DSpace Collection:
http://hdl.handle.net/2381/3823
Tue, 19 Jun 2018 03:09:06 GMT2018-06-19T03:09:06ZOn local super-penalization of interior penalty discontinuous Galerkin methods
http://hdl.handle.net/2381/42423
Title: On local super-penalization of interior penalty discontinuous Galerkin methods
Authors: Cangiani, Andrea; Chapman, John; Georgoulis, Emmanuil; Jensen, Max
Abstract: We prove in an abstract setting that standard (continuous) Galerkin finite element
approximations are the limit of interior penalty discontinuous Galerkin approximations as the
penalty parameter tends to infinity. We apply this result to equations of non-negative characteristic
form and the non-linear, time dependent system of incompressible miscible displacement.
Moreover, we investigate varying the penalty parameter on only a subset of a triangulation and the
effects of local super-penalization on the stability of the method, resulting in a partly continuous,
partly discontinuous method in the limit. An iterative automatic procedure is also proposed for
the determination of the continuous region of the domain without loss of stability of the method.
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.Wed, 06 Jun 2018 13:49:00 GMThttp://hdl.handle.net/2381/424232018-06-06T13:49:00ZHilbert's sixth problem: the endless road to rigour
http://hdl.handle.net/2381/42374
Title: Hilbert's sixth problem: the endless road to rigour
Authors: Gorban, A. N.
Abstract: In this introduction, the essence of the sixth problem is discussed and the content of this issue is introduced.
This article is part of the theme issue ‘Hilbert’s sixth problem’.Mon, 04 Jun 2018 11:48:44 GMThttp://hdl.handle.net/2381/423742018-06-04T11:48:44ZCritical domain problem for the reaction-telegraph equation model of population dynamics
http://hdl.handle.net/2381/42272
Title: Critical domain problem for the reaction-telegraph equation model of population dynamics
Authors: Alharbi, Weam; Petrovskii, Sergei
Abstract: A telegraph equation is believed to be an appropriate model of population dynamics as it accounts for the directional persistence of individual animal movement. Being motivated by the problem of habitat fragmentation, which is known to be a major threat to biodiversity that causes species extinction worldwide, we consider the reaction-telegraph equation (i.e., telegraph equation combined with the population growth) on a bounded domain with the goal to establish the conditions of species survival. We first show analytically that, in the case of linear growth, the expression for the domain's critical size coincides with the critical size of the corresponding reaction-diffusion model. We then consider two biologically relevant cases of nonlinear growth, i.e., the logistic growth and the growth with a strong Allee effect. Using extensive numerical simulations, we show that in both cases the critical domain size of the reaction-telegraph equation is larger than the critical domain size of the reaction-diffusion equation. Finally, we discuss possible modifications of the model in order to enhance the positivity of its solutions.Thu, 24 May 2018 14:23:47 GMThttp://hdl.handle.net/2381/422722018-05-24T14:23:47ZModel reduction in chemical dynamics: slow invariant manifolds, singular perturbations, thermodynamic estimates, and analysis of reaction graph
http://hdl.handle.net/2381/42215
Title: Model reduction in chemical dynamics: slow invariant manifolds, singular perturbations, thermodynamic estimates, and analysis of reaction graph
Authors: Gorban, A. N.
Abstract: The paper has two goals: (1) It presents basic ideas, notions, and methods for reduction of reaction kinetics models: quasi-steady-state, quasi-equilibrium, slow invariant manifolds, and limiting steps.(2) It describes briefly the current state of the art and some latest achievements in the broad area of model reduction in chemical and biochemical kinetics, including new results in methods of invariant manifolds, computation singular perturbation, bottleneck methods, asymptotology, tropical equilibration, and reaction mechanism skeletonization.
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.Fri, 18 May 2018 12:22:38 GMThttp://hdl.handle.net/2381/422152018-05-18T12:22:38ZSemiclassical regularization of Vlasov equations and wavepackets for nonlinear Schrödinger equations
http://hdl.handle.net/2381/42208
Title: Semiclassical regularization of Vlasov equations and wavepackets for nonlinear Schrödinger equations
Authors: Athanassoulis, Agissilaos
Abstract: We consider the semiclassical limit of nonlinear Schrödinger equations with initial data that are well localized in both position and momentum (non-parametric wavepackets). We recover the Wigner measure (WM) of the problem, a macroscopic phase-space density which controls the propagation of the physical observables such as mass, energy and momentum. WMs have been used to create effective models for wave propagation in: random media, quantum molecular dynamics, mean field limits, and the propagation of electrons in graphene. In nonlinear settings, the Vlasov-type equations obtained for the WM are often ill-posed on the physically interesting spaces of initial data. In this paper we are able to select the measure-valued solution of the 1 + 1 dimensional Vlasov-Poisson equation which correctly captures the semiclassical limit, thus finally resolving the non-uniqueness in the seminal result of Zhang et al (2012 Comm. Pure Appl. Math. 55 582-632). The same approach is also applied to the Vlasov-Dirac-Benney equation with small wavepacket initial data, extending several known results.
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.Fri, 18 May 2018 09:04:48 GMThttp://hdl.handle.net/2381/422082018-05-18T09:04:48ZFirst Measurement of Several β-Delayed Neutron Emitting Isotopes Beyond N=126.
http://hdl.handle.net/2381/42176
Title: First Measurement of Several β-Delayed Neutron Emitting Isotopes Beyond N=126.
Authors: Caballero-Folch, R.; Domingo-Pardo, C.; Agramunt, J.; Algora, A.; Ameil, F.; Arcones, A.; Ayyad, Y.; Benlliure, J.; Borzov, I. N.; Bowry, M.; Calviño, F.; Cano-Ott, D.; Cortés, G.; Davinson, T.; Dillmann, I.; Estrade, A.; Evdokimov, A.; Faestermann, T.; Farinon, F.; Galaviz, D.; García, A. R.; Geissel, H.; Gelletly, W.; Gernhäuser, R.; Gómez-Hornillos, M. B.; Guerrero, C.; Heil, M.; Hinke, C.; Knöbel, R.; Kojouharov, I.; Kurcewicz, J.; Kurz, N.; Litvinov, Y. A.; Maier, L.; Marganiec, J.; Marketin, T.; Marta, M.; Martínez, T.; Martínez-Pinedo, G.; Montes, F.; Mukha, I.; Napoli, D. R.; Nociforo, C.; Paradela, C.; Pietri, S.; Podolyák, Z.; Prochazka, A.; Rice, S.; Riego, A.; Rubio, B.; Schaffner, H.; Scheidenberger, C.; Smith, K.; Sokol, E.; Steiger, K.; Sun, B.; Taín, J. L.; Takechi, M.; Testov, D.; Weick, H.; Wilson, E.; Winfield, J. S.; Wood, R.; Woods, P.; Yeremin, A.
