DSpace Community:http://hdl.handle.net/2381/4452019-07-23T00:57:58Z2019-07-23T00:57:58ZDynamical Systems, Cocycles and Cohomology of Action GroupoidsAl-Bayati, Mudheher A. H.http://hdl.handle.net/2381/448452019-07-16T02:09:21Z2019-07-15T10:18:55ZTitle: Dynamical Systems, Cocycles and Cohomology of Action Groupoids
Authors: Al-Bayati, Mudheher A. H.
Abstract: In this thesis, we study general cocycles of dynamical systems in topological, measurable and smooth (differentiable) settings. Dynamical systems are viewed here as given by actions of a discrete, topological, measurable or Lie group on a set, topological space, measurable space or smooth manifold respectively depending on the given geometrical setting to be considered. We will mostly concentrate on the topological and smooth settings in this thesis, but will comment about the necessary alterations in the discrete and measurable setting. Cocycles are functions on the Cartesian product of the spaces and groups involved with values in an abelian group depending again on the given geometrical settings. A main task of this thesis is to interpret these cocycles as general cohomology classes of certain action groupoids, which decode the dynamical system. Similarly, we show that cohomology classes of action groupoids associated to dynamical systems can be viewed as cocycles. The action groupoids which arise out of the dynamical systems and the given geometrical setting are discrete groupoids, topological groupoids, measurable groupoids or Lie groupoids. We will introduce a very general groupoid cohomology and homology theory with values in vector bundles and discuss its basic properties generalising group cohomology and singular cohomology. Furthermore, we will study extensions of dynamical systems via cocycles and interpret these as low-dimensional cohomology classes. Some low-dimensional homology and cohomology groups are calculated. Finally, we interpret cocycle cohomology classes as cohomological obstructions for extending dynamical systems following a suggestion by Tao.2019-07-15T10:18:55ZConsistent Preference Similarity Network Clustering and Influence Based Consensus Group Decision MakingKamis, Nor H.http://hdl.handle.net/2381/447902019-07-11T02:09:02Z2019-07-10T09:19:57ZTitle: Consistent Preference Similarity Network Clustering and Influence Based Consensus Group Decision Making
Authors: Kamis, Nor H.
Abstract: In this thesis, we introduce a novel consensus-based group decision making (CGDM) model by integrating the notions of Social Network Analysis (SNA), clustering and Social Influence Network (SIN). Four main contributions are presented in order to handle a number of issues in CGDM. In dealing with the issue of the consistency of preferences, we introduce a consistency operator and construct a consistency control module for the purpose of securing the correctness of expert preferences. The proposed work guarantees a sufficient preference consistency level for each expert. In the case of inconsistent experts, only minimum changes of preferences are required for them to be consistent, depending on their personal level of inconsistency.
The second area of interest focuses on consensus modeling. We develop a novel consensus model by firstly defining the preference similarity network based on the structural equivalence concept. Structurally equivalent experts are partitioned into clusters, thus intra-clusters’ experts are high in density and inter-clusters’ experts are rich in sparsity. A measure of consensus is defined and the consensus degree of a group of experts obtained reflects the overall agreed solution.
A feedback mechanism is presented in dealing with insufficient consensus. We introduce the influence-based feedback system by incorporating the influence score measure in nominating a network leader. Our proposed procedure positively influenced the experts with low consensus contribution to change their preferences closer to each other, by following recommendations from a network influencer. This work guarantees a sufficient consensus level with better clustering solution.
Lastly, a procedure of aggregating preferences is laid out whereby the influence function is used in defining a new fusion operator, which helps to aggregate all individual expert preferences into a collective one. This is necessary to ensure that all the properties contained in all the individual preferences are summarized and appropriately taken into considerations.2019-07-10T09:19:57ZContravariant form on tensor product of highest weight modulesMudrov, Andrey I.http://hdl.handle.net/2381/447722019-07-10T02:08:48Z2019-07-09T14:25:21ZTitle: Contravariant form on tensor product of highest weight modules
Authors: Mudrov, Andrey I.
Abstract: We give a criterion for complete reducibility of tensor product V ⊗ Z of two irreducible highest weight modules V and Z over a classical or quantum semi-simple group in terms of a contravariant symmetric bilinear form on V ⊗ Z. This form is the product of the canonical contravariant forms on V and Z. Then V ⊗ Z is completely reducible if and only if the form is non-degenerate when restricted to the sum of all highest weight submodules in V ⊗ Z or equivalently to the span of singular vectors.
Description: 2010 Mathematics Subject Classification: 17B10; 17B372019-07-09T14:25:21ZThe Two-Faced God Janus or What Does n-Hausdorfness Have to Do With Dynamics and Topology?Staynova, Petra G.http://hdl.handle.net/2381/447672019-07-10T02:09:07Z2019-07-09T13:20:46ZTitle: The Two-Faced God Janus or What Does n-Hausdorfness Have to Do With Dynamics and Topology?
Authors: Staynova, Petra G.
Abstract: This thesis is centered around the study of topological dynamics and analytic topology, as well as an unexpected intersection between the two, which revolves around the notion of an n-Hausdorff space. In the Dynamics part of this thesis, we discuss the author's two main results in topological dynamics. The first is about the Ellis semigroup of substitution systems, which extends previous results in this area. It states that the Ellis semigroup of a certain type of constant-length substitution dynamical systems has two minimal ideals, and further calculates the number of idempotents in these ideals. This requires a novel approach towards considering the factor maps to the maximal equicontinuous factor of these dynamical systems - a reworking of an old theorem which takes up a chapter in the thesis. The second result is about the Furstenberg topology of a point-distal dynamical system. Since the constantlength substitution systems we had considered in the previous sections are also point-distal, it can be considered a rather general result. It shows that if a pointdistal system is an almost k-to-1 extension of its maximal equicontinuous factor, the Furstenberg topology restricted to a (in some sense canonical) subspace is at most k + 1-Hausdorff. In the Analytic Topology part of the thesis, we discuss the n-Hausdorff property in its original context, as a natural part of a series of combinatorial generalisations of separation axioms. These combinatorial generalisations were introduced by several authors throughout the past 20 years. However, n-Hausdorfness in particular is interesting in light of a couple of still-open questions of Arhangelskii. The more easily stateable of the two is whether the cardinality of a T1 first countable Lindel of space exceeds continuum. The main work of the author in this part involves the many examples of spaces which satisfy a combinatorial separation axiom and also have (or lack) various other properties, such as being Lindel of, first countable, compact, or being T1. The author has contributed towards the proofs of the theorems given in this part.2019-07-09T13:20:46ZThe "Lévy or diffusion" Controversy: How important is the movement pattern in the context of trapping?Ahmed, Danish A.Petrovskii, Sergei V.Tilles, Paulo F. C.http://hdl.handle.net/2381/447062019-07-04T02:08:35Z2019-07-03T16:09:14ZTitle: The "Lévy or diffusion" Controversy: How important is the movement pattern in the context of trapping?
Authors: Ahmed, Danish A.; Petrovskii, Sergei V.; Tilles, Paulo F. C.
Abstract: Many empirical and theoretical studies indicate that Brownian motion and diffusion models as its mean field counterpart provide appropriate modeling techniques for individual insect movement. However, this traditional approach has been challenged, and conflicting evidence suggests that an alternative movement pattern such as Lévy walks can provide a better description. Lévy walks differ from Brownian motion since they allow for a higher frequency of large steps, resulting in a faster movement. Identification of the 'correct' movement model that would consistently provide the best fit for movement data is challenging and has become a highly controversial issue. In this paper, we show that this controversy may be superficial rather than real if the issue is considered in the context of trapping or, more generally, survival probabilities. In particular, we show that almost identical trap counts are reproduced for inherently different movement models (such as the Brownian motion and the Lévy walk) under certain conditions of equivalence. This apparently suggests that the whole 'Levy or diffusion' debate is rather senseless unless it is placed into a specific ecological context, e.g., pest monitoring programs.2019-07-03T16:09:14ZProgress in Mathematical EcologyPetrovskiy, Sergeihttp://hdl.handle.net/2381/447052019-07-04T02:08:37Z2019-07-03T16:05:54ZTitle: Progress in Mathematical Ecology
Authors: Petrovskiy, Sergei
Abstract: Mathematical modelling plays a special role in ecology. Although traditional ecology is a largely empirical science, replicated experiments are not often possible because of the high complexity of ecological interactions and the impossibility to reproduce the weather conditions. Moreover, large-scale field experiments (where the consequences are usually not fully known) can be damaging for the ecological communities and costly or even dangerous for humans. Mathematical modelling provides an efficient supplement and sometimes even a substitute to an empirical study; it creates a virtual laboratory where different hypotheses can be tested safely, and at relatively low cost2019-07-03T16:05:54ZRadial Basis Function Solution for the LIBOR Market Model PDELalami, S. Z. RezaeiLevesley, JeremySajjad, Muhammad F.http://hdl.handle.net/2381/446292019-06-28T02:09:18Z2019-06-27T13:43:30ZTitle: Radial Basis Function Solution for the LIBOR Market Model PDE
Authors: Lalami, S. Z. Rezaei; Levesley, Jeremy; Sajjad, Muhammad F.
