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  • 301.
    Nyström, Kaj
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Önskog, Thomas
    The Skorohod oblique reflection problem in time-dependent domains2010In: Annals of Probability, ISSN 0091-1798, E-ISSN 2168-894X, Vol. 38, no 6, p. 2170-2223Article in journal (Refereed)
  • 302.
    Nyström, Kaj
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Önskog, Thomas
    Weak approximation of obliquely reflected diffusions in time-dependent domains2010In: Journal of Computational Mathematics, ISSN 0254-9409, E-ISSN 1991-7139, Vol. 28, p. 579-605Article in journal (Refereed)
  • 303.
    Oleynik, Anna
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics. Norwegian Univ Life Sci, Dept Math Sci & Technol, N-1432 As, Norway.;Norwegian Univ Life Sci, Ctr Integrat Genet, N-1432 As, Norway..
    Ponosov, Arcady
    Norwegian Univ Life Sci, Dept Math Sci & Technol, N-1432 As, Norway.;Norwegian Univ Life Sci, Ctr Integrat Genet, N-1432 As, Norway..
    Wyller, John
    Norwegian Univ Life Sci, Dept Math Sci & Technol, N-1432 As, Norway.;Norwegian Univ Life Sci, Ctr Integrat Genet, N-1432 As, Norway..
    Iterative Schemes for Bump Solutions in a Neural Field Model2015In: Differential Equations and Dynamical Systems, ISSN 0971-3514, E-ISSN 0974-6870, Vol. 23, no 1, p. 79-98Article in journal (Refereed)
    Abstract [en]

    We develop two iteration schemes for construction of localized stationary solutions (bumps) of a one-population Wilson-Cowan model with a smooth firing rate function. The first scheme is based on the fixed point formulation of the stationary Wilson-Cowan model. The second one is formulated in terms of the excitation width of a bump. Using the theory of monotone operators in ordered Banach spaces we justify convergence of both iteration schemes.

  • 304.
    Olofsson, Rikard
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Large Newforms of the Quantized Cat Map Revisited2010In: Annales de l'Institute Henri Poincare. Physique theorique, ISSN 1424-0637, E-ISSN 1424-0661, Vol. 11, no 7, p. 1285-1302Article in journal (Refereed)
    Abstract [en]

    We study the eigenfunctions of the quantized cat map, desymmetrized by Hecke operators. In the papers (Olofsson in Ann Henri Poincar, 10(6):1111-1139, 2009; Math Phys 286(3):1051-1072, 2009) it was observed that when the inverse of Planck's constant is a prime exponent N = p (n) , with n > 2, half of these eigenfunctions become large at some points, and half remains small for all points. In this paper we study the large eigenfunctions more carefully. In particular, we answer the question of for which q the L (q) norms remain bounded as N goes to infinity. The answer is q a parts per thousand currency sign 4.

  • 305.
    Olofsson, Rikard
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Properties of the Beurling generalized primes2011In: Journal of Number Theory, ISSN 0022-314X, E-ISSN 1096-1658, Vol. 131, no 1, p. 45-58Article in journal (Refereed)
    Abstract [en]

    Text. In this paper, we prove a generalization of Mertens' theorem to Beurling primes, namely that lim(x ->infinity) 1/Inx Pi(p <= x)(1 - p(-1))(-1) = Ae(gamma), where gamma is Euler's constant and Ax is the asymptotic number of generalized integers less than x. Thus the limit M = lim(x ->infinity) (Sigma(p <= x) p(-1) - In(Inx)) exists. We also show that this limit coincides with lim(alpha -> 0+)(Sigma(p) p(-1)(In p)(-alpha) - 1/alpha); for ordinary primes this claim is called Meissel's theorem. Finally, we will discuss a problem posed by Beurling, namely how small vertical bar N(x)-[4]vertical bar can be made for a Beurling prime number system Q not equal P. where P is the rational primes. We prove that for each c > 0 there exists a Q such that vertical bar N(x) - [x]vertical bar < cInx and conjecture that this is the best possible bound. Video. For a video summary of this paper, please click here or visit http://www.youtube.com/watch?v=Kw3iNo3fAbk/. (C) 2010 Elsevier Inc. All rights reserved.