Abstract: The β-delayed neutron emission probabilities of neutron rich Hg and Tl nuclei have been measured together with β-decay half-lives for 20 isotopes of Au, Hg, Tl, Pb, and Bi in the mass region N≳126. These are the heaviest species where neutron emission has been observed so far. These measurements provide key information to evaluate the performance of nuclear microscopic and phenomenological models in reproducing the high-energy part of the β-decay strength distribution. This provides important constraints on global theoretical models currently used in r-process nucleosynthesis.Wed, 16 May 2018 14:16:04 GMThttp://hdl.handle.net/2381/421762018-05-16T14:16:04ZRole of the Δ Resonance in the Population of a Four-Nucleon State in the ^{56}Fe→^{54}Fe Reaction at Relativistic Energies
http://hdl.handle.net/2381/42158
Title: Role of the Δ Resonance in the Population of a Four-Nucleon State in the ^{56}Fe→^{54}Fe Reaction at Relativistic Energies
Authors: Podolyák, Z.; Shand, C. M.; Lalović, N.; Gerl, J.; Rudolph, D.; Alexander, T.; Boutachkov, P.; Cortés, M. L.; Górska, M.; Kojouharov, I.; Kurz, N.; Louchart, C.; Merchán, E.; Michelagnoli, C.; Pérez-Vidal, R. M.; Pietri, S.; Ralet, D.; Reese, M.; Schaffner, H.; Stahl, C.; Weick, H.; Ameil, F.; de Angelis, G.; Arici, T.; Carroll, R.; Dombrádi, Z.; Gadea, A.; Golubev, P.; Lettmann, M.; Lizarazo, C.; Mahboub, D.; Pai, H.; Patel, Z.; Pietralla, N.; Regan, P. H.; Sarmiento, L. G.; Wieland, O.; Wilson, Emma; Birkenbach, B.; Bruyneel, B.; Burrows, I.; Charles, L.; Clément, E.; Crespi, F. C. L.; Cullen, D. M.; Désesquelles, P.; Eberth, J.; González, V.; Habermann, T.; Harkness-Brennan, L.; Hess, H.; Judson, D. S.; Jungclaus, A.; Korten, W.; Labiche, M.; Maj, A.; Mengoni, D.; Napoli, D. R.; Pullia, A.; Quintana, B.; Rainovski, G.; Reiter, P.; Salsac, M. D.; Sanchis, E.; Valiente Dóbon, J. J.
Abstract: The ^{54}Fe nucleus was populated from a ^{56}Fe beam impinging on a Be target with an energy of E/A=500 MeV. The internal decay via γ-ray emission of the 10^{+} metastable state was observed. As the structure of this isomeric state has to involve at least four unpaired nucleons, it cannot be populated in a simple two-neutron removal reaction from the ^{56}Fe ground state. The isomeric state was produced in the low-momentum (-energy) tail of the parallel momentum (energy) distribution of ^{54}Fe, suggesting that it was populated via the decay of the Δ^{0} resonance into a proton. This process allows the population of four-nucleon states, such as the observed isomer. Therefore, it is concluded that the observation of this 10^{+} metastable state in ^{54}Fe is a consequence of the quark structure of the nucleons.Tue, 15 May 2018 15:39:20 GMThttp://hdl.handle.net/2381/421582018-05-15T15:39:20ZPreference similarity network structural equivalence clustering based consensus group decision making model
http://hdl.handle.net/2381/42094
Title: Preference similarity network structural equivalence clustering based consensus group decision making model
Authors: Kamis, Nor Hanimah; Chiclana, Francisco; Levesley, Jeremy
Abstract: Social network analysis (SNA) methods have been developed to analyse social structures and patterns of network relationships, although they have been least explored and/or exploited purposely for decision-making processes. In this study, we bridge a gap between SNA and consensus-based decision making by defining undirected weighted preference network from the similarity of expert preferences using the concept of 'structural equivalence'. Structurally equivalent experts are represented using the agglomerative hierarchical clustering algorithm with complete link function, thus intra-clusters' experts are high in density and inter-clusters' experts are rich in sparsity. We derive cluster consensus based on internal and external cohesions, while group consensus is obtained by identifying the highest level consensus at optimal level of clustering. Thus, the clustering based approach to consensus measure contributes to present homogeneity of experts preferences as a whole. In the event of insufficient group consensus state, we construct a feedback mechanism procedure based on clustering that consists of three main phases: (1) identification of experts that contribute less to consensus; (2) identification of a leader in the network; and (3) advice generation. We make use of the centrality concept in SNA as a way of determining the most important person in a network, who is presented as a leader to provide advices in the feedback process. It is proved that the implementation of the proposed feedback mechanism increases consensus and, because of the bounded condition of consensus measure, convergence to sufficient group agreement is guaranteed. The centrality concept is also applied in the construction of a new aggregation operator, namely as cent-IOWA operator, that is used to derive the collective preference relation from which the feasible alternative of consensus solution, based on the concept of dominance, is achieved according to a majority of the central experts in the network, which is represented in this paper by the linguistic quantifier '. most of.' For validation purposes, an existing literature study is used to perform a comparative analysis from which conclusions are drawn and explained.Mon, 14 May 2018 07:56:05 GMThttp://hdl.handle.net/2381/420942018-05-14T07:56:05ZReduced fusion systems over p-groups with abelian subgroup of index p: II
http://hdl.handle.net/2381/42066
Title: Reduced fusion systems over p-groups with abelian subgroup of index p: II
Authors: Semeraro, Jason; Oliver, Bob; Craven, David A.
Abstract: Let p be an odd prime, and let S be a p-group with a unique elementary abelian subgroup A of index p. We classify the simple fusion systems over all such groups S in which A is essential. The resulting list, which depends on the classification of finite simple groups, includes a large variety of new, exotic simple fusion 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.Thu, 10 May 2018 14:49:50 GMThttp://hdl.handle.net/2381/420662018-05-10T14:49:50ZBasic model of purposeful kinesis
http://hdl.handle.net/2381/42061
Title: Basic model of purposeful kinesis
Authors: Gorban, Alexander N.; Cabukoglu, N.
Abstract: The notions of taxis and kinesis are introduced and used to describe two types of behaviour of an organism in non-uniform conditions: (i) Taxis means the guided movement to more favourable conditions; (ii) Kinesis is the non-directional change in space motion in response to the change of conditions. Migration and dispersal of animals has evolved under control of natural selection. In a simple formalisation, the strategy of dispersal should increase Darwinian fitness. We introduce new models of purposeful kinesis with diffusion coefficient dependent on fitness. The local and instant evaluation of Darwinian fitness is used, the reproduction coefficient. New models include one additional parameter, intensity of kinesis, and may be considered as the minimal models of purposeful kinesis. The properties of models are explored by a series of numerical experiments. It is demonstrated how kinesis could be beneficial for assimilation of patches of food or of periodic fluctuations. Kinesis based on local and instant estimations of fitness is not always beneficial: for species with the Allee effect it can delay invasion and spreading. It is proven that kinesis cannot modify stability of homogeneous positive steady states.
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.Thu, 10 May 2018 14:09:42 GMThttp://hdl.handle.net/2381/420612018-05-10T14:09:42ZRegularization of Mickelsson generators for nonexceptional quantum groups
http://hdl.handle.net/2381/42045
Title: Regularization of Mickelsson generators for nonexceptional quantum groups
Authors: Mudrov, Andrey I
Abstract: Let g′ ⊂ g be a pair of Lie algebras of either symplectic or orthogonal infinitesimal endomorphisms of the complex vector spaces C N−2 ⊂ C N and U q (g′) ⊂ U q (g) be a pair of quantum groups with a triangular decomposition U q (g) = U q (g-)U q (g+)U q (h). Let Z q (g, g′) be the corresponding step algebra. We assume that its generators are rational trigonometric functions h ∗ → U q (g±). We describe their regularization such that the resulting generators do not vanish for any choice of the weight.
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.Thu, 10 May 2018 09:34:58 GMThttp://hdl.handle.net/2381/420452018-05-10T09:34:58ZRecovered finite element methods
http://hdl.handle.net/2381/42043
Title: Recovered finite element methods
Authors: Georgoulis, Emmanuil H.; Pryer, Tristan
Abstract: We introduce a family of Galerkin finite element methods which are constructed via recovery operators over element-wise discontinuous approximation spaces. This new family, termed collectively as recovered finite element methods (R-FEM) has a number of attractive features over both classical finite element and discontinuous Galerkin approaches, most important of which is its potential to produce stable conforming approximations in a variety of settings. Moreover, for special choices of recovery operators, R-FEM produces the same approximate solution as the classical conforming finite element method, while, trivially, one can recast (primal formulation) discontinuous Galerkin methods. A priori error bounds are shown for linear second order boundary value problems, verifying the optimality of the proposed method. Residual-type a posteriori bounds are also derived, highlighting the potential of R-FEM in the context of adaptive computations. Numerical experiments highlight the good approximation properties of the method in practice. A discussion on the potential use of R-FEM in various settings is also included.