Abstract: This research paper is intended at analyzing the interpolation of
LIBOR (London Inter Bank Offer Rate) Model PDE (Partial Differential
Equation) in one and two dimensions using Radial Basis Functions (RBF)
on full grids. The LIBOR Market model is considered an effective and
standard approach for pricing the derivatives which is based on interest
rates. In recent times, Monte Carlo methods are often used in practice
to price derivatives instruments because of the high dimensionality of the
model. This research paper highlights the applicability of the RBF method
rather than Finite Difference Method (FDM) for solving the LMM PDE,
LIBOR Market Model, with the Bermudan Swaption or Chooser Option
as a boundary condition. The results have suggested faster convergence
to reference value than FDM in one dimension. Also, the calculation of
price is similar to FDM in two dimension.
Description: The file associated with this record is under a permanent embargo in accordance with the publisher's policy. The full text may be available through the publisher links provided above.2019-06-27T13:43:30ZManifold-like matchbox manifoldsClark, AlexHurder, StevenLukina, Olgahttp://hdl.handle.net/2381/446222019-06-27T02:09:03Z2019-06-26T11:24:46ZTitle: Manifold-like matchbox manifolds
Authors: Clark, Alex; Hurder, Steven; Lukina, Olga
Abstract: A matchbox manifold is a generalized lamination, which is a continuum whose arc-components define the leaves of a foliation of the space. The main result of this paper implies that a matchbox manifold which is manifold-like must be homeomorphic to a weak solenoid.
Description: MSC (2010): Primary 57N25, 37B45; Secondary 54F152019-06-26T11:24:46ZOn sign-coherence of c-vectorsTreffinger, Hipolitohttp://hdl.handle.net/2381/446012019-06-26T02:08:46Z2019-06-25T12:37:47ZTitle: On sign-coherence of c-vectors
Authors: Treffinger, Hipolito
Abstract: Given a finite dimensional algebra A over an algebraically closed field, we consider the c-vectors such as defined by Fu in [18] and we give a new proof of its sign-coherence. Moreover, we characterise the modules whose dimension vectors are c-vectors as bricks respecting a functorially finiteness condition.2019-06-25T12:37:47ZSingle-cell trajectories reconstruction, exploration and mapping of omics data with STREAM.Chen, HAlbergante, LHsu, JYLareau, CALo Bosco, GGuan, JZhou, SGorban, ANBauer, DEAryee, MJLangenau, DMZinovyev, ABuenrostro, JDYuan, G-CPinello, Lhttp://hdl.handle.net/2381/445692019-06-25T02:09:12Z2019-06-24T10:54:07ZTitle: Single-cell trajectories reconstruction, exploration and mapping of omics data with STREAM.
Authors: Chen, H; Albergante, L; Hsu, JY; Lareau, CA; Lo Bosco, G; Guan, J; Zhou, S; Gorban, AN; Bauer, DE; Aryee, MJ; Langenau, DM; Zinovyev, A; Buenrostro, JD; Yuan, G-C; Pinello, L
Abstract: Single-cell transcriptomic assays have enabled the de novo reconstruction of lineage differentiation trajectories, along with the characterization of cellular heterogeneity and state transitions. Several methods have been developed for reconstructing developmental trajectories from single-cell transcriptomic data, but efforts on analyzing single-cell epigenomic data and on trajectory visualization remain limited. Here we present STREAM, an interactive pipeline capable of disentangling and visualizing complex branching trajectories from both single-cell transcriptomic and epigenomic data. We have tested STREAM on several synthetic and real datasets generated with different single-cell technologies. We further demonstrate its utility for understanding myoblast differentiation and disentangling known heterogeneity in hematopoiesis for different organisms. STREAM is an open-source software package.
Description: The authors declare that the data supporting the findings of this study are available within the paper and its supplementary information files (Supplementary Data 1 and 2). STREAM is available as a user-friendly open-source software and can be used interactively as a web-application at http://stream.pinellolab.org (Supplementary Fig. 11, Supplementary Note 4), a bioconda package ‘stream’ for step-by-step analysis https://bioconda.github.io/recipes/stream/README.html (Supplementary Note 5), or as a standalone command-line tool: https://github.com/pinellolab/STREAM (Supplementary Note 6). All the analyses presented in this manuscript can be reproduced using the bioconda package and the provided Jupyter notebooks in Supplementary Data 1 and 2.2019-06-24T10:54:07ZTowards the Construction of a Mathematically Rigorous Framework for the Modelling of Evolutionary Fitness.Kuzenkov, OlegMorozov, Andrewhttp://hdl.handle.net/2381/445612019-06-25T02:09:10Z2019-06-24T10:28:40ZTitle: Towards the Construction of a Mathematically Rigorous Framework for the Modelling of Evolutionary Fitness.
Authors: Kuzenkov, Oleg; Morozov, Andrew
Abstract: Modelling of natural selection in self-replicating systems has been heavily influenced by the concept of fitness which was inspired by Darwin's original idea of the survival of the fittest. However, so far the concept of fitness in evolutionary modelling is still somewhat vague, intuitive and often subjective. Unfortunately, as a result of this, using different definitions of fitness can lead to conflicting evolutionary outcomes. Here we formalise the definition of evolutionary fitness to describe the selection of strategies in deterministic self-replicating systems for generic modelling settings which involve an arbitrary function space of inherited strategies. Our mathematically rigorous definition of fitness is closely related to the underlying population dynamic equations which govern the selection processes. More precisely, fitness is defined based on the concept of the ranking of competing strategies which compares the long-term dynamics of measures of sets of inherited units in the space of strategies. We also formulate the variational principle of modelling selection which states that in a self-replicating system with inheritance, selection will eventually maximise evolutionary fitness. We demonstrate how expressions for evolutionary fitness can be derived for a class of models with age structuring including systems with delay, which has previously been considered as a challenge.2019-06-24T10:28:40ZSteady oscillations in aggregation-fragmentation processesBrilliantov, NVOtieno, WMatveev, SASmirnov, APTyrtyshnikov, EEKrapivsky, PLhttp://hdl.handle.net/2381/444162019-06-15T02:08:48Z2019-06-14T13:10:09ZTitle: Steady oscillations in aggregation-fragmentation processes
Authors: Brilliantov, NV; Otieno, W; Matveev, SA; Smirnov, AP; Tyrtyshnikov, EE; Krapivsky, PL
Abstract: We report surprising steady oscillations in aggregation-fragmentation processes. Oscillating solutions are
observed for the class of aggregation kernels Ki,j = iν jμ + j ν iμ homogeneous in masses i and j of merging
clusters and fragmentation kernels, Fij = λKij , with parameter λ quantifying the intensity of the disruptive
impacts. We assume a complete decomposition (shattering) of colliding partners into monomers. We show that
an assumption of a steady-state distribution of cluster sizes, compatible with governing equations, yields a
power law with an exponential cutoff. This prediction agrees with simulation results when θ ≡ ν − μ < 1. For
θ = ν − μ > 1, however, the densities exhibit an oscillatory behavior. While these oscillations decay for not very
small λ, they become steady if θ is close to 2 and λ is very small. Simulation results lead to a conjecture that for
θ < 1 the system has a stable fixed point, corresponding to the steady-state density distribution, while for any
θ > 1 there exists a critical value λc, such that for λ<λc, the system has an attracting limit cycle. This is rather
striking for a closed system of Smoluchowski-like equations, lacking any sinks and sources of mass.2019-06-14T13:10:09ZFree and Bound States of Ions in Ionic Liquids, Conductivity, and Underscreening ParadoxBrilliantov, NGuang, GChen, MBi, SGoodwin, ZPostnikov, EUrbakh, MKornyshev, Ahttp://hdl.handle.net/2381/444152019-06-15T02:08:51Z2019-06-14T13:06:34ZTitle: Free and Bound States of Ions in Ionic Liquids, Conductivity, and Underscreening Paradox
Authors: Brilliantov, N; Guang, G; Chen, M; Bi, S; Goodwin, Z; Postnikov, E; Urbakh, M; Kornyshev, A
Abstract: Using molecular dynamics simulations and theoretical analysis of velocity-autocorrelation functions, we study ion transport mechanisms in typical room-temperature ionic liquids. We show that ions may reside in two states: free and bound with an interstate exchange. We investigate quantitatively the exchange process and reveal new qualitative features of this process. To this end, we propose a dynamic criterion for free and bound ions based on the ion trajectory density and demonstrate that this criterion is consistent with a static one based on interionic distances. Analyzing the trajectories of individual cations and anions, we estimate the time that ions spend in bound “clustered states” and when they move quasifreely. Using this method, we evaluate the average portion of “free” ions as approximately 15%–25%, increasing with temperature in the range of 300–600 K. The ion diffusion coefficients and conductivities as a function of the temperature calculated from the velocity and electrical-current autocorrelation functions reproduce the reported experimental data very well. The experimental data for the direct-current conductivity (constant ionic current) is in good agreement with theoretical predictions of the Nernst-Einstein equation based on the concentrations and diffusion coefficients of free ions obtained in our simulations. In analogy with electronic semiconductors, we scrutinize an “ionic semiconductor” model for ionic liquids, with valence and conduction “bands” for ions separated by an energy gap. The obtained band gap for the ionic liquid is small, around 26 meV, allowing for easy interchange between the two dynamic states. Moreover, we discuss the underscreening paradox in the context of the amount of free charge carriers, showing that the obtained results do not yet approve its simplistic resolution.