  • 306.
    Perna, Andrea
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Granovskiy, Boris
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Garnier, Simon
    Nicolis, Stamatios C.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Labédan, Marjorie
    Theraulaz, Guy
    Fourcassié, Vincent
    Sumpter, David J. T.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Individual Rules for Trail Pattern Formation in Argentine Ants (Linepithema humile)2012In: PloS Computational Biology, ISSN 1553-734X, E-ISSN 1553-7358, Vol. 8, no 7, p. e1002592-Article in journal (Refereed)
    Abstract [en]

    Many ant species produce large dendritic networks of trails around their nest. These networks result from self-organized feedback mechanisms: ants leave small amounts of a chemical -a pheromone- as they move across space. In turn, they are attracted by this same pheromone so that eventually a trail is formed. In our study, we introduce a new image analysis technique to estimate the concentrations of pheromone directly on the trails. In this way, we can characterise the ingredients of the feedback loop that ultimately leads to the formation of trails. We show that the response to pheromone concentrations is linear: an ant will turn to the left with frequency proportional to the difference between the pheromone concentrations on its left and right sides. Such a linear individual response was rejected by previous literature, as it would be incompatible with the results of a large number of experiments: trails can only be reinforced if the ants have a disproportionally higher probability to select the trail with higher pheromone concentration. However, we show that the required non-linearity does not reside in the perceptual response of the ants, but in the noise associated with their movement.

  • 307.
    Perna, Andrea
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Kuntz, Pascale
    Douady, Stephane
    Characterization of spatial networklike patterns from junction geometry2011In: Physical Review E, ISSN 1539-3755, Vol. 83, no 6, p. 066106-Article in journal (Refereed)
    Abstract [en]

    We propose a method for quantitative characterization of spatial networklike patterns with loops, such as surface fracture patterns, leaf vein networks, and patterns of urban streets. Such patterns are not well characterized by purely topological estimators: also patterns that both look different and result from different morphogenetic processes can have similar topology. A local geometric cue-the angles formed by the different branches at junctions-can complement topological information and allow the quantification of the large scale spatial coherence of the pattern. For patterns that grow over time, such as fracture lines on the surface of ceramics, the rank assigned by our method to each individual segment of the pattern approximates the order of appearance of that segment. We apply the method to various networklike patterns and find a continuous but sharp dichotomy between two classes of spatial networks: hierarchical and homogeneous. The former class results from a sequential growth process and presents large scale organization, and the latter presents local, but not global, organization.

  • 308.
    Persson, Jonas
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Eriksson, Jonatan
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Pricing turbo warrants2006Report (Other academic)
  • 309.
    Persson Mattsson, Pär
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Inverse Quantum Problem2011Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
  • 310.
    Petersson, Niclas
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Asymptotic properties of a rank estimate in heteroscedastic linear regression2008Report (Other academic)
  • 311.
    Pour Abdollah Farshchi, Elham
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Option Pricing with Extreme Events2011Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
  • 312.
    Pöder, Sebastian
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Morse homology of RPn2013Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
  • 313. Reid, Chris R.
    et al.
    Sumpter, David J. T.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Beekman, Madeleine
    Optimisation in a natural system: Argentine ants solve the Towers of Hanoi2011In: Journal of Experimental Biology, ISSN 0022-0949, E-ISSN 1477-9145, Vol. 214, no 1, p. 50-58Article in journal (Refereed)
    Abstract [en]

    Natural systems are a source of inspiration for computer algorithms designed to solve optimisation problems. Yet most 'nature-inspired' algorithms take only superficial inspiration from biology, and little is known about how real biological systems solve difficult problems. Moreover, ant algorithms, neural networks and similar methods are usually applied to static problems, whereas most biological systems have evolved to perform under dynamically changing conditions. We used the Towers of Hanoi puzzle to test whether Argentine ants can solve a potentially difficult optimisation problem. We also tested whether the ants can adapt to dynamic changes in the problem. We mapped all possible solutions to the Towers of Hanoi on a single graph and converted this into a maze for the ants to solve. We show that the ants are capable of solving the Towers of Hanoi, and are able to adapt when sections of the maze are blocked off and new sections installed. The presence of exploration pheromone increased the efficiency of the resulting network and increased the ants' ability to adapt to changing conditions. Contrary to previous studies, our study shows that mass-recruiting ant species such as the Argentine ant can forage effectively in a dynamic environment. Our results also suggest that novel optimisation algorithms can benefit from stronger biological mimicry.