Description: The file associated with this record is under embargo until 24 months after publication, in accordance with the publisher's self-archiving policy. The full text may be available through the publisher links provided above.Thu, 10 May 2018 09:00:31 GMThttp://hdl.handle.net/2381/420432018-05-10T09:00:31ZThe cycle polynomial of a permutation group
http://hdl.handle.net/2381/42027
Title: The cycle polynomial of a permutation group
Authors: Cameron, Peter J.; Semeraro, Jason
Abstract: The cycle polynomial of a finite permutation group G is the generating function
for the number of elements of G with a given number of cycles:
FG(x) = X
g∈G
x
c(g)
,
where c(g) is the number of cycles of g on Ω. In the first part of the paper, we
develop basic properties of this polynomial, and give a number of examples.
In the 1970s, Richard Stanley introduced the notion of reciprocity for pairs of
combinatorial polynomials. We show that, in a considerable number of cases, there
is a polynomial in the reciprocal relation to the cycle polynomial of G; this is the
orbital chromatic polynomial of Γ and G, where Γ is a G-invariant graph, introduced
by the first author, Jackson and Rudd. We pose the general problem of finding all
such reciprocal pairs, and give a number of examples and characterisations: the
latter include the cases where Γ is a complete or null graph or a tree.
The paper concludes with some comments on other polynomials associated with
a permutation group.
Description: Mathematics Subject Classifications: 20B05, 05C31Wed, 09 May 2018 11:58:38 GMThttp://hdl.handle.net/2381/420272018-05-09T11:58:38ZFusion systems over a Sylow p-subgroup of G 2 (p) G2(p)
http://hdl.handle.net/2381/41936
Title: Fusion systems over a Sylow p-subgroup of G 2 (p) G2(p)
Authors: Parker, Chris; Semeraro, Jason
Abstract: For S a Sylow p-subgroup of the group G2 (p) for p odd, up to isomorphism of fusion systems, we determine all saturated fusion systems F on S with O p (F) = 1. For p≠7, all such fusion systems are realized by finite groups whereas for p=7 there are 29 saturated fusion systems of which 27 are exotic.Thu, 03 May 2018 09:23:09 GMThttp://hdl.handle.net/2381/419362018-05-03T09:23:09ZHigh-Dimensional Brain: A Tool for Encoding and Rapid Learning of Memories by Single Neurons
http://hdl.handle.net/2381/41920
Title: High-Dimensional Brain: A Tool for Encoding and Rapid Learning of Memories by Single Neurons
Authors: Tyukin, Ivan; Gorban, Alexander N.; Calvo, Carlos; Makarova, Julia; Makarov, Valeri A.
Abstract: Codifying memories is one of the fundamental problems of modern Neuroscience. The functional mechanisms behind this phenomenon remain largely unknown. Experimental evidence suggests that some of the memory functions are performed by stratified brain structures such as the hippocampus. In this particular case, single neurons in the CA1 region receive a highly multidimensional input from the CA3 area, which is a hub for information processing. We thus assess the implication of the abundance of neuronal signalling routes converging onto single cells on the information processing. We show that single neurons can selectively detect and learn arbitrary information items, given that they operate in high dimensions. The argument is based on stochastic separation theorems and the concentration of measure phenomena. We demonstrate that a simple enough functional neuronal model is capable of explaining: (i) the extreme selectivity of single neurons to the information content, (ii) simultaneous separation of several uncorrelated stimuli or informational items from a large set, and (iii) dynamic learning of new items by associating them with already "known" ones. These results constitute a basis for organization of complex memories in ensembles of single neurons. Moreover, they show that no a priori assumptions on the structural organization of neuronal ensembles are necessary for explaining basic concepts of static and dynamic memories.Wed, 02 May 2018 15:22:57 GMThttp://hdl.handle.net/2381/419202018-05-02T15:22:57ZExtremal twist and tensor product of highest weight modules
http://hdl.handle.net/2381/41871
Title: Extremal twist and tensor product of highest weight modules
Authors: Mudrov, Andrey
Abstract: We give a criterion for complete reducibility of tensor product of two highest weight modules over a quantum group. It is found to be controlled by an extremal twist operator related to the Shapovalov inverse of either of the modules. As an application, we construct homogeneous vector bundles over quantum projective spaces $\mathbb{P}^n$ on $\mathbb{C}$-homs between certain parabolic Verma modules. Using an alternative realization of $\mathbb{C}_q[\mathbb{P}^n]$ as a subalgebra in $\mathbb{C}_q[GL(n+1)]$, we reformulate quantum vector bundles in terms of symmetric pairs. In this way, we prove complete reducibility of modules over the 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.Tue, 01 May 2018 09:27:12 GMThttp://hdl.handle.net/2381/418712018-05-01T09:27:12ZOscillations in Aggregation-Shattering Processes
http://hdl.handle.net/2381/41826
Title: Oscillations in Aggregation-Shattering Processes
Authors: Matveev, S. A.; Krapivsky, P. L.; Smirnov, A. P.; Tyrtyshnikov, E. E.; Brilliantov, Nikolai V.
Abstract: We observe never-ending oscillations in systems undergoing collision-controlled aggregation and shattering. Specifically, we investigate aggregation-shattering processes with aggregation kernels Ki,j=(i/j)a+(j/i)a and shattering kernels Fi,j=λKi,j, where i and j are cluster sizes, and parameter λ quantifies the strength of shattering. When 0≤a<1/2, there are no oscillations, and the system monotonically approaches a steady state for all values of λ; in this region, we obtain an analytical solution for the stationary cluster size distribution. Numerical solutions of the rate equations show that oscillations emerge in the 1/2<a≤1 range. When λ is sufficiently large, oscillations decay and eventually disappear, while for λ<λc(a), oscillations apparently persist forever. Thus, never-ending oscillations can arise in closed aggregation-shattering processes without sinks and sources of particles.Mon, 30 Apr 2018 08:58:54 GMThttp://hdl.handle.net/2381/418262018-04-30T08:58:54ZPhase transitions in systems with aggregation and shattering
http://hdl.handle.net/2381/41804
Title: Phase transitions in systems with aggregation and shattering
Authors: Krapivsky, P. L.; Otieno, W.; Brilliantov, Nikolai V.
