of specific protein distribution patterns within the platelets, STED imaging can thus have a role in future platelet-based cancer diagnostics and therapeutic monitoring. The presented approach can also bring further clarity into fundamental mechanisms for cancer cell-platelet interactions, and into non-contact cell-to-cell interactions in general.

• 141.
KTH, Skolan för teknikvetenskap (SCI), Tillämpad fysik, Kvant- och biofotonik.
KTH, Skolan för teknikvetenskap (SCI), Tillämpad fysik, Kvant- och biofotonik. KTH, Skolan för teknikvetenskap (SCI), Tillämpad fysik, Kvant- och biofotonik. Karolinska Institutet, Department of Medicine, Karolinska University Hospital, L7:03, SE-171 76 Stockholm, Sweden. KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.). Karolinska Institutet, Department of Medicine, Karolinska University Hospital, L7:03, SE-171 76 Stockholm, Sweden. Karolinska Institutet, Department of Medicine, Karolinska University Hospital, L7:03, SE-171 76 Stockholm, Sweden. Karolinska Institutet, Department of Medicine, Karolinska University Hospital, L7:03, SE-171 76 Stockholm, Sweden. KTH, Skolan för teknikvetenskap (SCI), Tillämpad fysik, Kvant- och biofotonik.
Super-resolution microscopy can identify specific protein distribution patterns in platelets incubated with cancer cellsManuskript (preprint) (Övrigt vetenskapligt)

Protein contents in platelets are frequently changed upon tumor development and metastasis. However, how cancer cells can influence protein-selective redistribution and release within platelets, thereby promoting tumor development, remains largely elusive. With fluorescence-based super-resolution stimulated emission depletion (STED) imaging we reveal how specific proteins, implicated in tumor progression and metastasis, re-distribute within platelets, when subject to soluble activators (thrombin, adenosine-diphosphate and thromboxaneA2), and when incubated with cancer (MCF-7, MDA-MB-231, EFO21) or non-cancer cells (184A1, MCF10A). Upon cancer cell incubation, the cell-adhesion protein P-selectin was found to re-distribute into circular nano-structures, consistent with accumulation into the membrane of protein-storing alpha-granules within the platelets. These changes were to a significantly lesser extent, if at all, found in platelets incubated with normal cells, or in platelets subject to soluble platelet activators. From these patterns, we developed a classification procedure, whereby platelets exposed to cancer cells, to non-cancer cells, soluble activators as well as non-activated platelets all could be identified in an automatic, objective manner. We demonstrate that STED imaging, in contrast to electron and confocal microscopy, has the necessary spatial resolution and labelling efficiency to identify protein distribution patterns in platelets and can resolve how they specifically change upon different activations. Combined with image analyses of specific protein distribution patterns within the platelets, STED imaging can thus have a role in future platelet-based cancer diagnostics and therapeutic monitoring. The presented approach can also bring further clarity into fundamental mechanisms for cancer cell-platelet interactions, and into non-contact cell-to-cell interactions in general.

• 142.
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
CNRS.
Inversion of series and the cohomology of the moduli spaces $\scr M\sb 0,n\sp δ$2010Ingår i: Motives, quantum field theory, and pseudodifferential operators, American Mathematical Society (AMS), 2010, Vol. 12, s. 119-126Kapitel i bok, del av antologi (Övrigt vetenskapligt)

For $n\geq 3$, let $\mathcal{M}_{0,n}$ denote the moduli space of genus 0 curves with $n$ marked points, and $\overline{\mathcal{M}}_{0,n}$ its smooth compactification. A theorem due to Ginzburg, Kapranov and Getzler states that the inverse of the exponential generating series for the Poincar\'e polynomial of $H^{\bullet}(\mathcal{M}_{0,n})$ is given by the corresponding series for $H^{\bullet}(\overline{\mathcal{M}}_{0,n})$. In this paper, we prove that the inverse of the ordinary generating series for the Poincar\'e polynomial of $H^{\bullet}(\mathcal{M}_{0,n})$ is given by the corresponding series for $H^{\bullet}(\mathcal{M}^{\delta}_{0,n})$, where $\mathcal{M}_{0,n}\subset \mathcal{M}^{\delta}_{0,n} \subset \overline{\mathcal{M}}_{0,n}$ is a certain smooth affine scheme.

• 143. Bergström, Jonas
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
Siegel modular forms of degree three and the cohomology of local systems2014Ingår i: Selecta Mathematica, New Series, ISSN 1022-1824, E-ISSN 1420-9020, Vol. 20, nr 1, s. 83-124Artikel i tidskrift (Refereegranskat)

We give an explicit conjectural formula for the motivic Euler characteristic of an arbitrary symplectic local system on the moduli space of principally polarized abelian threefolds. The main term of the formula is a conjectural motive of Siegel modular forms of a certain type; the remaining terms admit a surprisingly simple description in terms of the motivic Euler characteristics for lower genera. The conjecture is based on extensive counts of curves of genus three and abelian threefolds over finite fields. It provides a lot of new information about vector-valued Siegel modular forms of degree three, such as dimension formulas and traces of Hecke operators. We also use it to predict several lifts from genus 1 to genus 3, as well as lifts from and new congruences of Harder type.