  • 314.
    Rodriguez-Lopez, Salvador
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Staubach, Wolfgang
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Estimates for rough Fourier integral and pseudodifferential operators and applications to the boundedness of multilinear operators2013In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 264, no 10, p. 2356-2385Article in journal (Refereed)
    Abstract [en]

    We study the boundedness of rough Fourier integral and pseudodifferential operators, defined by general rough Hörmander class amplitudes, on Banach and quasi-Banach LpLp spaces. Thereafter we apply the aforementioned boundedness in order to improve on some of the existing boundedness results for Hörmander class bilinear pseudodifferential operators and certain classes of bilinear (as well as multilinear) Fourier integral operators. For these classes of amplitudes, the boundedness of the aforementioned Fourier integral operators turn out to be sharp. Furthermore we also obtain results for rough multilinear operators.

  • 315.
    Sheng, Gong
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Filtered historical simulation and option pricing2011Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
  • 316.
    Stepanov, Vladimir D.
    et al.
    Moskva.
    Ushakova, Elena
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Kernel Operators with Variable Intervals of Integration in Lebesgue Spaces and Applications2008Report (Other academic)
  • 317.
    Stepanov, Vladimir D.
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Ushakova, Elena P.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Kernel operators with variable intervals of integration in Lebesgue spaces and applications2010In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 13, no 3, p. 449-510Article in journal (Refereed)
    Abstract [en]

    New criteria of L-p - L-q boundedness of Hardy-Steklov type operator (1.1) with both increasing on (0, infinity) boundary functions a(x) and b(x) are obtained for 1 < p <= q < infinity and 0 < q < p < infinity, p > 1. This result is applied for two-weighted L-p - L-q characterization of the corresponding geometric Steklov operator (1.3) and other related problems.

  • 318.
    Strömbergsson, Andreas
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    On the limit distribution of Frobenius numbers2012In: Acta Arithmetica, ISSN 0065-1036, E-ISSN 1730-6264, Vol. 152, no 1, p. 81-107Article in journal (Refereed)
  • 319.
    Strömbergsson, Andreas
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    On the probability of a random lattice avoiding a large convex set2011In: Proceedings of the London Mathematical Society, ISSN 0024-6115, E-ISSN 1460-244X, Vol. 103, no 6, p. 950-1006Article in journal (Refereed)
    Abstract [en]

    Given a set ℭ ⊂ ℝd, let p(ℭ) be the probability that a random d-dimensional unimodular lattice, chosen according to Haar measure on SL(d, ℤ)\ SL(d, ℝ), is disjoint from ℭ \ {0}. For special convex sets ℭ we prove bounds on p(ℭ) that are sharp up to a scaling of ℭ by a constant. We also prove bounds on a variant of p(ℭ) where the probability is conditioned on the random lattice containing a fixed given point p0. Our bounds have applications, among other things, to the asymptotic properties of the collision kernel of the periodic Lorentz gas in the Boltzmann–Grad limit, in arbitrary dimension d.

  • 320.
    Strömbergsson, Andreas
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Marklof, Jens
    University of Bristol.
    The periodic Lorentz gas in the Boltzmann-Grad limit: asymptotic estimates2011In: Geometric and Functional Analysis, ISSN 1016-443X, E-ISSN 1420-8970, Vol. 21, no 3, p. 560-647Article in journal (Refereed)
    Abstract [en]

    The dynamics of a point particle in a periodic array of spherical scatterers converges, in the limit of small scatterer size, to a random flight process, whose paths are piecewise linear curves generated by a Markov process with memory two. The corresponding transport equation is distinctly different from the linear Boltzmann equation observed in the case of a random configuration of scatterers. In the present paper we provide asymptotic estimates for the transition probabilities of this Markov process. Our results in particular sharpen previous upper and lower bounds on the distribution of free path lengths obtained by Bourgain, Golse and Wennberg.

  • 321.
    Strömbom, Daniel
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Collective motion from local attraction2011In: Journal of Theoretical Biology, ISSN 0022-5193, E-ISSN 1095-8541, Vol. 283, no 1, p. 145-151Article in journal (Refereed)
    Abstract [en]

    Many animal groups, for example schools of fish or flocks of birds, exhibit complex dynamic patterns while moving cohesively in the same direction. These flocking patterns have been studied using self-propelled particle models, most of which assume that collective motion arises from individuals aligning with their neighbours. Here, we propose a self-propelled particle model in which the only social force between individuals is attraction. We show that this model generates three different phases: swarms, undirected mills and moving aligned groups. By studying our model in the zero noise limit, we show how these phases depend on the relative strength of attraction and individual inertia. Moreover, by restricting the field of vision of the individuals and increasing the degree of noise in the system, we find that the groups generate both directed mills and three dynamically moving, 'rotating chain' structures. A rich diversity of patterns is generated by social attraction alone, which may provide insight into the dynamics of natural flocks.

