Matematisk institutt
http://hdl.handle.net/10852/6
Sat, 19 Oct 2019 10:37:56 GMT2019-10-19T10:37:56ZPitfalls of machine learning for tail events in high risk environments
http://hdl.handle.net/10852/70337
Pitfalls of machine learning for tail events in high risk environments
Agrell, Christian; Eldevik, Simen; Hafver, Andreas; Pedersen, Frank Børre; Stensrud, Erik; Huseby, Arne
Most of today’s Machine Learning (ML) methods and implementations are based on correlations, in the sense of a statistical relationship between a set of inputs and the output(s) under inves- tigation. The relationship might be obscure to the human mind, but through the use of ML, mathematics and statistics makes it seemingly apparent. However, to base safety critical decisions on such methods suffer from the same pitfalls as decisions based on any other correlation metric that disregards causality. Causality is key to ensure that applied mitigation tactics will actually affect the outcome in the desired way. This paper reviews the current situation and challenges of applying ML in high risk environments. It further outlines how phenomenological knowledge, together with an uncertainty-based risk perspective can be incorporated to alleviate the missing causality considerations in current practice.; Pitfalls of machine learning for tail events in high risk environments
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10852/703372018-01-01T00:00:00ZDecidable and Undecidable Fragments of First-Order Concatenation Theory
http://hdl.handle.net/10852/69677
Decidable and Undecidable Fragments of First-Order Concatenation Theory
Kristiansen, Lars; Murwanashyaka, Juvenal
We identify a number of decidable and undecidable fragments of first-order concatenation theory. We also give a purely universal axiomatization which is complete for the fragments we identify. Furthermore, we prove some normal-form results.
This is a post-peer-review, pre-copyedit version of an article. The final authenticated version is available online at: https://link.springer.com/
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10852/696772018-01-01T00:00:00ZNica–Toeplitz algebras associated with product systems over right LCM semigroups
http://hdl.handle.net/10852/69247
Nica–Toeplitz algebras associated with product systems over right LCM semigroups
Larsen, Nadia S.; Kwasniewski, Bartosz K.
We prove uniqueness of representations of Nica–Toeplitz algebras associated to product systems of C∗-correspondences over right LCM semigroups by applying our previous abstract uniqueness results developed for C∗-precategories. Our results provide an interpretation of conditions identified in work of Fowler and Fowler– Raeburn, and apply also to their crossed product twisted by a product system, in the new context of right LCM semigroups, as well as to a new, Doplicher–Roberts type C∗-algebra associated to the Nica–Toeplitz algebra. As a derived construction we develop Nica–Toeplitz crossed products by actions with completely positive maps. This provides a unified framework for Nica–Toeplitz semigroup crossed products by endomorphisms and by transfer operators. We illustrate these two classes of examples with semigroup C∗-algebras of right and left semidirect products.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10852/692472018-01-01T00:00:00ZMajor concerns about late hypothermia study
http://hdl.handle.net/10852/69117
Major concerns about late hypothermia study
Walløe, Lars; Hjort, Nils Lid; Thoresen, Marianne
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10852/691172018-01-01T00:00:00ZPractical Convergence Rates for Degenerate Parabolic Equations
http://hdl.handle.net/10852/68797
Practical Convergence Rates for Degenerate Parabolic Equations
Karlsen, Kenneth Hvistendahl; Risebro, Nils Henrik; Storrøsten, Erlend Briseid
We investigate the convergence rates of numerical schemes for degenerate convection diffusion equations. Recent results bound these rates as 1∕3 in one space dimension and 2∕(19 + d) in several space dimension. In our numerical experiments, we obtain much better rates, indicating that the theoretical bounds are not optimal.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10852/687972017-01-01T00:00:00ZCrossed products by Hecke Pairs
http://hdl.handle.net/10852/68793
Crossed products by Hecke Pairs
Palma, Rui Miguel Coutinho
We develop a theory of crossed products by actions of Hecke pairs (G, Γ), motivated by applications in non-abelian C ∗ -duality. Our approach gives back the usual crossed product construction whenever G/Γ is a group and retains many of the aspects of crossed products by groups. We start by laying the ∗ -algebraic foundations of these crossed products by Hecke pairs and exploring their representation theory, and then proceed to study their different C ∗ -completions. We establish that our construction coincides with that of Laca, Larsen and Neshveyev [15] whenever they are both definable and, as an application of our theory, we prove a Stonevon Neumann theorem for Hecke pairs which encompasses the work of an Huef, Kaliszewski and Raeburn [9].
