DSpace Collection:
http://hdl.handle.net/2381/3823
2019-08-25T16:47:00ZTHE μ–DARBOUX TRANSFORMATION OF MINIMAL SURFACES
http://hdl.handle.net/2381/45264
Title: THE μ–DARBOUX TRANSFORMATION OF MINIMAL SURFACES
Authors: Leschke, K.; Moriya, K.
Abstract: The classical notion of the Darboux transformation of isothermic surfaces can be generalised to a transformation for conformal immersions. Since a minimal surface is Willmore, we
can use the associated C∗–family of flat connections of the harmonic conformal Gauss map to construct such transforms, the so–called µ–Darboux transforms. We show that a µ–Darboux transform
of a minimal surface is not minimal but a Willmore surface in 4–space. More precisely, we show
that a µ–Darboux transform of a minimal surface f is a twistor projection of a holomorphic curve
in CP3 which is canonically associated to a minimal surface fp,q in the right–associated family of
f . Here we use an extension of the notion of the associated family fp,q of a minimal surface to
allow quaternionic parameters. We prove that the pointwise limit of Darboux transforms of f is the
associated Willmore surface of f at µ = 1. Moreover, the family of Willmore surfaces µ–Darboux
transforms, µ ∈ C∗, extends to a CP1
family of Willmore surfaces f
µ
: M → S
4 where µ ∈ CP1
.
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.2019-08-19T10:21:18ZA Quantum-Type Approach to Non-Life Insurance Risk Modelling
http://hdl.handle.net/2381/45255
Title: A Quantum-Type Approach to Non-Life Insurance Risk Modelling
Authors: Lefèvre, Claude; Loisel, Stéphane; Tamturk, Muhsin; Utev, Sergey
Abstract: A quantum mechanics approach is proposed to model non-life insurance risks and to compute the future reserve amounts and the ruin probabilities. The claim data, historical or simulated, are treated as coming from quantum observables and analyzed with traditional machine learning tools. They can then be used to forecast the evolution of the reserves of an insurance company. The following methodology relies on the Dirac matrix formalism and the Feynman path-integral method.2019-08-19T09:11:04ZSupport varieties - an axiomatic approach
http://hdl.handle.net/2381/45241
Title: Support varieties - an axiomatic approach
Authors: Buan, Aslak Bakke; Krause, Henning; Snashall, Nicole; Solberg, Øyvind
Abstract: We provide an axiomatic approach for studying support varieties of objects in a triangulated category via the action of a tensor triangulated category, where the tensor product is not necessarily symmetric. This is illustrated by examples, taken in particular from representation theory of finite dimensional algebras.
Description: Some of this work was presented at the Mini-Workshop ‘Support Varieties’ at Oberwolfach in
February 2009 (see [35]).2019-08-16T15:58:35ZModelling evolution of virulence in populations with a distributed parasite load
http://hdl.handle.net/2381/45240
Title: Modelling evolution of virulence in populations with a distributed parasite load
Authors: Sandhu, Simran K.; Morozov, Andrew Yu.; Farkas, József Z.
Abstract: Modelling evolution of virulence in host-parasite systems is an actively developing area of research with ever-growing literature. However, most of the existing studies overlook the fact that individuals within an infected population may have a variable infection load, i.e. infected populations are naturally structured with respect to the parasite burden. Empirical data suggests that the mortality and infectiousness of individuals can strongly depend on their infection load; moreover, the shape of distribution of infection load may vary on ecological and evolutionary time scales. Here we show that distributed infection load may have important consequences for the eventual evolution of virulence as compared to a similar model without structuring. Mathematically, we consider an SI model, where the dynamics of the infected subpopulation is described by a von Förster-type equation, in which the infection load plays the role of age. We implement the adaptive dynamics framework to predict evolutionary outcomes in this model. We demonstrate that for simple trade-off functions between virulence, disease transmission and parasite growth rates, multiple evolutionary attractors are possible. Interestingly, unlike in the case of unstructured models, achieving an evolutionary stable strategy becomes possible even for a variation of a single ecological parameter (the parasite growth rate) and keeping the other parameters constant. We conclude that evolution in disease-structured populations is strongly mediated by alterations in the overall shape of the parasite load distribution.
Description: The online version of this article (https://doi.org/10.1007/s00285-019-01351-6) contains supplementary material, which is available to authorized users.2019-08-16T15:43:08ZHow Deep Should be the Depth of Convolutional Neural Networks: a Backyard Dog Case Study
http://hdl.handle.net/2381/45168
Title: How Deep Should be the Depth of Convolutional Neural Networks: a Backyard Dog Case Study
Authors: Gorban, Alexander N.; Mirkes, Evgeny M.; Tyukin, Ivan Y.