  • 322.
    Sumpter, David
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Q & A2012In: Current Biology, ISSN 0960-9822, E-ISSN 1879-0445, Vol. 22, no 17, p. R666-R667Article in journal (Other academic)
  • 323.
    Sumpter, David
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Buhl, Jerome
    Biro, Dora
    Couzin, Iain
    Information transfer in moving animal groups2008In: Theory in biosciences, ISSN 1431-7613, E-ISSN 1611-7530, Vol. 127, no 2, p. 177-186Article in journal (Refereed)
    Abstract [en]

    Moving animal groups provide some of the most intriguing and difficult to characterise examples of collective behaviour. We review some recent (and not so recent) empirical research on the motion of animal groups, including fish, locusts and homing pigeons. An important concept which unifies our understanding of these groups is that of transfer of directional information. Individuals which change their direction of travel in response to the direction taken by their near neighbours can quickly transfer information about the presence of a predatory threat or food source. We show that such information transfer is optimised when the density of individuals in a group is close to that at which a phase transition occurs between random and ordered motion. Similarly, we show that even relatively small differences in information possessed by group members can lead to strong collective-level decisions for one of two options. By combining the use of self-propelled particle and social force models of collective motion with thinking about the evolution of flocking we aim to better understand how complexity arises within these groups.

  • 324.
    Sumpter, David J. T.
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Mann, Richard P.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Perna, Andrea
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    The modelling cycle for collective animal behaviour2012In: INTERFACE FOCUS, ISSN 2042-8898, Vol. 2, no 6, p. 764-773Article, review/survey (Refereed)
    Abstract [en]

    Collective animal behaviour is the study of how interactions between individuals produce group level patterns, and why these interactions have evolved. This study has proved itself uniquely interdisciplinary, involving physicists, mathematicians, engineers as well as biologists. Almost all experimental work in this area is related directly or indirectly to mathematical models, with regular movement back and forth between models, experimental data and statistical fitting. In this paper, we describe how the modelling cycle works in the study of collective animal behaviour. We classify studies as addressing questions at different levels or linking different levels, i.e. as local, local to global, global to local or global. We also describe three distinct approaches-theory-driven, data-driven and model selection-to these questions. We show, with reference to our own research on species across different taxa, how we move between these different levels of description and how these various approaches can be applied to link levels together.

  • 325.
    Södergren, Anders
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    On the distribution of angles between the N shortest vectors in a random lattice2011In: Journal of the London Mathematical Society, ISSN 0024-6107, E-ISSN 1469-7750, Vol. 84, no 3, p. 749-764Article in journal (Refereed)
    Abstract [en]

    We determine the joint distribution of the lengths of, and angles between, the N shortest lattice vectors in a random n-dimensional lattice as n→∞. Moreover, we interpret the result in terms of eigenvalues and eigenfunctions of the Laplacian on flat tori. Finally, we discuss the limit distribution of any finite number of successive minima of a random n-dimensional lattice as n→∞.

  • 326.
    Södergren, Anders
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    On the Poisson distribution of lengths of lattice vectors in a random lattice2011In: Mathematische Zeitschrift, ISSN 0025-5874, E-ISSN 1432-1823, Vol. 269, no 3-4, p. 945-954Article in journal (Refereed)
    Abstract [en]

    We prove that the volumes determined by the lengths of the non-zero vectors +/- x in a random lattice L of covolume 1 define a stochastic process that, as the dimension n tends to infinity, converges weakly to a Poisson process on the positive real line with intensity 1/2. This generalizes earlier results by Rogers (Proc Lond Math Soc (3) 6:305-320, 1956, Thm. 3) and Schmidt (Acta Math 102: 159-224, 1959, Satz 10).