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10852/687932018-01-01T00:00:00ZA plea for taking all available clinical information into account when assessing the predictive value of omics data
http://hdl.handle.net/10852/68771
A plea for taking all available clinical information into account when assessing the predictive value of omics data
Volkmann, Alexander; De Bin, Riccardo; Sauerbrei, Willi; Boulesteix, Anne-Laure
Background: Omics data can be very informative in survival analysis and may improve the prognostic ability of classical models based on clinical risk factors for various diseases, for example breast cancer. Recent research has focused on integrating omics and clinical data, yet has often ignored the need for appropriate model building for clinical variables. Medical literature on classical prognostic scores, as well as biostatistical literature on appropriate model selection strategies for low dimensional (clinical) data, are often ignored in the context of omics research. The goal of this paper is to fill this methodological gap by investigating the added predictive value of gene expression data for models using varying amounts of clinical information.
Methods: We analyze two data sets from the field of survival prognosis of breast cancer patients. First, we construct several proportional hazards prediction models using varying amounts of clinical information based on established medical knowledge. These models are then used as a starting point (i.e. included as a clinical offset) for identifying informative gene expression variables using resampling procedures and penalized regression approaches (model based boosting and the LASSO). In order to assess the added predictive value of the gene signatures, measures of prediction accuracy and separation are examined on a validation data set for the clinical models and the models that combine the two sources of information.
Results: For one data set, we do not find any substantial added predictive value of the omics data when compared to clinical models. On the second data set, we identify a noticeable added predictive value, however only for scenarios where little or no clinical information is included in the modeling process. We find that including more clinical information can lead to a smaller number of selected omics predictors.
Conclusions: New research using omics data should include all available established medical knowledge in order to allow an adequate evaluation of the added predictive value of omics data. Including all relevant clinical information in the analysis might also lead to more parsimonious models. The developed procedure to assess the predictive value of the omics data can be readily applied to other scenarios.
Keywords: Data integration, Cox regression, Model building
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10852/687712019-01-01T00:00:00ZModel uncertainty stochastic mean-field control
http://hdl.handle.net/10852/68604
Model uncertainty stochastic mean-field control
Agram, Nacira; Øksendal, Bernt
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10852/686042018-01-01T00:00:00ZAn investigation into the interaction between waves and ice
http://hdl.handle.net/10852/67624
An investigation into the interaction between waves and ice
Rabault, Jean
The polar regions are the focus of increased attention due to a combination of environmental, political and economic reasons. In order to help support human activities in the arctic and monitor the state of the ecosystem, detailed understanding and models of the state of sea ice are necessary. Sea ice is affected by incoming waves, and therefore studying wave-ice interaction is an important part of this effort. In my thesis work, I investigated how waves propagate through different types of ice covers.
More specifically, two phenomena of practical importance were studied. First, I looked at how waves attenuate as they propagate through sea ice. This, in turn, determines how much ice can be broken by incoming waves and should be part of waves and ice forecasts. Second, I investigated the currents created under the ice as a consequence of the propagation of the waves. There it was shown experimentally that mean currents can arise, which are expected to play a role in the dispersion of nutriments and pollutants.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10852/676242018-01-01T00:00:00ZExperiments on wave propagation in grease ice: combined wave gauges and particle image velocimetry measurements
http://hdl.handle.net/10852/67612
Experiments on wave propagation in grease ice: combined wave gauges and particle image velocimetry measurements
Rabault, Jean; Sutherland, Graig J.; Jensen, Atle; Christensen, Kai Håkon; Marchenko, Aleksey
Water wave attenuation by grease ice is a key mechanism for the polar regions, as waves in ice influence many phenomena such as ice drift, ice breaking and ice formation. However, the models presented so far in the literature are limited in a number of regards, and more insights are required from either laboratory experiments or fieldwork for these models to be validated and improved. Unfortunately, performing detailed measurements of wave propagation in grease ice, either in the field or in the laboratory, is challenging. As a consequence, laboratory data are relatively scarce, and often consist of only a couple of wave elevation measurements along the length of the wave tank. We present combined measurements of wave elevation using an array of ultrasonic probes, and water kinematics using particle image velocimetry (PIV), in a small-scale wave tank experiment. Experiments are performed over a wider frequency range than has been previously investigated. The wave elevation measurements are used to compute the wavenumber and exponential damping coefficient. In contrast to a previous study in grease ice, we find that the wavenumber is consistent with the mass loading model, i.e. it increases compared with the open water case. Wave attenuation is compared with a series of one-layer models, and we show that they satisfactorily describe the viscous damping occurring. PIV data are also consistent with exponential wave amplitude attenuation, and a proper orthogonal decomposition analysis reveals the existence of mean flows under the ice that are a consequence of the displacement and packing of the ice induced by the gradient in the wave-induced stress. Finally, we show that the dynamics of grease ice can generate eddy structures that inject eddy viscosity into the water under the grease ice, which would lead to enhanced mixing and participating in energy dissipation.