Description: See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevX.9.021024 for (1) comparison of results for the temperature-dependent percentage of free ions obtained by three different methods;
(2) detailed study of the kinetics of exchange process
characterized through survival probabilities for anions in
[Bmim][TFSI]; (3) additional analysis of the velocityautocorrelation functions (VACFs) and diffusion coefficients; (4) demonstration of how (exceptionally) well the
two state theory developed in the main text can fit the
simulated VACFs for anions in [Bmim][TFSI]; (5) analysis of the temperature effect on electric-current autocorrelation function (ECACF) and its Fourier spectrum;
(6) analysis of ECACFs and the corresponding values
of electrical conductivities obtained by integration of
ECAFCs over time; additional information on the results
obtained for two other RTILs [Emim][TFSI] and [Bmim]
[PF6], including the temperature-dependent (7) percentage of free ions and (8) conductivities; (9) study of the
effect of the simulation system size on the ion diffusion
coefficient.2019-06-14T13:06:34ZComparison of CdZnTe neutron detector models using MCNP6 and Geant4Wilson, EmmaAnderson, MikePrendergasty, DavidCheneler, Davidhttp://hdl.handle.net/2381/443982019-06-15T02:09:08Z2019-06-14T11:11:20ZTitle: Comparison of CdZnTe neutron detector models using MCNP6 and Geant4
Authors: Wilson, Emma; Anderson, Mike; Prendergasty, David; Cheneler, David
Abstract: The production of accurate detector models is of high importance in the development and use of detectors. Initially, MCNP and Geant were developed to specialise in neutral particle models and accelerator models, respectively; there is now a greater overlap of the capabilities of both, and it is therefore useful to produce comparative models to evaluate detector characteristics. In a collaboration between Lancaster University, UK, and Innovative Physics Ltd., UK, models have been developed in both MCNP6 and Geant4 of Cadmium Zinc Telluride (CdZnTe) detectors developed by Innovative Physics Ltd. Herein, a comparison is made of the relative strengths of MCNP6 and Geant4 for modelling neutron flux and secondary γ-ray emission. Given the increasing overlap of the modelling capabilities of MCNP6 and Geant4, it is worthwhile to comment on differences in results for simulations which have similarities in terms of geometries and source configurations.2019-06-14T11:11:20ZConvergence of multilevel stationary Gaussian convolutionHubbert, SimonLevesley, Jeremyhttp://hdl.handle.net/2381/443692019-06-13T02:11:58Z2019-06-12T09:32:27ZTitle: Convergence of multilevel stationary Gaussian convolution
Authors: Hubbert, Simon; Levesley, Jeremy
Abstract: In this paper we give a short note showing convergence rates for periodic approximation of smooth functions by multilevel Gaussian convolution. We will use the Gaussian scaling in the convolution at the finest level as a proxy for degrees of freedom d in the model. We will show that, for functions in the native space of the Gaussian, convergence is of the order (Formula Presented.). This paper provides a baseline for what should be expected in discrete convolution, which will be the subject of a follow up paper.
Description: The file associated with this record is under embargo until 12 months after publication, in accordance with the publisher's self-archiving policy. The full text may be available through the publisher links provided above.2019-06-12T09:32:27ZClassifying Matchbox ManifoldsClark, AlexHurder, StevenLukina, Olgahttp://hdl.handle.net/2381/441712019-05-22T02:10:33Z2019-05-21T10:50:12ZTitle: Classifying Matchbox Manifolds
Authors: Clark, Alex; Hurder, Steven; Lukina, Olga
Abstract: Matchbox manifolds are foliated spaces with totally disconnected transversals. Two matchbox manifolds which are homeomorphic have return equivalent dynamics, so that invariants of return equivalence can be applied to distinguish nonhomeomorphic matchbox manifolds. In this work we study the problem of showing the converse implication: when does return equivalence imply homeomorphism? For the class of weak solenoidal matchbox manifolds, we show that if the base manifolds satisfy a strong form of the Borel conjecture, then return equivalence for the dynamics of their foliations implies the total spaces are homeomorphic. In particular, we show that two equicontinuous Tn–like matchbox manifolds of the same dimension are homeomorphic if and only if their corresponding restricted pseudogroups are return equivalent. At the same time, we show that these results cannot be extended to include the “adic surfaces”, which are a class of weak solenoids fibering over a closed surface of genus 2.2019-05-21T10:50:12ZCorrection of AI systems by linear discriminants: Probabilistic foundationsGrechuk, BGorban, AGolubkov, AMirkes, ETyukin, Ihttp://hdl.handle.net/2381/441672019-05-22T02:10:29Z2019-05-21T09:55:24ZTitle: Correction of AI systems by linear discriminants: Probabilistic foundations
Authors: Grechuk, B; Gorban, A; Golubkov, A; Mirkes, E; Tyukin, I
Abstract: Artificial Intelligence (AI) systems sometimes make errors and will make errors in the future, from time to time. These errors are usually unexpected, and can lead to dramatic consequences. Intensive development of AI and its practical applications makes the problem of errors more important. Total re-engineering of the systems can create new errors and is not always possible due to the resources involved. The important challenge is to develop fast methods to correct errors without damaging existing skills. We formulated the technical requirements to the ‘ideal’ correctors. Such correctors include binary classifiers, which separate the situations with high risk of errors from the situations where the AI systems work properly. Surprisingly, for essentially high-dimensional data such methods are possible: simple linear Fisher discriminant can separate the situations with errors from correctly solved tasks even for exponentially large samples. The paper presents the probabilistic basis for fast non-destructive correction of AI systems. A series of new stochastic separation theorems is proven. These theorems provide new instruments for fast non-iterative correction of errors of legacy AI systems. The new approaches become efficient in high-dimensions, for correction of high-dimensional systems in high-dimensional world (i.e. for processing of essentially high-dimensional data by large systems).