  • 327.
    Södergren, Anders
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    On the uniform equidistribution of closed horospheres in hyperbolic manifolds2012In: Proceedings of the London Mathematical Society, ISSN 0024-6115, E-ISSN 1460-244X, Vol. 105, p. 225-280Article in journal (Refereed)
    Abstract [en]

    We prove asymptotic equidistribution results for pieces of large closed horospheres in cofinite hyperbolic manifolds of arbitrary dimension. This extends earlier results by Hejhal ['On the uniform equidistribution of long closed horocycles', Loo-Keng Hua: a great mathematician of the twentieth century, Asian J. Math. 4 (2000) 839-853] and Strombergsson ['On the uniform equidistribution of long closed horocycles', Duke Math. J. 123 (2004) 507-547] in dimension 2. Our proofs use spectral methods, and lead to precise estimates on the rate of convergence to equidistribution.

  • 328.
    Södergren, Anders
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    On the value distribution and moments of the Epstein zeta function to the right of the critical strip2011In: Journal of Number Theory, ISSN 0022-314X, E-ISSN 1096-1658, Vol. 131, no 7, p. 1176-1208Article in journal (Refereed)
    Abstract [en]

    We study the Epstein zeta function E-n(L, S) for s > n/2 and a random lattice L of large dimension n. For any fixed c > 1/2 we determine the value distribution and moments of E-n(., cn) (suitably normalized) as n -> infinity. We further discuss the random function C -> E-n(., cn) for c is an element of [A, B] with 1/2 < A < B and determine its limit distribution as n -> infinity.

  • 329.
    Södergren, Anders
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    On The Value Distribution Of The Epstein Zeta Function In The Critical Strip2013In: Duke mathematical journal, ISSN 0012-7094, E-ISSN 1547-7398, Vol. 162, no 1, p. 1-48Article in journal (Refereed)
    Abstract [en]

    We study the value distribution of the Epstein zeta function E-n (L, s) for 0 <s < n/2 and a random lattice L of large dimension n. For any fixed c is an element of (1/4, 1/2) and n -> infinity, we prove that the random variable V-n(-2c) E-n(.,cn) has a limit distribution, which we give explicitly (here V-n is the volume of the n-dimensional unit ball). More generally, for any fixed epsilon > 0, we determine the limit distribution of the random function c bar right arrow V-n(-2c) E-n(., cn), c epsilon [1/4 + epsilon, 1/2 - epsilon]. After compensating for the pole at c = 1/2, we even obtain a limit result on the whole interval [1/4 + epsilon, 1/2], and as a special case we deduce the following strengthening of a result by Sarnak and Strombergsson concerning the height function h(n) (L) of the flat torus R-n/L: the random variable n{h(n) (L) - (log(4 pi) - gamma + 1)} + log n has a limit distribution as n -> infinity, which we give explicitly. Finally, we discuss a question posed by Sarnak and Strombergsson as to whether there exists a lattice L subset of R-n for which E-n(L, s) has no zeros in (0, infinity).

  • 330.
    Tayibov, Khayyam
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Pricing options on defaultable stocks2012Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
  • 331.
    Tucker, Warwick
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Computer-Aided Proofs via Interval Analysis2015In: The Princeton Companion to Applied Mathematics / [ed] Nicholas J. Higham, Princeton University Press, 2015, p. 790-795Chapter in book (Refereed)
  • 332.
    Tucker, Warwick
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Interval Analysis2015In: The Princeton Companion to Applied Mathematics / [ed] Nicholas J. Higham, Princeton University Press, 2015, p. 105-106Chapter in book (Refereed)
  • 333.
    Tucker, Warwick
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Interval Methods2015In: Uncertainty in Biology: A Computational Modeling Approach / [ed] Liesbet Geris and David Gomez-Cabrero, Springer Publishing Company, 2015, p. 99-211Chapter in book (Refereed)
  • 334.
    Tucker, Warwick
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Validated numerics: A Short Introduction to Rigorous Computations2011Book (Refereed)
  • 335.
    Vannestål, Martin
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Optimal stopping and the American put under incomplete information2011Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
  • 336.
    von Würtemberg, Ina
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Ill-posed problems and their applications to climate research2011Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
  • 337.
    Wang, Bing
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Wang, Ling
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
     Pricing Barrier Options using Monte Carlo Methods2011Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
  • 338.
    Wang, Ning
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Price sensitivity to the exponent in the CEV model2012Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
  • 339.
    Wang, Yan
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Finding the Value at Risk for Credit Default Swaps2012Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
  • 340.
    Ward, Ashley
    et al.
    School of Biological Sciences, University of Sydney.
    Herbert-Read, James
    Jordan, Lyndon
    BEES, UNSW.
    James, Richard
    Krause, Jens
    Ma, Qi
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Rubenstein, Daniel
    Sumpter, David
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Morrell, Lesley
    Initiators, leaders and recruitment mechanisms in the collective movements of damselfish2013In: American Naturalist, ISSN 0003-0147, E-ISSN 1537-5323, Vol. 181, no 6, p. 748-760Article in journal (Refereed)
    Abstract [en]