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10852/676122019-01-01T00:00:00ZCurving to fly: Synthetic adaptation unveils optimal flight performance of whirling fruits
http://hdl.handle.net/10852/67611
Curving to fly: Synthetic adaptation unveils optimal flight performance of whirling fruits
Rabault, Jean; Fauli, Richard Andre; Carlson, Andreas
Appendages of seeds, fruits and other diaspores (dispersal units) are essential for their wind dispersal, as they act as wings and enable them to fly. Whirling fruits generate an auto-gyrating motion from their sepals, a leaf like structure, which curve upwards and outwards, creating a lift force that counteracts gravitational force. The link of the fruit’s sepal shape to flight performance, however, is as yet unknown. We develop a theoretical model and perform experiments for doublewinged bio-mimetic 3D-printed fruits, where we assume that the plant has a limited amount of energy that it can convert into a mass to build sepals and, additionally, allow them to curve. Both hydrodynamic theory and experiments involving synthetic, double-winged fruits show that to produce a maximal flight time there is an optimal fold angle for the desiccated sepals. A similar sepal fold angle is found for a wide range of whirling fruits collected in the wild, highlighting that wing curvature can aid as an efficient mechanism for wind dispersal of seeds and may improve the fitness of their producers in the context of an ecological strategy.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10852/676112019-01-01T00:00:00ZArtificial neural networks trained through deep reinforcement learning discover control strategies for active flow control
http://hdl.handle.net/10852/67610
Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control
Rabault, Jean; Kuchta, Miroslav; Jensen, Atle; Reglade, Ulysse; Cerardi, Nicolas
We present the first application of an Artificial Neural Network trained through a Deep Reinforcement Learning agent to perform active flow control. It is shown that, in a 2D simulation of the Kármán vortex street at moderate Reynolds number (Re = 100), our Artificial Neural Network is able to learn an active control strategy from experimenting with the mass flow rates of two jets on the sides of a cylinder. By interacting with the unsteady wake, the Artificial Neural Network successfully stabilizes the vortex alley and reduces drag by about 8 %. This is performed while using small mass flow rates for the actuation, on the order of 0.5 % of the mass flow rate intersecting the cylinder cross section once a new pseudo-periodic shedding regime is found. This opens the way to a new class of methods for performing active flow control.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10852/676102019-01-01T00:00:00ZModulational instability and rogue waves in crossing sea states
http://hdl.handle.net/10852/67534
Modulational instability and rogue waves in crossing sea states
Gramstad, Odin; Bitner-Gregersen, Elzbieta; Trulsen, Karsten; Nieto Borge, Jose Carlos
Wave statistical properties and occurrence of extreme and rogue waves in crossing sea states are investigated. Compared to previous studies a more extensive set of crossing sea states are investigated, both with respect to spectral shape of the individual wave systems and with respect to the crossing angle and separation in peak frequency of the two wave systems. It is shown that, because of the effects described by Piterbarg, for a linear sea state the expected maximum crest elevation over a given surface area depends on the crossing angle so that the expected maximum crest elevation is largest when two wave systems propagate with a crossing angle close to 90°. It is further shown by nonlinear phase-resolving numerical simulations that nonlinear effects have an opposite effect, such that maximum sea surface kurtosis is expected for relatively large and small crossing angles, with a minimum around 90°, and that the expected maximum crest height is almost independent of the crossing angle. The numerical results are accompanied by analysis of the modulational instability of two crossing Stokes waves, which is studied using the Zakharov equation so that, different from previous studies, results are valid for arbitrary-bandwidth perturbations. It is shown that there is a positive correlation between the value of kurtosis in the numerical simulations and the maximum unstable growth rate of two crossing Stokes waves, even for realistic broadband crossing sea states.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10852/675342018-01-01T00:00:00ZQuantitative Prediction of Multivalent Ligand-Receptor Binding Affinities for Influenza, Cholera, and Anthrax Inhibition
http://hdl.handle.net/10852/67514
Quantitative Prediction of Multivalent Ligand-Receptor Binding Affinities for Influenza, Cholera, and Anthrax Inhibition
Liese, Susanne; Netz, Roland R.