We prove that this separability property holds for a wide class of distributions including log-concave distributions and distributions with a special ‘SMeared Absolute Continuity’ (SmAC) property defined through relations between the volume and probability of sets of vanishing volume. These classes are much wider than the Gaussian distributions. The requirement of independence and identical distribution of data is significantly relaxed. The results are supported by computational analysis of empirical data sets.
Description: The file associated with this record is under embargo until 12 months after publication, in accordance with the publisher's self-archiving policy. The full text may be available through the publisher links provided above.2019-05-21T09:55:24ZSL_2-Tilings Do Not Exist in Higher Dimensions (mostly)Demonet, LPlamondon, P-GRupel, DStella, STumarkin, Phttp://hdl.handle.net/2381/441582019-05-21T02:09:47Z2019-05-20T14:16:06ZTitle: SL_2-Tilings Do Not Exist in Higher Dimensions (mostly)
Authors: Demonet, L; Plamondon, P-G; Rupel, D; Stella, S; Tumarkin, P
Abstract: We define a family of generalizations of SL2-tilings to higher dimensions called
epsilon-SL2-tilings. We show that, in each dimension 3 or greater, epsilon-SL2-tilings exist only for
certain choices of epsilon. In the case that they exist, we show that they are essentially unique
and have a concrete description in terms of odd Fibonacci numbers.2019-05-20T14:16:06ZA note on (co)homologies of algebras from unpunctured surfacesValdivieso-Díaz, Yadirahttp://hdl.handle.net/2381/441432019-05-21T02:09:51Z2019-05-20T10:22:22ZTitle: A note on (co)homologies of algebras from unpunctured surfaces
Authors: Valdivieso-Díaz, Yadira
Abstract: In a previous paper, the author computed the dimension of Hochschild cohomology groups of Jacobian algebras from (unpunctured) triangulated surfaces, and gave a geometric interpretation of those numbers in terms of the number of internal triangles, the number of vertices and the existence of certain kind of boundaries. The aim of this note is to compute the cyclic (co)homology and the Hochschild homology of the same family of algebras and to give an interpretation of those dimensions through elements of the triangulated surface.2019-05-20T10:22:22ZOn finite dimensional Jacobian algebrasTrepode, SoniaValdivieso-Díaz, Yadirahttp://hdl.handle.net/2381/441422019-05-21T02:09:51Z2019-05-20T10:18:56ZTitle: On finite dimensional Jacobian algebras
Authors: Trepode, Sonia; Valdivieso-Díaz, Yadira
Abstract: We show that Jacobian algebras arising from every tagged triangulation of a
sphere with n-punctures, with n ≥ 5, are finite dimensional algebras. We consider also
a family of cyclically oriented quivers and we prove that, for any primitive potential,
the associated Jacobian algebra is finite dimensional.2019-05-20T10:18:56ZJacobian algebras with periodic module category and exponential growthValdivieso-Díaz, Yadirahttp://hdl.handle.net/2381/441412019-05-21T02:09:51Z2019-05-20T10:15:14ZTitle: Jacobian algebras with periodic module category and exponential growth
Authors: Valdivieso-Díaz, Yadira
Abstract: Recently it was proven by Geiss, Labardini-Fragoso and Sh¨oer in [1] that every Jacobian
algebra associated to a triangulation of a closed surface S with a collection of marked points
M is tame and Ladkani proved in [2] these algebras are (weakly) symmetric. In this work we
show that for these algebras the Auslander-Reiten translation acts 2-periodically on objects.
Moreover, we show that excluding only the case of a sphere with 4 (or less) punctures, these
algebras are of exponential growth. These results imply that the existing characterization of
symmetric tame algebras whose non-projective indecomposable modules are Ω-periodic, has
at least a missing class (see [3, Theorem 6.2] or [4]).
As a consequence of the 2-periodical actions of the Auslander-Reiten translation on objects, we have that the Auslander-Reiten quiver of the generalized cluster category C(S,M)
consists only of stable tubes of rank 1 or 2.2019-05-20T10:15:14ZEquivariant Vector Bundles Over Quantum Projective SpacesMudrov, A. I.http://hdl.handle.net/2381/441362019-05-21T02:09:46Z2019-05-20T09:52:50ZTitle: Equivariant Vector Bundles Over Quantum Projective Spaces
Authors: Mudrov, A. I.
Abstract: We construct equivariant vector bundles over quantum projective spaces using parabolic Verma modules over the quantum general linear group. Using an alternative realization of the quantized coordinate ring of the projective space as a subalgebra in the algebra of functions on the quantum group, we reformulate quantum vector bundles in terms of quantum symmetric pairs. We thus prove the complete reducibility of modules over the corresponding coideal stabilizer subalgebras, via the quantum Frobenius reciprocity.
Description: The file associated with this record is under embargo until 12 months after publication, in accordance with the publisher's self-archiving policy. The full text may be available through the publisher links provided above.; Prepared from an English manuscript submitted by the author; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 198, No. 2, pp. 326–340, February, 2019.2019-05-20T09:52:50ZKinetic regimes in aggregating systems with spontaneous and collisional fragmentationBodrova, Anna S.Stadnichuk, VladimirKrapivsky, P. L.Schmidt, JürgenBrilliantov, Nikolai V.http://hdl.handle.net/2381/441332019-05-21T02:09:50Z2019-05-20T09:36:12ZTitle: Kinetic regimes in aggregating systems with spontaneous and collisional fragmentation
Authors: Bodrova, Anna S.; Stadnichuk, Vladimir; Krapivsky, P. L.; Schmidt, Jürgen; Brilliantov, Nikolai V.
Abstract: We analyze systems composed of clusters and interacting upon colliding---a collision between two clusters may lead to merging (an aggregation event) or fragmentation---and we also investigate the effect of additional, spontaneous fragmentation events. We consider closed systems in which the total mass remains constant and open systems driven by a source of small-mass clusters. In closed systems, the size distribution of aggregates approaches a steady state. For these systems the relaxation time and the steady state distribution are determined mostly by spontaneous fragmentation while collisional fragmentation plays a minor role. For open systems, in contrast, the collisional fragmentation dominates. In this case, the system relaxes to a quasi-stationary state where cluster densities linearly grow with time, while the functional form of the cluster size distribution persists and coincides with the steady state size distribution of a system which has the same aggregation and fragmentation rates and only collisional fragmentation, the spontaneous fragmentation is in this case negligible.
Description: The file associated with this record is under embargo until 12 months after publication, in accordance with the publisher's self-archiving policy. The full text may be available through the publisher links provided above.2019-05-20T09:36:12ZFusion systems on maximal class 3-groups of rank two revisitedParker, ChrisSemeraro, Jasonhttp://hdl.handle.net/2381/441312019-05-18T02:09:50Z2019-05-17T14:06:46ZTitle: Fusion systems on maximal class 3-groups of rank two revisited
Authors: Parker, Chris; Semeraro, Jason
Abstract: We complete the determination of saturated fusion systems on maximal class 3-groups
of rank two.