    Explaining how individual behavior and social interactions give rise to group-level outcomes and affect issues such as leadership is fundamental to the understanding of collective behavior. Here we examined individual and collective behavioral dynamics in groups of humbug damselfish both before and during a collective movement. During the predeparture phase, group activity increased until the collective movement occurred. Although such movements were precipitated by one individual, the success or failure of any attempt to instigate a collective movement was not solely dependent on this initiator’s behavior but on the behavior of the group as a whole. Specifically, groups were more active and less cohesive before a successful initiation attempt than before a failed attempt. Individuals who made the most attempts to initiate a collective movement during each trial were ultimately most likely to lead the collective movement. Leadership was not related to dominance but was consistent between trials. The probability of fish recruiting to a group movement initiative was an approximately linear function of the number of fish already recruited. Overall, these results are consistent with nonselective local mimetism, with the decision to leave based on a group’s, rather than any particular individual’s, readiness to leave.

  • 341. Ward, Ashley J. W.
    et al.
    Herbert-Read, James E.
    Sumpter, David J. T.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Krause, Jens
    Fast and accurate decisions through collective vigilance in fish shoals2011In: Proceedings of the National Academy of Sciences of the United States of America, ISSN 0027-8424, E-ISSN 1091-6490, Vol. 108, no 6, p. 2312-2315Article in journal (Refereed)
    Abstract [en]

    Although it has been suggested that large animal groups should make better decisions than smaller groups, there are few empirical demonstrations of this phenomenon and still fewer explanations of the how these improvements may be made. Here we show that both speed and accuracy of decision making increase with group size in fish shoals under predation threat. We examined two plausible mechanisms for this improvement: first, that groups are guided by a small proportion of high-quality decision makers and, second, that group members use self-organized division of vigilance. Repeated testing of individuals showed no evidence of different decision-making abilities between individual fish. Instead, we suggest that shoals achieve greater decision-making efficiencies through division of labor combined with social information transfer. Our results should prompt reconsideration of how we view cooperation in animal groups with fluid membership.

  • 342. Ward, Ashley J. W.
    et al.
    Krause, Jens
    Sumpter, David J. T.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Quorum Decision-Making in Foraging Fish Shoals2012In: PLoS ONE, ISSN 1932-6203, E-ISSN 1932-6203, Vol. 7, no 3, p. e32411-Article in journal (Refereed)
    Abstract [en]

    Quorum responses provide a means for group-living animals to integrate and filter disparate social information to produce accurate and coherent group decisions. A quorum response may be defined as a steep increase in the probability of group members performing a given behaviour once a threshold minimum number of their group mates already performing that behaviour is exceeded. In a previous study we reported the use of a quorum response in group decision-making of threespine sticklebacks (Gasterosteus aculeatus) under a simulated predation threat. Here we examine the use of quorum responses by shoals of sticklebacks in first locating and then leaving a foraging patch. We show that a quorum rule explains movement decisions by threespine sticklebacks toward and then away from a food patch. Following both to and from a food patch occurred when a threshold number of initiators was exceeded, with the threshold being determined by the group size.

  • 343.
    Xin, Mao
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    The VIX Volatility Index2011Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
  • 344.
    Xue, Jiang
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Pricing Callable Bonds2011Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
  • 345.
    Ye, Hui
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    A Comparison of Local Volatility and Implied Volatility2011Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
  • 346.
    Yuan, Huang
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Calculation of Expected Shortfall via Filtered Historical Simulation2011Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
  • 347.
    Zhang, Nan
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Properties of the SABR model2011Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
  • 348.
    Zhou, Long
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Irregularly-Spaced Financial High-Frequency Data Simulation Using Multi-Dimensional Hawkes Processes: Estimation, Prediction And Corresponding Trading Strategy2012Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
4567 301 - 348 of 348
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