• 144. Bergström, Jonas
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
Siegel Modular Forms of Genus 2 and Level 2: Cohomological Computations and Conjectures2008Ingår i: International mathematics research notices, ISSN 1073-7928, E-ISSN 1687-0247, s. rnn100-Artikel i tidskrift (Refereegranskat)
• 145.
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
UvA.
The Euler characteristic of local systems on the moduli of curves and abelian varieties of genus three2008Ingår i: Journal of Topology, ISSN 1753-8416, E-ISSN 1753-8424, Vol. 1, nr 3, s. 651-662Artikel i tidskrift (Refereegranskat)

We show how to calculate the Euler characteristic of a local system V(lambda) associated to an irreducible representation V(lambda) of the symplectic group of genus 3 on the moduli space M(3) of curves of genus 3 and the moduli space A(3) of principally polarised abelian varieties of dimension 3.

• 146. Besana, Gian Mario
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
Cell decomposition of almost smooth real algebraic surfaces2013Ingår i: Numerical Algorithms, ISSN 1017-1398, E-ISSN 1572-9265, Vol. 63, nr 4, s. 645-678Artikel i tidskrift (Refereegranskat)

Let Z be a two dimensional irreducible complex component of the solution set of a system of polynomial equations with real coefficients in N complex variables. This work presents a new numerical algorithm, based on homotopy continuation methods, that begins with a numerical witness set for Z and produces a decomposition into 2-cells of any almost smooth real algebraic surface contained in Z. Each 2-cell (a face) has a generic interior point and a boundary consisting of 1-cells (edges). Similarly, the 1-cells have a generic interior point and a vertex at each end. Each 1-cell and each 2-cell has an associated homotopy for moving the generic interior point to any other point in the interior of the cell, defining an invertible map from the parameter space of the homotopy to the cell. This work draws on previous results for the curve case. Once the cell decomposition is in hand, one can sample the 2-cells and 1-cells to any resolution, limited only by the computational resources available.

• 147. Besana, Gian Mario
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
Higher order bad loci2007Ingår i: Journal of Pure and Applied Algebra, ISSN 0022-4049, E-ISSN 1873-1376, Vol. 211, nr 2, s. 414-427Artikel i tidskrift (Refereegranskat)

Zero-schemes on smooth complex projective varieties, forcing all elements of ample and free linear systems to be reducible, are studied. Relationships among the minimal length of such zero-schemes, the positivity of the line bundle associated with the linear system, and the dimension of the variety are established. Bad linear spaces are also investigated.

• 148.
College of Computing and Digital Media - DePaul University, 1 E. Jackson - Chicago.
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.). Dip. di Matematica “F. Enriques” - Università degli Studi di Milano.
The variety of bad zero-schemes2012Ingår i: Journal of Pure and Applied Algebra, ISSN 0022-4049, E-ISSN 1873-1376, Vol. 216, nr 6, s. 1273-1281Artikel i tidskrift (Refereegranskat)

The locus of reduced bad zero-schemes, B-0 subset of X-vertical bar b0 vertical bar, for a linear system vertical bar V vertical bar on a non singular, n-dimensional, algebraic variety X is defined. The pairs (X, V) for which B-0 has the maximal dimension, nb(0) - 1, are characterized. For n = 2, non-reduced bad zero-schemes are also discussed.

• 149.
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
Investigations of solutions of Einstein's field equations close to lambda-Taub-NUT2008Ingår i: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 25, nr 23, s. 235005-Artikel i tidskrift (Refereegranskat)

We present investigations of a class of solutions of Einstein's field equations close to the family of lambda-Taub-NUT spacetimes. The studies are done using a numerical code introduced by the author elsewhere. One of the main technical complications is due to the S-3-topology of the Cauchy surfaces. Complementing these numerical results with heuristic arguments, we are able to yield some first insights into the strong cosmic censorship issue and the conjectures by Belinskii, Khalatnikov and Lifschitz in this class of spacetimes. In particular, the current investigations suggest that strong cosmic censorship holds in this class. We further identify open issues in our current approach and point to future research projects.

• 150. Billera, L. J.
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
Face numbers of polytopes and complexes2017Ingår i: Handbook of Discrete and Computational Geometry, Third Edition, CRC Press , 2017, s. 449-475Kapitel i bok, del av antologi (Övrigt vetenskapligt)

Geometric objects are often put together from simple pieces according to certain combinatorial rules. As such, they can be described as complexes with their constituent cells, which are usually polytopes and often simplices. Many constraints of a combinatorial and topological nature govern the incidence structure of cell complexes and are therefore relevant in the analysis of geometric objects. Since these incidence structures are in most cases too complicated to be well understood, it is worthwhile to focus on simpler invariants that still say something nontrivial about their combinatorial structure. The invariants to be discussed in this chapter are the f-vectors f = (f 0, f 1, …) $f=(f_0, f_1, \dots)$, where f i $f_i$ is the number of i-dimensional cells in the complex.

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