Description: 2010 Mathematics Subject Classification. 20D20, 20D052019-05-17T14:06:46ZWonder of sine-gordon Y -systemsNakanishi, TomokiStella, Salvatorehttp://hdl.handle.net/2381/441292019-05-18T02:09:51Z2019-05-17T09:48:41ZTitle: Wonder of sine-gordon Y -systems
Authors: Nakanishi, Tomoki; Stella, Salvatore
Abstract: The sine-Gordon Y -systems and the reduced sine-Gordon Y - systems were introduced by Tateo in the 1990’s in the study of the integrable deformation of conformal field theory by the thermodynamic Bethe ansatz method. The periodicity property and the dilogarithm identities concerning these Y -systems were conjectured by Tateo, and only a part of them have been proved so far. In this paper we formulate these Y -systems by the polygon realization of cluster algebras of types A and D and prove the conjectured periodicity and dilogarithm identities in full generality. As it turns out, there is a wonderful interplay among continued fractions, triangulations of polygons, cluster algebras, and Y -systems.2019-05-17T09:48:41ZThe greedy basis equals the theta basis: A rank two haikuCheung, Man WaiGross, MarkMuller, GregMusiker, GreggRupel, DylanStella, SalvatoreWilliams, Haroldhttp://hdl.handle.net/2381/441282019-05-18T02:09:50Z2019-05-17T09:45:56ZTitle: The greedy basis equals the theta basis: A rank two haiku
Authors: Cheung, Man Wai; Gross, Mark; Muller, Greg; Musiker, Gregg; Rupel, Dylan; Stella, Salvatore; Williams, Harold
Abstract: We prove the equality of two canonical bases of a rank 2 cluster algebra, the greedy basis of Lee–Li–Zelevinsky and the theta basis of Gross–Hacking–Keel–Kontsevich.2019-05-17T09:45:56ZPolytopal realizations of finite type g-vector fansHohlweg, ChristophePilaud, VincentStella, Salvatorehttp://hdl.handle.net/2381/441272019-05-18T02:09:48Z2019-05-17T09:41:22ZTitle: Polytopal realizations of finite type g-vector fans
Authors: Hohlweg, Christophe; Pilaud, Vincent; Stella, Salvatore
Abstract: This paper shows the polytopality of any finite type g-vector fan, acyclic or not. In fact, for any finite Dynkin type Γ, we construct a universal associahedron Assoun(Γ) with the property that any g-vector fan of type Γ is the normal fan of a suitable projection of Assoun(Γ).2019-05-17T09:41:22ZOn Generalized Minors and Quiver RepresentationsRupel, DylanStella, SalvatoreWilliams, Haroldhttp://hdl.handle.net/2381/441262019-05-18T02:09:52Z2019-05-17T09:34:54ZTitle: On Generalized Minors and Quiver Representations
Authors: Rupel, Dylan; Stella, Salvatore; Williams, Harold
Abstract: The cluster algebra of any acyclic quiver can be realized as the coordinate ring of a subvariety of a Kac-Moody group -- the quiver is an orientation of its Dynkin diagram, defining a Coxeter element and thereby a double Bruhat cell. We use this realization to connect representations of the quiver with those of the group. We show that cluster variables of preprojective (resp. postinjective) quiver representations are realized by generalized minors of highest-weight (resp. lowest-weight) group representations, generalizing results of Yang-Zelevinsky in finite type. In type $A_n^{\!(1)}$ and finitely many other affine types, we show that cluster variables of regular quiver representations are realized by generalized minors of group representations that are neither highest- nor lowest-weight; we conjecture this holds more generally.2019-05-17T09:34:54ZInitial-seed recursions and dualities for d-vectorsReading, NathanStella, Salvatorehttp://hdl.handle.net/2381/441252019-05-18T02:09:50Z2019-05-17T09:21:41ZTitle: Initial-seed recursions and dualities for d-vectors
Authors: Reading, Nathan; Stella, Salvatore
Abstract: We present an initial-seed-mutation formula for d-vectors of cluster variables in a cluster algebra. We also give two rephrasings of this recursion: one as a duality formula for d-vectors in the style of the g-vectors/c-vectors dualities of Nakanishi and Zelevinsky, and one as a formula expressing the highest powers in the Laurent expansion of a cluster variable in terms of the d-vectors of any cluster containing it. We prove that the initial-seedmutation recursion holds in a varied collection of cluster algebras, but not in general. We conjecture further that the formula holds for source-sink moves on the initial seed in an arbitrary cluster algebra, and we prove this conjecture in the case of surfaces.2019-05-17T09:21:41ZAffine cluster monomials are generalized minorsRupel, DylanStella, SalvatoreWilliams, Haroldhttp://hdl.handle.net/2381/441242019-05-18T02:09:52Z2019-05-17T09:11:48ZTitle: Affine cluster monomials are generalized minors
Authors: Rupel, Dylan; Stella, Salvatore; Williams, Harold
Abstract: We study the realization of acyclic cluster algebras as coordinate rings of Coxeter double Bruhat cells in Kac-Moody groups. We prove that all cluster monomials with g-vector lying in the doubled Cambrian fan are restrictions of principal generalized minors. As a corollary, cluster algebras of finite and affine type admit a complete and non-recursive description via (ind-)algebraic group representations, in a way similar in spirit to the Caldero-Chapoton description via quiver representations. In type A_1^{(1)}, we further show that elements of several canonical bases (generic, triangular, and theta) which complete the partial basis of cluster monomials are composed entirely of restrictions of minors. The discrepancy among these bases is accounted for by continuous parameters appearing in the classification of irreducible level-zero representations of affine Lie groups. We discuss how our results illuminate certain parallels between the classification of representations of finite-dimensional algebras and of integrable weight representations of Kac-Moody algebras.
Description: The file associated with this record is under embargo until publication, in accordance with the publisher's self-archiving policy. The full text may be available through the publisher links provided above.2019-05-17T09:11:48ZExchange relations for finite type cluster algebras with acyclic initial seed and principal coefficientsStella, SalvatoreTumarkin, Pavelhttp://hdl.handle.net/2381/441222019-05-18T02:09:51Z2019-05-17T08:53:29ZTitle: Exchange relations for finite type cluster algebras with acyclic initial seed and principal coefficients
Authors: Stella, Salvatore; Tumarkin, Pavel
Abstract: We give an explicit description of all the exchange relations in any finite type cluster algebra with acyclic initial seed and principal coefficients.2019-05-17T08:53:29ZA τ-tilting approach to dissections of polygonsPilaud, VincentPlamondon, Pierre-GuyStella, Salvatorehttp://hdl.handle.net/2381/441212019-05-18T02:09:51Z2019-05-17T08:50:55ZTitle: A τ-tilting approach to dissections of polygons
Authors: Pilaud, Vincent; Plamondon, Pierre-Guy; Stella, Salvatore
Abstract: We show that any accordion complex associated to a dissection of a convex polygon is isomorphic to the support τ-tilting simplicial complex of an explicit finite dimensional algebra. To this end, we prove a property of some induced subcomplexes of support τ-tilting simplicial complexes of finite dimensional algebras.2019-05-17T08:50:55ZComonad Cohomology of Track CategoriesBlanc, DavidPaoli, Simonahttp://hdl.handle.net/2381/439512019-05-01T02:10:07Z2019-04-30T14:57:03ZTitle: Comonad Cohomology of Track Categories
Authors: Blanc, David; Paoli, Simona
Abstract: We define a comonad cohomology of track categories and we show it is linked by a long exact sequence to its Dwyer-Kan-Smith cohomology . Under mild hypothesis on the track category, we show that its comonad cohomology coincides, up to dimension shift, with its Dwyer-Kan-Smith cohomology, therefore obtaining an algebraic formulation of the latter. We also specialize our results to the case where the track category is a $2$-groupoid.
Description: The file associated with this record is under embargo until 12 months after publication, in accordance with the publisher's self-archiving policy. The full text may be available through the publisher links provided above.2019-04-30T14:57:03ZOne-trial correction of legacy AI systems and stochastic separation theoremsGorban, Alexander N.Burton, RichardRomanenko, IlyaTyukin, Ivan Yuhttp://hdl.handle.net/2381/439132019-04-27T02:09:55Z2019-04-26T15:36:19ZTitle: One-trial correction of legacy AI systems and stochastic separation theorems
Authors: Gorban, Alexander N.; Burton, Richard; Romanenko, Ilya; Tyukin, Ivan Yu
Abstract: We consider the problem of efficient “on the fly” tuning of existing, or legacy, Artificial Intelligence (AI) systems. The legacy AI systems are allowed to be of arbitrary class, albeit the data they are using for computing interim or final decision responses should posses an underlying structure of a high-dimensional topological real vector space. The tuning method that we propose enables dealing with errors without the need to re-train the system. Instead of re-training a simple cascade of perceptron nodes is added to the legacy system. The added cascade modulates the AI legacy system’s decisions. If applied repeatedly, the process results in a network of modulating rules “dressing up” and improving performance of existing AI systems. Mathematical rationale behind the method is based on the fundamental property of measure concentration in high dimensional spaces. The method is illustrated with an example of fine-tuning a deep convolutional network that has been pre-trained to detect pedestrians in images.