Abstract: We consider a system of clusters made of elementary building blocks, monomers, and evolving via collisions between diffusing monomers and immobile composite clusters. In our model, the cluster-monomer collision can lead to the attachment of the monomer to the cluster (addition process) or to the total breakup of the cluster (shattering process). A phase transition, separating qualitatively different behaviors, occurs when the probability of shattering events exceeds a certain threshold. The novel feature of the phase transition is the dramatic dependence on the initial conditions.Fri, 27 Apr 2018 12:17:12 GMThttp://hdl.handle.net/2381/418042018-04-27T12:17:12ZIncreasing temperature of cooling granular gases
http://hdl.handle.net/2381/41751
Title: Increasing temperature of cooling granular gases
Authors: Brilliantov, Nikolai V.; Formella, Arno; Pöschel, Thorsten
Abstract: The kinetic energy of a force-free granular gas decays monotonously due to inelastic collisions of the particles. For a homogeneous granular gas of identical particles, the corresponding decay of granular temperature is quantified by Haff's law. Here, we report that for a granular gas of aggregating particles, the granular temperature does not necessarily decay but may even increase. Surprisingly, the increase of temperature is accompanied by the continuous loss of total gas energy. This stunning effect arises from a subtle interplay between decaying kinetic energy and gradual reduction of the number of degrees of freedom associated with the particles' dynamics. We derive a set of kinetic equations of Smoluchowski type for the concentrations of aggregates of different sizes and their energies. We find scaling solutions to these equations and a condition for the aggregation mechanism predicting growth of temperature. Numerical direct simulation Monte Carlo results confirm the theoretical predictions.Wed, 25 Apr 2018 15:03:29 GMThttp://hdl.handle.net/2381/417512018-04-25T15:03:29ZStar-product on complex sphere $\mathbb{S}^{2n}$
http://hdl.handle.net/2381/41677
Title: Star-product on complex sphere $\mathbb{S}^{2n}$
Authors: Mudrov, Andrey
Abstract: We construct a $U_q(\mathrm{so}(2n+1))$-equivariant local star-product on the complex sphere $\mathbb{S}^{2n}$ as a Non-Levi conjugacy class $SO(2n+1)/SO(2n)$.Mon, 23 Apr 2018 13:43:50 GMThttp://hdl.handle.net/2381/416772018-04-23T13:43:50ZRegression analysis: likelihood, error and entropy
http://hdl.handle.net/2381/41459
Title: Regression analysis: likelihood, error and entropy
Authors: Grechuk, Bogdan; Zabarankin, Michael
Abstract: In a regression with independent and identically distributed normal residuals, the log-likelihood function yields an empirical form of the L2L2-norm, whereas the normal distribution can be obtained as a solution of differential entropy maximization subject to a constraint on the L2L2-norm of a random variable. The L1L1-norm and the double exponential (Laplace) distribution are related in a similar way. These are examples of an “inter-regenerative” relationship. In fact, L2L2-norm and L1L1-norm are just particular cases of general error measures introduced by Rockafellar et al. (Finance Stoch 10(1):51–74, 2006) on a space of random variables. General error measures are not necessarily symmetric with respect to ups and downs of a random variable, which is a desired property in finance applications where gains and losses should be treated differently. This work identifies a set of all error measures, denoted by EE, and a set of all probability density functions (PDFs) that form “inter-regenerative” relationships (through log-likelihood and entropy maximization). It also shows that M-estimators, which arise in robust regression but, in general, are not error measures, form “inter-regenerative” relationships with all PDFs. In fact, the set of M-estimators, which are error measures, coincides with EE. On the other hand, M-estimators are a particular case of L-estimators that also arise in robust regression. A set of L-estimators which are error measures is identified—it contains EE and the so-called trimmed LpLp-norms.
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.Fri, 06 Apr 2018 09:00:07 GMThttp://hdl.handle.net/2381/414592018-04-06T09:00:07ZBlessing of dimensionality: mathematical foundations of the statistical physics of data
http://hdl.handle.net/2381/41439
Title: Blessing of dimensionality: mathematical foundations of the statistical physics of data
Authors: Gorban, A. N.; Tyukin, I. Y.
Abstract: The concentrations of measure phenomena were discovered as the mathematical background to statistical mechanics at the end of the nineteenth/beginning of the twentieth century and have been explored in mathematics ever since. At the beginning of the twenty-first century, it became clear that the proper utilization of these phenomena in machine learning might transform the curse of dimensionality into the blessing of dimensionality. This paper summarizes recently discovered phenomena of measure concentration which drastically simplify some machine learning problems in high dimension, and allow us to correct legacy artificial intelligence systems. The classical concentration of measure theorems state that i.i.d. random points are concentrated in a thin layer near a surface (a sphere or equators of a sphere, an average or median-level set of energy or another Lipschitz function, etc.). The new stochastic separation theorems describe the thin structure of these thin layers: the random points are not only concentrated in a thin layer but are all linearly separable from the rest of the set, even for exponentially large random sets. The linear functionals for separation of points can be selected in the form of the linear Fisher’s discriminant. All artificial intelligence systems make errors. Non-destructive correction requires separation of the situations (samples) with errors from the samples corresponding to correct behaviour by a simple and robust classifier. The stochastic separation theorems provide us with such classifiers and determine a non-iterative (one-shot) procedure for their construction.
This article is part of the theme issue ‘Hilbert’s sixth problem’.Thu, 05 Apr 2018 10:27:34 GMThttp://hdl.handle.net/2381/414392018-04-05T10:27:34ZNonparametric regression method with functional covariates and multivariate response
http://hdl.handle.net/2381/41347
Title: Nonparametric regression method with functional covariates and multivariate response
Authors: Wang, Bo; Omar, Kurdistan M. T.
Abstract: Nonparametric regression methods have been widely studied in functional regression analysis in the context of functional covariates and univariate response, but it is not the case for functional covariates with multivariate response. In this paper, we present two new solutions for the latter problem: the first is to directly extend the nonparametric method for univariate response to multivariate response, and in the second, the correlation among different responses is incorporated into the model. The asymptotic properties of the estimators are studied, and the effectiveness of the proposed methods is demonstrated through several simulation studies and a real data example.
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.Thu, 22 Mar 2018 09:49:53 GMThttp://hdl.handle.net/2381/413472018-03-22T09:49:53ZSensitivity Analysis in Applications with Deviation, Risk, Regret, and Error Measures
http://hdl.handle.net/2381/41299
Title: Sensitivity Analysis in Applications with Deviation, Risk, Regret, and Error Measures
Authors: Grechuk, Bogdan; Zabarankin, Michael
Abstract: The envelope formula is obtained for optimization problems with positively homogeneous convex functionals defined on a space of random variables. Those problems include linear regression with general error measures and optimal portfolio selection with the objective function being either a general deviation measure or a coherent risk measure subject to a constraint on the expected rate of return. The obtained results are believed to be novel even for Markowitz's mean-variance portfolio selection but are far more general and include explicit envelope relationships for the rates of return of portfolios that minimize lower semivariance, mean absolute deviation, deviation measures of ${\cal L}^p$-type and semi-${\cal L}^p$ type, and conditional value-at-risk. In each case, the envelope theorem yields explicit estimates for the absolute value of the difference between deviation/risk of optimal portfolios with the unperturbed and perturbed asset probability distributions in terms of a norm of the perturbation.Tue, 13 Mar 2018 15:48:19 GMThttp://hdl.handle.net/2381/412992018-03-13T15:48:19ZAdaptive discontinuous Galerkin methods for elliptic interface problems
http://hdl.handle.net/2381/41277
Title: Adaptive discontinuous Galerkin methods for elliptic interface problems
Authors: Cangiani, Andrea; Georgoulis, Emmanuil H.; Sabawi, Younis A.
Abstract: An interior-penalty discontinuous Galerkin (dG) method for an elliptic interface problem involving, possibly, curved interfaces, with flux-balancing interface conditions, e.g., modelling mass transfer of solutes through semi-permeable membranes, is considered. The method allows for extremely general curved element shapes employed to resolve the interface geometry exactly. A residual-type a posteriori error estimator for this dG method is proposed and upper and lower bounds of the error in the respective dG-energy norm are proven. The a posteriori error bounds are subsequently used to prove a basic a priori convergence result. The theory presented is complemented by a series of numerical experiments. The presented approach applies immediately to the case of curved domains with non-essential boundary conditions, too.Mon, 12 Mar 2018 09:48:43 GMThttp://hdl.handle.net/2381/412772018-03-12T09:48:43ZGeneration of mechanical force by grafted polyelectrolytes in an electric field: application to polyelectrolyte-based nano-devices
http://hdl.handle.net/2381/41270
Title: Generation of mechanical force by grafted polyelectrolytes in an electric field: application to polyelectrolyte-based nano-devices
Authors: Brilliantov, Nikolai V.; Budkov, Y. A.; Seidel, C.