Abstract: The work concerns the problem of reducing a pre-trained deep neuronal network to a smaller network, with just few layers, whilst retaining the network’s functionality on a given task. In this particular case study, we are focusing on the networks developed for the purposes of face recognition. The proposed approach is motivated by the observation that the aim to deliver the highest accuracy possible in the broadest range of operational conditions, which many deep neural networks models strive to achieve, may not necessarily be always needed, desired or even achievable due to the lack of data or technical constraints. In relation to the face recognition problem, we formulated an example of such a use case, the ‘backyard dog’ problem. The ‘backyard dog’, implemented by a lean network, should correctly identify members from a limited group of individuals, a ‘family’, and should distinguish between them. At the same time, the network must produce an alarm to an image of an individual who is not in a member of the family, i.e. a ‘stranger’. To produce such a lean network, we propose a network shallowing algorithm. The algorithm takes an existing deep learning model on its input and outputs a shallowed version of the model. The algorithm is non-iterative and is based on the advanced supervised principal component analysis. Performance of the algorithm is assessed in exhaustive numerical experiments. Our experiments revealed that in the above use case, the ‘backyard dog’ problem, the method is capable of drastically reducing the depth of deep learning neural networks, albeit at the cost of mild performance deterioration. In this work, we proposed a simple non-iterative method for shallowing down pre-trained deep convolutional networks. The method is generic in the sense that it applies to a broad class of feed-forward networks, and is based on the advanced supervise principal component analysis. The method enables generation of families of smaller-size shallower specialized networks tuned for specific operational conditions and tasks from a single larger and more universal legacy network.2019-08-12T10:22:29ZJordan-Lie inner ideals of finite dimensional associative algebras
http://hdl.handle.net/2381/45141
Title: Jordan-Lie inner ideals of finite dimensional associative algebras
Authors: Baranov, Alexander; Shlaka, Hasan M.
Abstract: We study Jordan-Lie inner ideals of finite dimensional associative algebras and the corresponding Lie algebras and show that they admit Levi decompositions. Moreover, we classify Jordan-Lie inner ideals satisfying a certain minimality condition and show that they are generated by pairs of idempotents.
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.2019-08-08T10:08:38ZMaximal zero product subrings and inner ideals of simple rings
http://hdl.handle.net/2381/45140
Title: Maximal zero product subrings and inner ideals of simple rings
Authors: Baranov, Alexander; Fernández López, Antonio
Abstract: Let Q be a (not necessarily unital) simple ring or algebra. A nonempty
subset S of Q is said to have zero product if S
2 = 0. We classify all maximal zero
product subsets of Q by proving that the map R 7→ R∩LeftAnn(R) is a bijection from
the set of all proper nonzero annihilator right ideals of Q onto the set of all maximal
zero product subsets of Q. We also describe the relationship between the maximal
zero product subsets of Q and the maximal inner ideals of its associated Lie algebra.
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.2019-08-08T09:37:40ZShape sensitivity analysis of metallic nano particles
http://hdl.handle.net/2381/45125
Title: Shape sensitivity analysis of metallic nano particles
Authors: Sargheini, Sahar; Paganini, Alberto; Hiptmair, Ralf; Hafner, Christian
Abstract: Shape sensitivity measures the impact of small perturbations of geometric features of a problem on certain quantities of interest. The shape sensitivity of PDE (partial differential equation) constrained output functionals is derived with the help of shape gradients. In electromagnetic scattering problems, the standard procedure of the Lagrangian approach cannot be applied because of solution of the state problem is complex valued. We derive a closed-form formula of the shape gradient of a generic output functional constrained by Maxwell's equations. We employ cubic B-splines to model local deformations of the geometry and derive sensitivity probings over the surface of the scatterer. We also define a sensitivity representative function over the surface of the scatterer on the basis of local sensitivity measurements. Several numerical experiments are conducted to investigate the shape sensitivity of different output functionals for different geometric settings.2019-08-07T09:14:59ZWeakly-normal basis vector fields in RKHS with an application to shape Newton methods
http://hdl.handle.net/2381/45111
Title: Weakly-normal basis vector fields in RKHS with an application to shape Newton methods
Authors: Paganini, Alberto; Sturm, Kevin
Abstract: We construct a space of vector fields that are normal to differentiable curves in the plane. Its basis functions are defined via saddle point variational problems in reproducing kernel Hilbert spaces (RKHSs). First, we study the properties of these basis vector fields and show how to approximate them. Then, we employ this basis to discretise shape Newton methods and investigate the impact of this discretisation on convergence rates.2019-08-05T15:31:06ZHigher-order moving mesh methods for PDE-constrained shape optimization
http://hdl.handle.net/2381/45109
Title: Higher-order moving mesh methods for PDE-constrained shape optimization
Authors: Paganini, Alberto; Wechsung, Florian; Farrell, Patrick E.