Description: The file associated with this record is under embargo until 12 months after publication, in accordance with the publisher's self-archiving policy. The full text may be available through the publisher links provided above.2019-04-26T15:36:19ZDiscrete and Continuous Ito-Malliavin Type Calculus with Illustration in FinanceFan, Junhttp://hdl.handle.net/2381/438142019-04-18T02:09:42Z2019-04-17T08:39:37ZTitle: Discrete and Continuous Ito-Malliavin Type Calculus with Illustration in Finance
Authors: Fan, Jun
Abstract: As reliable mathematical methods for finance, various concepts of the stochastic calculus are discussed in detail in this thesis such as the Ito integral, the (continuous and discrete) Malliavin calculus and the Stratonovich integral. The derivative of a natural number and the quantum calculus are also illustrated in this thesis. The Stroock lemma and the duality formula are two methods when the Malliavin calculus is applied to calculate the preceding quantities. To extend the range of application of these rules is a crucial purpose of this thesis. Solving certain equations based on the Ito integral and the Malliavin calculus has also
been introduced and analysed in this thesis. This equation, which is also a kind of stochastic differential equation, can be treated as an inverse application of the Malliavin derivative. Finally, the product rule for other derivative operators is extensively introduced and analysed throughout the whole thesis, since this rule in the stochastic calculus or the quantum calculus is sometimes
different from the traditional infinitesimal calculus. To explore the idea of differential dynamics with the non-standard and new
types of differentiation, the differential operators discussed and introduced in this thesis, such as the continuous and the discrete Malliavin derivative operator and the q-derivation operator are applied as transforms on some state spaces, such as measurable space and the space constructed by the finite fields.2019-04-17T08:39:37ZTransient phenomena in ecology.Hastings, AAbbott, KCCuddington, KFrancis, TGellner, GLai, Y-CMorozov, APetrovskii, SScranton, KZeeman, MLhttp://hdl.handle.net/2381/437532019-04-13T02:09:59Z2019-04-12T09:32:01ZTitle: Transient phenomena in ecology.
Authors: Hastings, A; Abbott, KC; Cuddington, K; Francis, T; Gellner, G; Lai, Y-C; Morozov, A; Petrovskii, S; Scranton, K; Zeeman, ML
Abstract: The importance of transient dynamics in ecological systems and in the models that describe them has become increasingly recognized. However, previous work has typically treated each instance of these dynamics separately. We review both empirical examples and model systems, and outline a classification of transient dynamics based on ideas and concepts from dynamical systems theory. This classification provides ways to understand the likelihood of transients for particular systems, and to guide investigations to determine the timing of sudden switches in dynamics and other characteristics of transients. Implications for both management and underlying ecological theories emerge.2019-04-12T09:32:01ZMetallome of cerebrovascular endothelial cells infected with Toxoplasma gondii using μ-XRF imaging and inductively coupled plasma mass spectrometryAl-Sandaqchi, ATBrignell, CCollingwood, JFGeraki, KMirkes, EMKong, KCastellanos, MMay, STStevenson, CWElsheikha, HMhttp://hdl.handle.net/2381/437362019-04-12T02:09:40Z2019-04-11T08:39:50ZTitle: Metallome of cerebrovascular endothelial cells infected with Toxoplasma gondii using μ-XRF imaging and inductively coupled plasma mass spectrometry
Authors: Al-Sandaqchi, AT; Brignell, C; Collingwood, JF; Geraki, K; Mirkes, EM; Kong, K; Castellanos, M; May, ST; Stevenson, CW; Elsheikha, HM
Abstract: In this study, we measured the levels of elements in human brain microvascular endothelial cells (ECs) infected with T. gondii. ECs were infected with tachyzoites of the RH strain, and at 6, 24, and 48 hours post infection (hpi), the intracellular concentrations of elements were determined using a synchrotron-microfocus X-ray fluorescence microscopy (μ-XRF) system. This method enabled the quantification of the concentrations of Zn and Ca in infected and uninfected (control) ECs at sub-micron spatial resolution. T. gondii-hosting ECs contained less Zn than uninfected cells only at 48 hpi (p < 0.01). The level of Ca was not significantly different between infected and control cells (p > 0.05). Inductively Coupled Plasma Mass Spectrometry (ICP-MS) analysis revealed infection-specific metallome profiles characterized by significant increases in the intracellular levels of Zn, Fe, Mn and Cu at 48 hpi (p < 0.01), and significant reductions in the extracellular concentrations of Co, Cu, Mo, V, and Ag at 24 hpi (p < 0.05) compared with control cells. Zn constituted the largest part (74%) of the total metal composition (metallome) of the parasite. Gene expression analysis showed infection-specific upregulation in the expression of five genes, MT1JP, MT1M, MT1E, MT1F, and MT1X, belonging to the metallothionein gene family. These results point to a possible correlation between T. gondii infection and increased expression of MT1 isoforms and altered intracellular levels of elements, especially Zn and Fe. Taken together, a combined μ-XRF and ICP-MS approach is promising for studies of the role of elements in mediating host-parasite interaction.
Description: The file associated with this record is under embargo until 12 months after publication, in accordance with the publisher's self-archiving policy. The full text may be available through the publisher links provided above.2019-04-11T08:39:50ZPrevalence of feline lungworm Aelurostrongylus abstrusus in EnglandElsheikha, HMWright, IWang, BSchaper, Rhttp://hdl.handle.net/2381/437122019-04-08T14:08:20Z2019-04-05T09:24:11ZTitle: Prevalence of feline lungworm Aelurostrongylus abstrusus in England
Authors: Elsheikha, HM; Wright, I; Wang, B; Schaper, R
Abstract: Infection of cats with lungworm Aelurostrongylus abstrusus has recently been documented in the UK. Here, we aimed to study the prevalence of A. abstrusus in fecal samples from cats across England. A total of 950 fecal samples were collected from cats together with information on their age, breed, gender, geographic region, lifestyle, and treatment history. A total of 17 (1.7%) cats were positive for A. abstrusus based on species-specific morphological features of the larvae isolated by Baermann's technique. There was no statistically significant difference in the proportion of positive samples between females (506; 53.2%) and males (444; 46.7%). Multiple regression analysis showed that prevalence of feline lungworm was significantly different across geographic regions: in comparison with East Midlands, some regions had shown significantly increased odds of A. abstrusus-positive samples (South East [odds ratio [OR] = 7.68; 95% confidence interval [CI] = 1.70 to 32.76; p =.01]; West Midlands [OR = 6.20; 95% CI = 1.21 to 26.84; p =.02]), while other regions had also increased odds although not statistically significant (Greater London [OR = 9.63; 95% CI = 0.43 to 84.05; p =.07]; North West [OR = 4.25; 95% CI = 0.59 to 20.89; p =.09]; South West [OR = 2.48; 95% CI = 0.12 to 17.64; p =.43]; and North East [OR = 1.88; 95% CI = 0.10 to 12.24; p =.57]). Keeping cats inside was protective against the risk of infection compared with those having outdoor access (OR = 0.09; 95% CI = 0.01 to 0.48; p =.02). On the other hand, age, breed, gender and deworming history did not have any significant effect on the likelihood of infection. Our data indicate that A. abstrusus is a parasite of potential significance in cats, in particular those from certain geographic regions in England. To reduce the spread of this parasite, an integrated feline lungworm control program needs to be implemented.
Description: The file associated with this record is under embargo until 12 months after publication, in accordance with the publisher's self-archiving policy. The full text may be available through the publisher links provided above.2019-04-05T09:24:11ZOne-trial correction of legacy AI systems and stochastic separation theoremsGorban, ANBurton, RRomanenko, ITyukin, IYhttp://hdl.handle.net/2381/437052019-04-05T02:10:04Z2019-04-04T12:09:01ZTitle: One-trial correction of legacy AI systems and stochastic separation theorems
Authors: Gorban, AN; Burton, R; Romanenko, I; Tyukin, IY
Abstract: We consider the problem of efficient “on the fly” tuning of existing, or legacy, Artificial Intelligence (AI) systems. The legacy AI systems are allowed to be of arbitrary class, albeit the data they are using for computing interim or final decision responses should posses an underlying structure of a high-dimensional topological real vector space. The tuning method that we propose enables dealing with errors without the need to re-train the system. Instead of re-training a simple cascade of perceptron nodes is added to the legacy system. The added cascade modulates the AI legacy system's decisions. If applied repeatedly, the process results in a network of modulating rules “dressing up” and improving performance of existing AI systems. Mathematical rationale behind the method is based on the fundamental property of measure concentration in high dimensional spaces. The method is illustrated with an example of fine-tuning a deep convolutional network that has been pre-trained to detect pedestrians in images.