Abstract: We analyse theoretically and by means of molecular dynamics (MD) simulations the generation of mechanical force by a polyelectrolyte (PE) chain grafted to a plane. The PE is exposed to an external electric field that favours its adsorption on the plane. The free end of the chain is linked to a deformable target body. By varying the field, one can alter the length of the non-adsorbed part of the chain. This entails variation of the deformation of the target body and hence variation of the force arising in the body. Our theoretical predictions for the generated force are in very good agreement with the MD data. Using the theory developed for the generated force, we study the effectiveness of possible PE-based nano-vices, composed of two clenching planes connected by PEs and exposed to an external electric field. We exploit the Cundall–Strack solid friction model to describe the friction between a particle and the clenching planes. We compute the diffusion coefficient of a clenched particle and show that it drastically decreases even in weak applied fields. This demonstrates the efficacy of the PE-based nano-vices, which may be a possible alternative to the existing nanotube nano-tweezers and optical tweezers.Wed, 07 Mar 2018 13:37:53 GMThttp://hdl.handle.net/2381/412702018-03-07T13:37:53ZExplicit Parameter-dependent Representations of Periodic Solutions for a Class of Nonlinear Systems
http://hdl.handle.net/2381/41208
Title: Explicit Parameter-dependent Representations of Periodic Solutions for a Class of Nonlinear Systems
Authors: Mohammed, J. Al-Ameri; Tyukin, I.
Abstract: We propose a method for deriving computationally efficient representations of periodic solutions of parameterized systems of nonlinear ordinary differential equations. These representations depend on parameters of the system explicitly, as quadratures of parameterized computable functions. The method applies to systems featuring both linear and nonlinear parametrization, and time-varying right-hand-side; it opens possibilities to invoke scalable parallel computations for numerical evaluation of solutions for various parameter values. Application of the method to parameter estimation problems is illustrated with constructing an algorithm for state and parameter estimation for the Morris-Lecar system.Mon, 19 Feb 2018 16:48:15 GMThttp://hdl.handle.net/2381/412082018-02-19T16:48:15ZSelf-organisation of small-world networks by adaptive rewiring in response to graph diffusion
http://hdl.handle.net/2381/41207
Title: Self-organisation of small-world networks by adaptive rewiring in response to graph diffusion
Authors: Jarman, Nicholas; Steur, Erik; Trengove, Chris; Tyukin, Ivan Y.; Van Leeuwen, Cees
Abstract: Complex networks emerging in natural and human-made systems tend to assume small-world structure. Is there a common mechanism underlying their self-organisation? Our computational simulations show that network diffusion (traffic flow or information transfer) steers network evolution towards emergence of complex network structures. The emergence is effectuated through adaptive rewiring: progressive adaptation of structure to use, creating short-cuts where network diffusion is intensive while annihilating underused connections. With adaptive rewiring as the engine of universal small-worldness, overall diffusion rate tunes the systems' adaptation, biasing local or global connectivity patterns. Whereas the former leads to modularity, the latter provides a preferential attachment regime. As the latter sets in, the resulting small-world structures undergo a critical shift from modular (decentralised) to centralised ones. At the transition point, network structure is hierarchical, balancing modularity and centrality - a characteristic feature found in, for instance, the human brain.
Description: Supplementary information accompanies this paper at https://doi.org/10.1038/s41598-017-12589-9Mon, 19 Feb 2018 16:38:51 GMThttp://hdl.handle.net/2381/412072018-02-19T16:38:51ZPatchy, not patchy, or how much patchy? Classification of spatial patterns appearing in a model of biological invasion
http://hdl.handle.net/2381/41157
Title: Patchy, not patchy, or how much patchy? Classification of spatial patterns appearing in a model of biological invasion
Authors: Petrovskaya, N.; Petrovskii, S.; Zhang, W.
Abstract: Good understanding of spatiotemporal patterns of species spread during biological invasion is needed for efficient monitoring and control of harmful alien pests. Various growth-dispersal-type models of population dynamics predict that invasive species spread can follow two qualitatively different scenarios such as the propagation of a continuous population front and the “no-front” patchy invasion. Distinguishing between these two patterns of spread is important, in particular because the patchy invasion poses a much greater challenge for monitoring and control. However, a mathematical theory of the patchy invasion is missing and it remains unclear what are the restrictions on parameter values and how much different this dynamical regime is from the continuous front propagation. In this paper, we address these issues in terms of a biologically meaningful mathematical model consisting of two coupled integral-difference equations. We show that the relevant domain of the parameter space has a complex intermittent structure. We also suggest a criterion that can be used to distinguish between the patchy invasion and the continuous front propagation: the patchy-invasion spatial pattern is shown to be much more sensitive to the cutoff at low densities.Tue, 13 Feb 2018 15:03:04 GMThttp://hdl.handle.net/2381/411572018-02-13T15:03:04ZOn the calibration of the Schwartz two-factor model to WTI crude oil options and the extended Kalman Filter
http://hdl.handle.net/2381/41156
Title: On the calibration of the Schwartz two-factor model to WTI crude oil options and the extended Kalman Filter
Authors: Ewald, Christian-Oliver; Zhang, Aihua; Zong, Zhe
Abstract: The Schwartz (J Finance 52(3):923–973, 1997) two factor model serves as a benchmark for pricing commodity contracts, futures and options. It is normally calibrated to fit the term-structure of a range of future contracts with varying maturities. In this paper, we investigate the effects on parameter estimates, if the model is fitted to prices of options, with varying maturities and strikes instead of futures, as is commonly done. The use of option prices rather than futures in the calibration leads to non-linearities, which the standard Kalman filter approach is unable to cope with. To overcome these issues, we use the extended Kalman Filter. We find that some parameters sensitively depend on the choice of strikes of the corresponding options, and are different from those estimates obtained from using futures prices. This effect is analogue to varying implied volatilities in the Black–Scholes model. This realization is important, as the use of ill-fitted models for pricing options in the Schwartz (1997) framework may cause traders to bear serious financial losses.Tue, 13 Feb 2018 14:52:38 GMThttp://hdl.handle.net/2381/411562018-02-13T14:52:38ZThe homology core of matchbox manifolds and invariant measures
http://hdl.handle.net/2381/41146
Title: The homology core of matchbox manifolds and invariant measures
Authors: Clark, Alex; Hunton, John
Abstract: Here we shall consider the topology and dynamics associated to a wide class of matchbox manifolds, including a large selection of tiling spaces and all minimal matchbox manifolds of dimension one. For such spaces we introduce topological invariants related to their expansions as an inverse sequence of simplicial complexes. These invariants are related to corresponding inverse sequences of groups arising from applying the top--dimension homology to these sequences. In many cases this leads to a computable invariant based on an inverse sequence of matrices. Significantly, we show that when the space is obtained by suspending a topologically transitive action of the fundamental group $\G$ of a closed orientable on a zero--dimensional compact space this invariant at the same time corresponds to the space of Borel measures on the Cantor set which are invariant under the action of $\G$. This leads to connections between the rank of homology groups we consider and the number of invariant, ergodic Borel probability measures for such actions. We illustrate with several examples how these invariants can be calculated and used for topological classification and how it leads to an understanding of the invariant measures.
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.Mon, 12 Feb 2018 17:07:06 GMThttp://hdl.handle.net/2381/411462018-02-12T17:07:06ZTowards developing a general framework for modelling vertical migration in zooplankton
http://hdl.handle.net/2381/41118
Title: Towards developing a general framework for modelling vertical migration in zooplankton
Authors: Morozov, Andrew Y.; Kuzenkov, Oleg A.
Abstract: Diel vertical migration (DVM) of zooplankton is a widespread phenomenon in both oceans and lakes, and
is generally considered to be the largest synchronized movement of biomass on Earth. Most existing
mathematical models of DVM are based on the assumption that animals maximize a certain criterion
such as the expected reproductive value, the venturous revenue, the ratio of energy gain/mortality or
some predator avoidance function when choosing their instantaneous depth. The major shortcoming of
this general point of view is that the predicted DVM may be strongly affected by a subjective choice of a
particular optimization criterion. Here we argue that the optimal strategy of DVM can be unambiguously
obtained as an outcome of selection in the underlying equations of genotype/traits frequency dynamics.