Abstract: We present a new approach to discretizing shape optimization problems that generalizes standard moving mesh methods to higher-order mesh deformations and that is naturally compatible with higher-order finite element discretizations of PDE-constraints. This shape optimization method is based on discretized deformation diffeomorphisms and allows for arbitrarily high resolution of shapes with arbitrary smoothness. Numerical experiments show that it allows the solution of PDE-constrained shape optimization problems to high accuracy.2019-08-05T15:19:10ZQuantum exceptional group G_2 and its semisimple conjugacy classes
http://hdl.handle.net/2381/45023
Title: Quantum exceptional group G_2 and its semisimple conjugacy classes
Authors: Baranov, Alexander; Mudrov, Andrey; Ostapenko, Vadim
Abstract: We construct quantization of semisimple conjugacy classes of the exceptional group
G = G2 along with and by means of their representations on highest weight modules
over the quantum group Uq(g). With every point t of a fixed maximal torus we associate
a highest weight module Mt over Uq(g) and realize the quantized polynomial algebra
of the class of t by linear operators on Mt
. Quantizations corresponding to points of
the same orbit of the Weyl group are isomorphic.
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.2019-07-30T13:35:17ZAnalysing the impact of trap shape and movement behaviour of ground-dwelling arthropods on trap efficiency
http://hdl.handle.net/2381/44947
Title: Analysing the impact of trap shape and movement behaviour of ground-dwelling arthropods on trap efficiency
Authors: Ahmed, Danish A.; Petrovskii, Sergei V.
Abstract: The most reliable estimates of the population abundance of ground-dwelling arthropods are obtained almost entirely through trap counts. Trap shape can be easily controlled by the researcher, commonly the same trap design is employed in all sites within a given study. Few researchers really try to compare abundances (numbers of collected individuals) between studies because these are heavily influenced by environmental conditions, e.g. temperature, habitat structure and food sources available, directly affecting insect movement activity. We propose that useful insights can be obtained from a theoretical-based approach. We focus on the interplay between trap shape (circle, square, slot), the underlying movement behaviour and the subsequent effect on captures. We simulate trap counts within these different geometries whilst considering movement processes with clear distinct properties, such as Brownian motion (BM), the correlated random walk (CRW) and the Lévy walk (LW). (a) We find that slot shaped traps are far less efficient than circular or square traps assuming same perimeter length, with differences which can exceed more than two-fold. Such impacts of trap geometry are only realized if insect mobility is sufficiently large, which is known to significantly vary depending on type of habitat. (b) If the movement pattern incorporates localized forward persistence then trap counts accumulate at a much slower rate, and this rate decreases further with higher persistency. (c) If the movement behaviour is of Lévy type, then fastest catch rates are recorded in the case of circular trap, and the slowest for the slot trap, indicating that trap counts can strongly depend on trap shape. Lévy walks exacerbate the impact of geometry while CRW make these differences more inconsequential. In this study we reveal trap efficiencies and how movement type can alter capture rates. Such information contributes towards improved trap count interpretations, as required in ecological studies which make use of trapping systems.
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.2019-07-24T13:51:32Zhp-adaptive discontinuous Galerkin methods for non-stationary convection–diffusion problems
http://hdl.handle.net/2381/44945
Title: hp-adaptive discontinuous Galerkin methods for non-stationary convection–diffusion problems
Authors: Cangiani, A.; Georgoulis, E. H.; Giani, S.; Metcalfe, S.
Abstract: An a posteriori error estimator for the error in the (L 2 (H 1 )+L ∞ (L 2 ))-type norm for an interior penalty discontinuous Galerkin (dG) spatial discretisation and backward Euler temporal discretisation of linear non-stationary convection–diffusion initial/boundary value problems is derived, allowing for anisotropic elements. The proposed error estimator is used to drive an hp-space–time adaptive algorithm wherein directional mesh refinement is employed to give rise to highly anisotropic elements able to accurately capture layers. The performance of the hp-space–time adaptive algorithm is assessed via a number of standard test problems characterised by sharp and/or moving layers.
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.2019-07-24T13:38:06ZSimple model of complex dynamics of activity patterns in developing networks of neuronal cultures.
http://hdl.handle.net/2381/44934
Title: Simple model of complex dynamics of activity patterns in developing networks of neuronal cultures.