Description: The file associated with this record is under embargo until 12 months after publication, in accordance with the publisher's self-archiving policy. The full text may be available through the publisher links provided above.2019-04-04T12:09:01ZReduction of SO(2) symmetry for spatially extended dynamical systemsBudanur, Nazmi BurakCvitanović, PredragDavidchack, Ruslan L.Siminos, Evangeloshttp://hdl.handle.net/2381/436892019-06-05T10:22:46Z2019-04-02T13:58:04ZTitle: Reduction of SO(2) symmetry for spatially extended dynamical systems
Authors: Budanur, Nazmi Burak; Cvitanović, Predrag; Davidchack, Ruslan L.; Siminos, Evangelos
Abstract: Spatially extended systems, such as channel or pipe flows, are often equivariant under continuous symmetry transformations, with each state of the flow having an infinite number of equivalent solutions obtained from it by a translation or a rotation. This multitude of equivalent solutions tends to obscure the dynamics of turbulence. Here we describe the "first Fourier mode slice," a very simple, easy to implement reduction of SO(2) symmetry. While the method exhibits rapid variations in phase velocity whenever the magnitude of the first Fourier mode is nearly vanishing, these near singularities can be regularized by a time-scaling transformation. We show that after application of the method, hitherto unseen global structures, for example, Kuramoto-Sivashinsky relative periodic orbits and unstable manifolds of traveling waves, are uncovered.2019-04-02T13:58:04ZEffect of complex landscape geometry on the invasive species spread: Invasion with stepping stonesAlharbi, WPetrovskii, Shttp://hdl.handle.net/2381/435152019-03-08T03:26:00Z2019-03-07T12:34:46ZTitle: Effect of complex landscape geometry on the invasive species spread: Invasion with stepping stones
Authors: Alharbi, W; Petrovskii, S
Abstract: Spatial proliferation of invasive species often causes serious damage to agriculture, ecology and environment. Evaluation of the extent of the area potentially invadable by an alien species is an important problem. Landscape features that reduces dispersal space to narrow corridors can make some areas inaccessible to the invading species. On the other hand, the existence of stepping stones - small areas or 'patches' with better environmental conditions - is known to assist species spread. How an interplay between these factors can affect the invasion success remains unclear. In this paper, we address this question theoretically using a mechanistic model of population dynamics. Such models have been generally successful in predicting the rate and pattern of invasive spread; however, they usually consider the spread in an unbounded, uniform space hence ignoring the complex geometry of a real landscape. In contrast, here we consider a reaction-diffusion model in a domain of a complex shape combining corridors and stepping stones. We show that the invasion success depends on a subtle interplay between the stepping stone size, location and the strength of the Allee effect inside. In particular, for a stepping stone of a small size, there is only a narrow range of locations where it can unblock the otherwise impassable corridor.
Description: The file associated with this record is under embargo until 12 months after publication, in accordance with the publisher's self-archiving policy. The full text may be available through the publisher links provided above.2019-03-07T12:34:46ZCoherent mortality forecasting by the weighted multilevel functional principal component approachWang, BWu, Rhttp://hdl.handle.net/2381/435112019-03-08T03:25:57Z2019-03-07T11:10:10ZTitle: Coherent mortality forecasting by the weighted multilevel functional principal component approach
Authors: Wang, B; Wu, R
Abstract: In human mortality modelling, if a population consists of several subpopulations it can be desirable to model their mortality rates simultaneously while taking into account the heterogeneity among them. The mortality forecasting methods tend to result in divergent forecasts for subpopulations when independence is assumed. However, under closely related social, economic and biological backgrounds, mortality patterns of these subpopulations are expected to be non-divergent in the future. In this article, we propose a new method for coherent modelling and forecasting of mortality rates for multiple subpopulations, in the sense of nondivergent life expectancy among subpopulations. The mortality rates of subpopulations are treated as multilevel functional data and a weighted multilevel functional principal component (wMFPCA) approach is proposed to model and forecast them. The proposed model is applied to sex-specific data for nine developed countries, and the results show that, in terms of overall forecasting accuracy, the model outperforms the independent model and the Product-Ratio model as well as the unweighted multilevel functional principal component approach.
Description: The file associated with this record is under embargo until 12 months after publication, in accordance with the publisher's self-archiving policy. The full text may be available through the publisher links provided above.2019-03-07T11:10:10ZFast Construction of Correcting Ensembles for Legacy Artificial Intelligence Systems: Algorithms and a Case StudyTyukin, IYGorban, ANGreen, SProkhorov, Dhttp://hdl.handle.net/2381/434952019-03-05T03:13:14Z2019-03-04T09:58:56ZTitle: Fast Construction of Correcting Ensembles for Legacy Artificial Intelligence Systems: Algorithms and a Case Study
Authors: Tyukin, IY; Gorban, AN; Green, S; Prokhorov, D
Abstract: This paper presents a technology for simple and computationally efficient improvements of a generic Artificial Intelligence (AI) system, including Multilayer and Deep Learning neural networks. The improvements are, in essence, small network ensembles constructed on top of the existing AI architectures. Theoretical foundations of the technology are based on Stochastic Separation Theorems and the ideas of the concentration of measure. We show that, subject to mild technical assumptions on statistical properties of internal signals in the original AI system, the technology enables instantaneous and computationally efficient removal of spurious and systematic errors with probability close to one on the datasets which are exponentially large in dimension. The method is illustrated with numerical examples and a case study of ten digits recognition from American Sign Language.
Description: The file associated with this record is under embargo until 12 months after publication, in accordance with the publisher's self-archiving policy. The full text may be available through the publisher links provided above.2019-03-04T09:58:56ZEffect of density-dependent individual movement on emerging spatial population distribution: Brownian motion vs Levy flightsEllis, JPetrovskaya, NPetrovskii, Shttp://hdl.handle.net/2381/434882019-03-02T03:15:50Z2019-03-01T11:58:47ZTitle: Effect of density-dependent individual movement on emerging spatial population distribution: Brownian motion vs Levy flights
Authors: Ellis, J; Petrovskaya, N; Petrovskii, S
Abstract: Individual animal movement has been a focus of intense research and considerable controversy over the last two decades, however the understanding of wider ecological implications of various movement behaviours is lacking. In this paper, we consider this issue in the context of pattern formation. Using an individual-based modelling approach and computer simulations, we first show that density dependence ("auto-taxis") of the individual movement in a population of random walkers typically results in the formation of a strongly heterogeneous population distribution consisting of clearly defined animals clusters or patches. We then show that, when the movement takes place in a large spatial domain, the properties of the clusters are significantly different in the populations of Brownian and non-Brownian walkers. Whilst clusters tend to be stable in the case of Brownian motion, in the population of Levy walkers clusters are dynamical so that the number of clusters fluctuates in the course of time. We also show that the population dynamics of non-Brownian walkers exhibits two different time scales: a short time scale of the relaxation of the initial condition and a long time scale when one type of dynamics is replaced by another. Finally, we show that the distribution of sample values in the populations of Brownian and non-Brownian walkers is significantly different.
Description: The file associated with this record is under embargo until 12 months after publication, in accordance with the publisher's self-archiving policy. The full text may be available through the publisher links provided above.2019-03-01T11:58:47ZOn determinant functors and K-theoryMuro, FTonks, AWitte, Mhttp://hdl.handle.net/2381/434652019-06-26T14:52:26Z2019-02-28T11:55:47ZTitle: On determinant functors and K-theory
Authors: Muro, F; Tonks, A; Witte, M
Abstract: We extend Deligne’s notion of determinant functor to Waldhausen categories and (strongly) triangulated categories. We construct explicit universal determinant functors in each case, whose target is an algebraic model for the 1-type of the corresponding K-theory spectrum. As applications, we answer open questions by Maltsiniotis and Neeman on the K-theory of (strongly) triangulated categories and a question of Grothendieck to Knudsen on determinant functors. We also prove additivity theorems for low-dimensional K-theory of (strongly) triangulated categories and obtain generators and (some) relations for various K1-groups. This is achieved via a unified theory of determinant functors which can be applied in further contexts, such as derivators.