Using this general paradigm, we explore the optimal strategy for the migration across different depths by
zooplankton grazers throughout the day. To illustrate our ideas we consider four generic DVM models,
each making different assumptions on the population dynamics of zooplankton, and demonstrate that in
each model we need to maximize a particular functional to find the optimal strategy. Surprisingly,
patterns of DVM obtained for different models greatly differ in terms of their parameters dependence.
We then show that the infinite dimensional trait space of different zooplankton trajectories can be
projected onto a low dimensional space of generalized parameters and the genotype evolution dynamics
can be easily followed using this low-dimensional space. Using this space of generalized parameters we
explore the influence of mutagenesis on evolution of DVM, and we show that strong mutagenesis allows
the coexistence of an infinitely large number of strategies whereas for weak mutagenesis the selection
results in the extinction of most strategies, with the surviving strategies all staying close to the optimal
strategy in the corresponding mutagenesis-free systemThu, 08 Feb 2018 09:49:13 GMThttp://hdl.handle.net/2381/411182018-02-08T09:49:13ZSize distribution of particles in Saturn's rings from aggregation and fragmentation
http://hdl.handle.net/2381/41102
Title: Size distribution of particles in Saturn's rings from aggregation and fragmentation
Authors: Brilliantov, Nikolai; Krapivsky, P. L.; Bodrova, Anna; Spahn, Frank; Hayakawa, Hisao; Stadnichuk, Vladimir; Schmidt, Jurgen
Abstract: Saturn's rings consist of a huge number of water ice particles, with a tiny addition of rocky material. They form a flat disk, as the result of an interplay of angular momentum conservation and the steady loss of energy in dissipative interparticle collisions. For particles in the size range from a few centimeters to a few meters, a power-law distribution of radii, ~r(-q) with q ≈ 3, has been inferred; for larger sizes, the distribution has a steep cutoff. It has been suggested that this size distribution may arise from a balance between aggregation and fragmentation of ring particles, yet neither the power-law dependence nor the upper size cutoff have been established on theoretical grounds. Here we propose a model for the particle size distribution that quantitatively explains the observations. In accordance with data, our model predicts the exponent q to be constrained to the interval 2.75 ≤ q ≤ 3.5. Also an exponential cutoff for larger particle sizes establishes naturally with the cutoff radius being set by the relative frequency of aggregating and disruptive collisions. This cutoff is much smaller than the typical scale of microstructures seen in Saturn's rings.Tue, 06 Feb 2018 12:09:55 GMThttp://hdl.handle.net/2381/411022018-02-06T12:09:55ZMechanism of Chain Collapse of Strongly Charged Polyelectrolytes
http://hdl.handle.net/2381/41101
Title: Mechanism of Chain Collapse of Strongly Charged Polyelectrolytes
Authors: Tom, Anvy Moly; Vemparala, Satyavani; Rajesh, R.; Brilliantov, Nikolai V.
Abstract: We perform extensive molecular dynamics simulations of a charged polymer in a good solvent in the
regime where the chain is collapsed. We analyze the dependence of the gyration radius Rg on the reduced
Bjerrum length lB and find two different regimes. In the first one, called a weak electrostatic regime,
Rg ∼ l−1=2
B , which is consistent only with the predictions of the counterion-fluctuation theory. In the second
one, called a strong electrostatic regime, we find Rg ∼ l−1=5
B . To explain the novel regime we modify the
counterion-fluctuation theory.Tue, 06 Feb 2018 11:56:20 GMThttp://hdl.handle.net/2381/411012018-02-06T11:56:20ZConway groupoids and completely transitive codes
http://hdl.handle.net/2381/41056
Title: Conway groupoids and completely transitive codes
Authors: Gill, Nick; Gillespie, Neil I.; Semeraro, Jason
Abstract: To each supersimple 2−(n,4,λ) design D one associates a ‘Conway groupoid’, which may
be thought of as a natural generalisation of Conway’s Mathieu groupoid M13 which is
constructed from P3.
We show that Sp2m(2) and 22m.Sp2m(2) naturally occur as Conway groupoids associated
to certain designs. It is shown that the incidence matrix associated to one of these
designs generates a new family of completely transitive F2-linear codes with minimum
distance 4 and covering radius 3, whereas the incidence matrix of the other design gives
an alternative construction of a previously known family of completely transitive codes.
We also give a new characterization of M13 and prove that, for a fixed λ > 0, there
are finitely many Conway groupoids for which the set of morphisms does not contain all
elements of the full alternating group.
Description: Mathematics Subject Classification (2010): 20B15, 20B25, 05B05; 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.Mon, 29 Jan 2018 17:35:23 GMThttp://hdl.handle.net/2381/410562018-01-29T17:35:23ZTournaments, 4-uniform hypergraphs, and an exact extremal result
http://hdl.handle.net/2381/41055
Title: Tournaments, 4-uniform hypergraphs, and an exact extremal result
Authors: Gunderson, Karen; Semeraro, Jason
Abstract: We consider 4-uniform hypergraphs with the maximum number of hyperedges subject to the condition that every set of 5 vertices spans either 0 or exactly 2 hyperedges and give a construction, using quadratic residues, for an infinite family of such hypergraphs with the maximum number of hyperedges. Baber has previously given an asymptotically best-possible result using random tournaments. We give a connection between Baber's result and our construction via Paley tournaments and investigate a ‘switching’ operation on tournaments that preserves hypergraphs arising from this construction.
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.Mon, 29 Jan 2018 17:31:24 GMThttp://hdl.handle.net/2381/410552018-01-29T17:31:24ZCharacterization of melting properties of several Fe-C model potentials
http://hdl.handle.net/2381/41040
Title: Characterization of melting properties of several Fe-C model potentials
Authors: Melnykov, Mykhailo; Davidchack, Ruslan L.
Abstract: We use the coexisting phases approach to calculate melting phase diagrams of several Fe-C interaction potentials, such as Embedded Atom Method (EAM) potential of Lau et al. [Phys. Rev. Lett. 98 (2007) 215501], EAM potential of Hepburn and Ackland [Phys. Rev. B 78 (2008) 165115] , and two flavours of the Analytic Bond Order potential (ABOP) of Henriksson and Nordlund [Phys. Rev. B 79 (2009) 144107]. Melting of both bcc (ferrite) and fcc (austenite) crystals is investigated with C concentrations up to 5 wt%. The results are compared with the experimental data and suggest that the potential of Hepburn and Ackland is the most accurate in reproducing the melting phase diagram of the ferrite, although the austenite cannot be stabilized at any C concentration for this potential. The potential of Lau et al. yields the best qualitative agreement with the real phase diagram in that the ferrite-liquid coexistence at low C concentrations is replaced by the austenite-liquid coexistence at higher C concentrations. However, the crossover C concentration is much larger and the ferrite melting temperature is much higher than in the real Fe-C alloy. The ABOP of Henriksson and Nordlund without the Ziegler-Biersack-Littmark (ZBL) correction correctly predicts the relative stability of ferrite and austenite at melting, but significantly underestimates the solubility of C in the solid phases, while the same potential with the ZBL correction predicts the austenite to be more stable compared to the ferrite at all C concentrations near the melting transition.