Authors: Tyukin, IY; Iudin, D; Iudin, F; Tyukina, T; Kazantsev, V; Mukhina, I; Gorban, AN
Abstract: Living neuronal networks in dissociated neuronal cultures are widely known for their ability to generate highly robust spatiotemporal activity patterns in various experimental conditions. Such patterns are often treated as neuronal avalanches that satisfy the power scaling law and thereby exemplify self-organized criticality in living systems. A crucial question is how these patterns can be explained and modeled in a way that is biologically meaningful, mathematically tractable and yet broad enough to account for neuronal heterogeneity and complexity. Here we derive and analyse a simple network model that may constitute a response to this question. Our derivations are based on few basic phenomenological observations concerning the input-output behavior of an isolated neuron. A distinctive feature of the model is that at the simplest level of description it comprises of only two variables, the network activity variable and an exogenous variable corresponding to energy needed to sustain the activity, and few parameters such as network connectivity and efficacy of signal transmission. The efficacy of signal transmission is modulated by the phenomenological energy variable. Strikingly, this simple model is already capable of explaining emergence of network spikes and bursts in developing neuronal cultures. The model behavior and predictions are consistent with published experimental evidence on cultured neurons. At the larger, cellular automata scale, introduction of the energy-dependent regulatory mechanism results in the overall model behavior that can be characterized as balancing on the edge of the network percolation transition. Network activity in this state shows population bursts satisfying the scaling avalanche conditions. This network state is self-sustainable and represents energetic balance between global network-wide processes and spontaneous activity of individual elements.
Description: Numerical experiments data as well as relevant codes can be accessed via https://github.com/tt51Storage/Simple-model-of-complex-dynamics-in-neuronal-cultures. All other relevant data are within the manuscript and its Supporting Information files.2019-07-24T08:34:55ZContravariant form on tensor product of highest weight modules
http://hdl.handle.net/2381/44772
Title: 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 "Lévy or diffusion" Controversy: How important is the movement pattern in the context of trapping?
http://hdl.handle.net/2381/44706
Title: 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 Ecology
http://hdl.handle.net/2381/44705
Title: 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 PDE
http://hdl.handle.net/2381/44629
Title: 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 manifolds
http://hdl.handle.net/2381/44622
Title: 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-vectors
http://hdl.handle.net/2381/44601
Title: 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.
http://hdl.handle.net/2381/44569
Title: 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.
http://hdl.handle.net/2381/44561
Title: 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 processes
http://hdl.handle.net/2381/44416
Title: 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 Paradox
http://hdl.handle.net/2381/44415
Title: 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.2019-06-14T13:06:34ZClassifying Matchbox Manifolds
http://hdl.handle.net/2381/44171
Title: 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 foundations
http://hdl.handle.net/2381/44167
Title: 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)
http://hdl.handle.net/2381/44158
Title: 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 surfaces
http://hdl.handle.net/2381/44143
Title: 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 algebras
http://hdl.handle.net/2381/44142
Title: 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 growth
http://hdl.handle.net/2381/44141
Title: 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 Spaces
http://hdl.handle.net/2381/44136
Title: 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 fragmentation
http://hdl.handle.net/2381/44133
Title: 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 revisited
http://hdl.handle.net/2381/44131
Title: 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 -systems
http://hdl.handle.net/2381/44129
Title: 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 haiku
http://hdl.handle.net/2381/44128
Title: 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 fans
http://hdl.handle.net/2381/44127
Title: 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 Representations
http://hdl.handle.net/2381/44126
Title: 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-vectors
http://hdl.handle.net/2381/44125
Title: 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 minors
http://hdl.handle.net/2381/44124
Title: 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 coefficients
http://hdl.handle.net/2381/44122
Title: 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 polygons
http://hdl.handle.net/2381/44121
Title: 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 Categories
http://hdl.handle.net/2381/43951
Title: 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.2019-04-30T14:57:03ZOne-trial correction of legacy AI systems and stochastic separation theorems
http://hdl.handle.net/2381/43913
Title: 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.2019-04-26T15:36:19ZTransient phenomena in ecology.
http://hdl.handle.net/2381/43753
Title: 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 spectrometry
http://hdl.handle.net/2381/43736
Title: 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 England
http://hdl.handle.net/2381/43712
Title: 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 theorems
http://hdl.handle.net/2381/43705
Title: 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 systems
http://hdl.handle.net/2381/43689
Title: 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 stones
http://hdl.handle.net/2381/43515
Title: 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 approach
http://hdl.handle.net/2381/43511
Title: 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.2019-03-07T11:10:10Z