Description: The file associated with this record is under embargo while permission to archive is sought from the publisher. The full text may be available through the publisher links provided above.2019-02-28T11:55:47ZR-matrix and Mickelsson algebras for orthosymplectic quantum groupsAshton, ThomasMudrov, Andreyhttp://hdl.handle.net/2381/434282019-02-26T03:21:26Z2019-02-25T16:38:44ZTitle: R-matrix and Mickelsson algebras for orthosymplectic quantum groups
Authors: Ashton, Thomas; Mudrov, Andrey
Abstract: Let 𝔤 be a complex orthogonal or symplectic Lie algebra and 𝔤′ ⊂ 𝔤 the Lie subalgebra of rank rk 𝔤′ = rk 𝔤 − 1 of the same type. We give an explicit construction of generators of the Mickelsson algebra Zq(𝔤, 𝔤′) in terms of Chevalley generators via the R-matrix of Uq(𝔤).2019-02-25T16:38:44ZDecomposition spaces, incidence algebras and Möbius inversion I: Basic theoryGálvez-Carrillo, IKock, JTonks, Ahttp://hdl.handle.net/2381/433552019-06-20T01:45:07Z2019-02-15T09:56:45ZTitle: Decomposition spaces, incidence algebras and Möbius inversion I: Basic theory
Authors: Gálvez-Carrillo, I; Kock, J; Tonks, A
Abstract: This is the first in a series of papers devoted to the theory of decomposition spaces, a general framework for incidence algebras and Möbius inversion, where algebraic identities are realised by taking homotopy cardinality of equivalences of ∞-groupoids. A decomposition space is a simplicial ∞-groupoid satisfying an exactness condition, weaker than the Segal condition, expressed in terms of active and inert maps in [Figure presented]. Just as the Segal condition expresses composition, the new exactness condition expresses decomposition, and there is an abundance of examples in combinatorics. After establishing some basic properties of decomposition spaces, the main result of this first paper shows that to any decomposition space there is an associated incidence coalgebra, spanned by the space of 1-simplices, and with coefficients in ∞-groupoids. We take a functorial viewpoint throughout, emphasising conservative ULF functors; these induce coalgebra homomorphisms. Reduction procedures in the classical theory of incidence coalgebras are examples of this notion, and many are examples of decalage of decomposition spaces. An interesting class of examples of decomposition spaces beyond Segal spaces is provided by Hall algebras: the Waldhausen S•-construction of an abelian (or stable infinity) category is shown to be a decomposition space. In the second paper in this series we impose further conditions on decomposition spaces, to obtain a general Möbius inversion principle, and to ensure that the various constructions and results admit a homotopy cardinality. In the third paper we show that the Lawvere–Menni Hopf algebra of Möbius intervals is the homotopy cardinality of a certain universal decomposition space. Two further sequel papers deal with numerous examples from combinatorics. Note: The notion of decomposition space was arrived at independently by Dyckerhoff and Kapranov [17] who call them unital 2-Segal spaces. Our theory is quite orthogonal to theirs: the definitions are different in spirit and appearance, and the theories differ in terms of motivation, examples, and directions.
Description: The file associated with this record is under embargo until 12 months after publication, in accordance with the publisher's self-archiving policy. The full text may be available through the publisher links provided above.2019-02-15T09:56:45ZDecomposition spaces, incidence algebras and Möbius inversion II: Completeness, length filtration, and finitenessGálvez-Carrillo, IKock, JTonks, Ahttp://hdl.handle.net/2381/433542019-02-16T03:57:46Z2019-02-15T09:48:00ZTitle: Decomposition spaces, incidence algebras and Möbius inversion II: Completeness, length filtration, and finiteness
Authors: Gálvez-Carrillo, I; Kock, J; Tonks, A
Abstract: This is the second in a trilogy of papers introducing and studying the notion of decomposition space as a general framework for incidence algebras and Möbius inversion, with coefficients in ∞-groupoids. A decomposition space is a simplicial ∞-groupoid satisfying an exactness condition weaker than the Segal condition. Just as the Segal condition expresses composition, the new condition expresses decomposition. In this paper, we introduce various technical conditions on decomposition spaces. The first is a completeness condition (weaker than Rezk completeness), needed to control simplicial nondegeneracy. For complete decomposition spaces we establish a general Möbius inversion principle, expressed as an explicit equivalence of ∞-groupoids. Next we analyse two finiteness conditions on decomposition spaces. The first, that of locally finite length, guarantees the existence of the important length filtration for the associated incidence coalgebra. We show that a decomposition space of locally finite length is actually the left Kan extension of a semi-simplicial space. The second finiteness condition, local finiteness, ensures we can take homotopy cardinality to pass from the level of ∞-groupoids to the level of Q-vector spaces. These three conditions — completeness, locally finite length, and local finiteness — together define our notion of Möbius decomposition space, which extends Leroux's notion of Möbius category (in turn a common generalisation of the locally finite posets of Rota et al. and of the finite decomposition monoids of Cartier–Foata), but which also covers many coalgebra constructions which do not arise from Möbius categories, such as the Faà di Bruno and Connes–Kreimer bialgebras. Note: The notion of decomposition space was arrived at independently by Dyckerhoff and Kapranov [6] who call them unital 2-Segal spaces.
Description: The file associated with this record is under embargo until 12 months after publication, in accordance with the publisher's self-archiving policy. The full text may be available through the publisher links provided above.2019-02-15T09:48:00ZGroupoids and Faà di Bruno formulae for Green functions in bialgebras of treesGálvez-Carrillo, IKock, JTonks, Ahttp://hdl.handle.net/2381/433532019-02-16T03:57:45Z2019-02-15T09:32:26ZTitle: Groupoids and Faà di Bruno formulae for Green functions in bialgebras of trees
Authors: Gálvez-Carrillo, I; Kock, J; Tonks, A
Abstract: We prove a Faà di Bruno formula for the Green function in the bialgebra of P-trees, for any polynomial endofunctor P. The formula appears as relative homotopy cardinality of an equivalence of groupoids.2019-02-15T09:32:26ZDependence Structures and Risk Aggregation Using CopulasIsmail, Isaudinhttp://hdl.handle.net/2381/433032019-07-22T12:58:46Z2019-02-13T11:27:11ZTitle: Dependence Structures and Risk Aggregation Using Copulas
Authors: Ismail, Isaudin
Abstract: Insurance and reinsurance companies have to calculate solvency capital requirements in order to ensure that they can meet their future obligations to policyholders and beneficiaries. The solvency capital requirement is a risk management tool essential when extreme catastrophic events happen, resulting in high number of possibly interdependent claims. In this thesis, we study the problem of aggregating the risks coming from several insurance lines of business and analyse the effect of reinsurance in the level of risk. Our starting point is to use a Hierarchical Risk Aggregation method, which was initially based on 2-dimensional elliptical copulas. We use copulas from the Archimedean family and a mixture of different copulas. The results show that a mixture of copulas can provide a better fit to the data than the plain (single) copulas and consequently avoid overestimation or underestimation of the capital requirement of an insurance company. We also investigate the significance of reinsurance in reducing the insurance company's business risk and its effect on diversification. The results show that reinsurance does not always reduce the level of risk but can reduce the effect of diversification for insurance companies with multiple business lines. To extend the literature on modelling multivariate distributions, we investigate the dependence structure of multiple insurance business lines risks using C-vine copulas. In particular, we use bivariate copulas, and aggregate the insurance risks. We employ three C-vine models such as mixed C-vine, C-vine Gaussian and C-vine t-copula to develop a new capital requirement model for insurance companies. Our findings suggest that the mixed C-vine copula is the best model which allows a variety of dependence structure estimated by its respective copula families.
Description: The file associated with this record is under embargo until 12 months after publication.2019-02-13T11:27:11Z