Description: Supplementary data associated with this article can be found, in the online version, at https://doi.org/10.1016/j.commatsci.2017.12.052.Fri, 26 Jan 2018 17:06:43 GMThttp://hdl.handle.net/2381/410402018-01-26T17:06:43ZNew Findings on Key Factors Influencing the UK's Referendum on Leaving the EU
http://hdl.handle.net/2381/40932
Title: New Findings on Key Factors Influencing the UK's Referendum on Leaving the EU
Authors: Zhang, Aihua
Abstract: The UK’s EU in/out referendum raised significant debate and speculation of the intention of the electorate
and its motivations in voting; much of this debate was informed by simple data analysis examining individual
factors, in isolation, and using opinion polling data. This, in the case of the EU referendum where
multiple factors influence the decision simultaneously, failed to predict the eventual outcome. On June
23, 2016, Britain’s vote to leave the EU came as a surprise to most observers, with a bigger voter turnout
than that of any UK general election in the past decade. In this research, we apply multivariate regression
analysis and a Logit Model to real voting data to identify statistically significant factors influencing the EU
referendum voting preference simultaneously as well as the odd ratio in favor of Leave. Visualizations of
the key findings are also provided with heat maps and graphs. We find that higher education is the predominant factor dividing the nation, with a marginal effect on the referendum decision being stronger than any other factors particularly in England and Wales, where most Leave voters reside. An increase of about 3% in the proportion of British adults accessing to higher education in England and Wales could have reversed the referendum result in the UK. We also find that areas in England and Wales with a lower unemployment rate tend to have a higher turnout to support
Leave while areas in Scotland and Northern Ireland with a higher proportion of university-educated
British adults have a higher turnout to support Remain. Further we find that areas with high proportions
of British male adults show a higher percentage of Leave votes. A higher proportion of elderly British contributes
to a higher percentage of Leave votes, but does not lead to Leave outcomes on their own.
Description: The file associated with this record is under embargo until 24 months after publication, in accordance with the publisher's self-archiving policy. The full text may be available through the publisher links provided above.Wed, 17 Jan 2018 13:11:27 GMThttp://hdl.handle.net/2381/409322018-01-17T13:11:27ZWedderburn-Malcev decomposition of one-sided ideals of finite dimensional algebras
http://hdl.handle.net/2381/40922
Title: Wedderburn-Malcev decomposition of one-sided ideals of finite dimensional algebras
Authors: Baranov, A. A.; Mudrov, A.; Shlaka, H. M.
Abstract: Let $A$ be a finite dimensional associative algebra over a perfect field and let $R$ be the radical of $A$. We show that for every one-sided ideal I of A there is a semisimple subalgebra $S$ of $A$ such that $I=I_S\oplus I_R$ where $I_S=I\cap S$ and $I_R=I\cap R$.
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.Wed, 17 Jan 2018 11:33:53 GMThttp://hdl.handle.net/2381/409222018-01-17T11:33:53ZAnalysis of discontinuous Galerkin methods using mesh-dependent norms and applications to problems with rough data
http://hdl.handle.net/2381/40909
Title: Analysis of discontinuous Galerkin methods using mesh-dependent norms and applications to problems with rough data
Authors: Georgoulis, Emmanuil H.; Pryer, Tristan
Abstract: We prove the inf-sup stability of a discontinuous Galerkin scheme for second order elliptic operators in (unbalanced) mesh-dependent norms for quasi-uniform meshes for all spatial dimensions. This results in a priori error bounds in these norms. As an application we examine some problems with rough source term where the solution can not be characterised as a weak solution and show quasi-optimal error control.Wed, 17 Jan 2018 10:10:28 GMThttp://hdl.handle.net/2381/409092018-01-17T10:10:28ZTheoretical and numerical analysis of nano-actuators based on grafted polyelectrolytes in an electric field
http://hdl.handle.net/2381/40847
Title: Theoretical and numerical analysis of nano-actuators based on grafted polyelectrolytes in an electric field
Authors: Brilliantov, Nikolai V.; Budkov, Y. A.; Seidel, C.
Abstract: We analyze, theoretically and by means of molecular dynamics (MD) simulations, the generation of mechanical force by a polyelectrolyte (PE) chain grafted to a plane and exposed to an external electric field; the free end of the chain is linked to a deformable target body. Varying the field, one can alter the length of the non-adsorbed (bulk) part of the chain and hence the deformation of the target body and the arising force. We focus on the impact of added salt on the magnitude of the generated force, which is especially important for applications. In particular, we develop a simple variational theory for the double layer formed near electrodes to compute the electric field acting on the bulk part of the chain. Our theoretical predictions agree well with the MD simulations. Next, we study the effectiveness of possible PE-based nano-vices, comprised of two clenching planes connected by PEs exposed to an external electric field. We analyze a novel phenomenon – two-dimensional diffusion of a nano-particle, clenched between two planes, and introduce a quantitative criterion for clenching efficiency, the clenching coefficient. It is defined as a logarithm of the ratio of the diffusion coefficients of a free and clenched particle. Using first a microscopic counterpart of the Coulomb friction model, and then a novel microscopic model based on surface phonons, with the vibration direction normal to the surface, we calculate the clenching coefficient as a function of the external electric field. Our results demonstrate a dramatic decrease of the diffusion coefficient of a clenched nano-particle for the range of parameters relevant for applications; this proves the effectiveness of the PE-based nano-vices.Thu, 11 Jan 2018 13:51:17 GMThttp://hdl.handle.net/2381/408472018-01-11T13:51:17ZOrthogonal basis for the Shapovalov form on U-q (sl(n+1))
http://hdl.handle.net/2381/40845
Title: Orthogonal basis for the Shapovalov form on U-q (sl(n+1))
Authors: Mudrov, Andrey
Abstract: Let U be either the classical or quantized universal enveloping algebra of the Lie algebra sl(n + 1) extended over the field of fractions of the Cartan subalgebra. We suggest a PBW basis in U over the extended Cartan subalgebra diagonalizing the contravariant Shapovalov form on generic Verma module. The matrix coefficients of the form are calculated and the inverse form is explicitly constructed.Thu, 11 Jan 2018 12:32:41 GMThttp://hdl.handle.net/2381/408452018-01-11T12:32:41ZHilbert's 6th Problem: exact and approximate hydrodynamic manifolds for kinetic equations
http://hdl.handle.net/2381/40822
Title: Hilbert's 6th Problem: exact and approximate hydrodynamic manifolds for kinetic equations
Authors: Gorban, Alexander N; Karlin, Ilya
Abstract: The problem of the derivation of hydrodynamics from the Boltzmann
equation and related dissipative systems is formulated as the problem
of a slow invariant manifold in the space of distributions. We review a few
instances where such hydrodynamic manifolds were found analytically both as
the result of summation of the Chapman–Enskog asymptotic expansion and by
the direct solution of the invariance equation. These model cases, comprising
Grad’s moment systems, both linear and nonlinear, are studied in depth in
order to gain understanding of what can be expected for the Boltzmann equation.
Particularly, the dispersive dominance and saturation of dissipation rate
of the exact hydrodynamics in the short-wave limit and the viscosity modification
at high divergence of the flow velocity are indicated as severe obstacles to
the resolution of Hilbert’s 6th Problem. Furthermore, we review the derivation
of the approximate hydrodynamic manifold for the Boltzmann equation using
Newton’s iteration and avoiding smallness parameters, and compare this to
the exact solutions. Additionally, we discuss the problem of projection of the
Boltzmann equation onto the approximate hydrodynamic invariant manifold
using entropy concepts. Finally, a set of hypotheses is put forward where we
describe open questions and set a horizon for what can be derived exactly or
proven about the hydrodynamic manifolds for the Boltzmann equation in the
future.Thu, 11 Jan 2018 09:10:47 GMThttp://hdl.handle.net/2381/408222018-01-11T09:10:47ZDirect data-based decision making under uncertainty
http://hdl.handle.net/2381/40793
Title: Direct data-based decision making under uncertainty
Authors: Grechuk, Bogdan; Zabarankin, Michael
Abstract: In a typical one-period decision making model under uncertainty, unknown consequences are modeled as random variables. However, accurately estimating probability distributions of the involved random variables from historical data is rarely possible. As a result, decisions made may be suboptimal or even unacceptable in the future. Also, an agent may not view data occurred at different time moments, e.g. yesterday and one year ago, as equally probable. The agent may apply a so-called “time” profile (weights) to historical data. To address these issues, an axiomatic framework for decision making based directly on historical time series is presented. It is used for constructing data-based analogues of mean-variance and maxmin utility approaches to optimal portfolio selection.
Description: The file associated with this record is under embargo until 24 months after publication, in accordance with the publisher's self-archiving policy. The full text may be available through the publisher links provided above.Wed, 10 Jan 2018 09:54:13 GMThttp://hdl.handle.net/2381/407932018-01-10T09:54:13ZGeometric integrator for Langevin systems with quaternion-based rotational degrees of freedom and hydrodynamic interactions.
http://hdl.handle.net/2381/40791
Title: Geometric integrator for Langevin systems with quaternion-based rotational degrees of freedom and hydrodynamic interactions.
Authors: Davidchack, R. L.; Ouldridge, T. E.; Tretyakov, M. V.
Abstract: We introduce new Langevin-type equations describing the rotational and translational motion of rigid bodies interacting through conservative and non-conservative forces and hydrodynamic coupling. In the absence of non-conservative forces, the Langevin-type equations sample from the canonical ensemble. The rotational degrees of freedom are described using quaternions, the lengths of which are exactly preserved by the stochastic dynamics. For the proposed Langevin-type equations, we construct a weak 2nd order geometric integrator that preserves the main geometric features of the continuous dynamics. The integrator uses Verlet-type splitting for the deterministic part of Langevin equations appropriately combined with an exactly integrated Ornstein-Uhlenbeck process. Numerical experiments are presented to illustrate both the new Langevin model and the numerical method for it, as well as to demonstrate how inertia and the coupling of rotational and translational motion can introduce qualitatively distinct behaviours.
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.Wed, 10 Jan 2018 09:43:04 GMThttp://hdl.handle.net/2381/407912018-01-10T09:43:04ZPseudo-outcrop Visualization of Borehole Images and Core Scans
http://hdl.handle.net/2381/40768
Title: Pseudo-outcrop Visualization of Borehole Images and Core Scans
Authors: Mirkes, Evgeny M.; Gorban, Alexander N.; Levesley, Jeremy; Elkington, Peter A. S.; Whetton, James A.
Abstract: A pseudo-outcrop visualization is demonstrated for borehole and full-diameter rock core images to augment the ubiquitous unwrapped cylinder view and thereby assist nonspecialist interpreters. The pseudo-outcrop visualization is equivalent to a nonlinear projection of the image from borehole to earth frame of reference that creates a solid volume sliced longitudinally to reveal two or more faces in which the orientations of geological features indicate what is observed in the subsurface. A proxy for grain size is used to modulate the external dimensions of the plot to mimic profiles seen in real outcrops. The volume is created from a mixture of geological boundary elements and texture, the latter being the residue after the sum of boundary elements is subtracted from the original data. In the case of measurements from wireline microresistivity tools, whose circumferential coverage is substantially <100 %, the missing circumferential data are first inpainted using multiscale directional transforms, which decompose the image into its elemental building structures, before reconstructing the full image. The pseudo-outcrop view enables direct observation of the angular relationships between features and aids visual comparison between borehole and core images, especially for the interested nonspecialist.
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.Tue, 09 Jan 2018 11:49:11 GMThttp://hdl.handle.net/2381/407682018-01-09T11:49:11ZPatterns of invasive species spread in a landscape with a complex geometry
http://hdl.handle.net/2381/40746
Title: Patterns of invasive species spread in a landscape with a complex geometry
Authors: Alharbi, Weam; Petrovskii, Sergei
Abstract: Patterns and rates of invasive species spread have been a focus of attention for several decades. Majority of studies focused on the species proliferation in a relatively uniform "open space" thus leaving aside the effects of the landscape geometry as given by size and shape of inaccessible areas. In this paper, we address this issue by considering the spatiotemporal dynamics of an alien species in a domain where two large uniform habitats are connected by a narrow corridor. We consider the case where the species is originally introduced into one of the habitats but not to the other. The alien species is assumed to be affected by a predator, so that mathematically our system consists of two coupled diffusion-reaction equations. We show that the corridor tends to slow down the spread: it takes the alien population an extra time to penetrate through the corridor, and this delay time can be significant in the case of patchy spread. We also show that a sufficiently narrow corridor blocks the spread; simple analytical estimates for the critical width of the corridor are obtained. Finally, we show that the corridor can become a refuge for the alien population. If considered on a longer timescale that includes species adaptation and/or climate change, the corridor may then become a source of a secondary invasion.
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.Mon, 08 Jan 2018 16:34:27 GMThttp://hdl.handle.net/2381/407462018-01-08T16:34:27ZDecomposition spaces, incidence algebras and Möbius inversion III: the decomposition space of Möbius intervals
http://hdl.handle.net/2381/40684
Title: Decomposition spaces, incidence algebras and Möbius inversion III: the decomposition space of Möbius intervals
Authors: Gálvez-Carrillo, Imma; Kock, Joachim; Tonks, Andrew
Abstract: Decomposition spaces are simplicial ∞-groupoids subject to a certain
exactness condition, needed to induce a coalgebra structure on the space of arrows.
Conservative ULF functors (CULF) between decomposition spaces induce
coalgebra homomorphisms. Suitable added finiteness conditions define the notion
of Möbius decomposition space, a far-reaching generalisation of the notion of
Möbius category of Leroux. In this paper, we show that the Lawvere–Menni Hopf
algebra of Möbius intervals, which contains the universal Möbius function (but is
not induced by a Möbius category), can be realised as the homotopy cardinality
of a Möbius decomposition space U of all Möbius intervals, and that in a certain
sense U is universal for Möbius decomposition spaces and CULF functors.
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.Mon, 18 Dec 2017 14:36:54 GMThttp://hdl.handle.net/2381/406842017-12-18T14:36:54ZA posteriori error estimates for the virtual element method
http://hdl.handle.net/2381/40683
Title: A posteriori error estimates for the virtual element method
Authors: Cangiani, Andrea; Georgoulis, Emmanuil H.; Pryer, Tristan; Sutton, Oliver J.
Abstract: An posteriori error analysis for the virtual element method (VEM) applied to general elliptic problems is presented. The resulting error estimator is of residual-type and applies on very general polygonal/polyhedral meshes. The estimator is fully computable as it relies only on quantities available from the VEM solution, namely its degrees of freedom and element-wise polynomial projection. Upper and lower bounds of the error estimator with respect to the VEM approximation error are proven. The error estimator is used to drive adaptive mesh refinement in a number of test problems. Mesh adaptation is particularly simple to implement since elements with consecutive co-planar edges/faces are allowed and, therefore, locally adapted meshes do not require any local mesh post-processing.Mon, 18 Dec 2017 14:26:58 GMThttp://hdl.handle.net/2381/406832017-12-18T14:26:58ZHow priors of initial hyperparameters affect Gaussian process regression models
http://hdl.handle.net/2381/40631
Title: How priors of initial hyperparameters affect Gaussian process regression models
Authors: Chen, Zexun; Wang, Bo
Abstract: The hyperparameters in Gaussian process regression (GPR) model with a specified kernel are often estimated from the data via the maximum marginal likelihood. Due to the non-convexity of marginal likelihood with respect to the hyperparameters, the optimisation may not converge to the global maxima. A common approach to tackle this issue is to use multiple starting points randomly selected from a specific prior distribution. As a result the choice of prior distribution may play a vital role in the predictability of this approach. However, there exists little research in the literature to study the impact of the prior distributions on the hyperparameter estimation and the performance of GPR. In this paper, we provide the first empirical study on this problem using simulated and real data experiments. We consider different types of priors for the initial values of hyperparameters for some commonly used kernels and investigate the influence of the priors on the predictability of GPR models. The results reveal that, once a kernel is chosen, different priors for the initial hyperparameters have no significant impact on the performance of GPR prediction, despite that the estimates of the hyperparameters are very different to the true values in some cases.
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.Tue, 28 Nov 2017 14:12:55 GMThttp://hdl.handle.net/2381/406312017-11-28T14:12:55Z