Multivalency achieves strong, yet reversible binding by the simultaneous formation of multiple weak bonds. It is a key interaction principle in biology and promising for the synthesis of high-affinity inhibitors of pathogens. We present a molecular model for the binding affinity of synthetic multivalent ligands onto multivalent receptors consisting of n receptor units arranged on a regular polygon. Ligands consist of a geometrically matching rigid polygonal core to which monovalent ligand units are attached via flexible linker polymers, closely mimicking existing experimental designs. The calculated binding affinities quantitatively agree with experimental studies for cholera toxin (n = 5) and anthrax receptor (n = 7) and allow to predict optimal core size and optimal linker length. Maximal binding affinity is achieved for a core that matches the receptor size and for linkers that have an equilibrium end-to-end distance that is slightly longer than the geometric separation between ligand core and receptor sites. Linkers that are longer than optimal are greatly preferable compared to shorter linkers. The angular steric restriction between ligand unit and linker polymer is shown to be a key parameter. We construct an enhancement diagram that quantifies the multivalent binding affinity compared to monovalent ligands. We conclude that multivalent ligands against influenza viral hemagglutinin (n = 3), cholera toxin (n = 5), and anthrax receptor (n = 7) can outperform monovalent ligands only for a monovalent ligand affinity that exceeds a core-size dependent threshold value. Thus, multivalent drug design needs to balance core size, linker length, as well as monovalent ligand unit affinity.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10852/675142018-01-01T00:00:00ZRogue Waves in the Ocean, the Role of Modulational Instability, and Abrupt Changes of Environmental Conditions that Can Provoke Non Equilibrium Wave Dynamics
http://hdl.handle.net/10852/67513
Rogue Waves in the Ocean, the Role of Modulational Instability, and Abrupt Changes of Environmental Conditions that Can Provoke Non Equilibrium Wave Dynamics
Trulsen, Karsten
Modulational instability is an efficient mechanism for the generation of rogue waves in the limit of narrow-banded and long-crested wave fields. While such wave fields are easily achieved in laboratories, there appears to be lacking evidence that known occurrences of rogue waves in the ocean (e.g. Draupner “New Year” wave, Andrea wave) or ship accidents that could have been provoked by rogue waves (e.g. the Prestige accident) actually happened in sea states favorable for the modulational instability to have played an important role. The absence of modulational instability does not mean that nonlinear interactions are unimportant. Here we point out recent results that suggest large deviations from Gaussian statistics can happen due to nonlinearity in the absence of modulational instability, the key ingredient seems to be that the wave field is brought into a state of non-equilibrium.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10852/675132018-01-01T00:00:00ZStochastic systems with memory and jumps
http://hdl.handle.net/10852/67500
Stochastic systems with memory and jumps
Banos, David; Cordoni, Francesco; Di Nunno, Giulia; Di Persio, Luca; Røse, Elin Engen
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10852/675002018-01-01T00:00:00ZDivisibility and Information Flow Notions of Quantum Markovianity for Noninvertible Dynamical Maps
http://hdl.handle.net/10852/67415
Divisibility and Information Flow Notions of Quantum Markovianity for Noninvertible Dynamical Maps
Chruscinski, Dariusz; Rivas, Angel; Størmer, Erling
We analyze the relation between completely positive (CP) divisibility and the lack of information backflow for an arbitrary—not necessarily invertible—dynamical map. It is well known that CP divisibility always implies a lack of information backflow. Moreover, these two notions are equivalent for invertible maps. In this Letter, it is shown that for a map which is not invertible the lack of information backflow always implies the existence of a completely positive propagator which, however, needs not be trace preserving. Interestingly, for a wide class of image nonincreasing dynamical maps, this propagator becomes trace preserving as well, and hence, the lack of information backflow implies CP divisibility. This result sheds new light into the structure of the time-local generators giving rise to CP-divisible evolutions. We show that if the map is not invertible then positivity of dissipation/decoherence rates is no longer necessary for CP divisibility.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10852/674152018-01-01T00:00:00ZTurbulence Scaling Comparisons in the Ocean Surface Boundary Layer
http://hdl.handle.net/10852/67414
Turbulence Scaling Comparisons in the Ocean Surface Boundary Layer
Esters, Leonie; Breivik, Øyvind; Landwehr, Sebastian; ten Doeschate, Anneke; Sutherland, Graig; Christensen, Kai Håkon; Bidlot, Jean-Raymond; Ward, Brian
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10852/674142018-01-01T00:00:00ZCharacterization of flow dynamics and reduced-order description of experimental two-phase pipe flow
http://hdl.handle.net/10852/67413
Characterization of flow dynamics and reduced-order description of experimental two-phase pipe flow
Viggiano, Bianca; Skjæraasen, Olaf; Schümann, Heiner; Tutkun, Murat; Cal, Raúl Bayoán
Two-phase dispersed and slug flows in a pipe are investigated using proper orthogonal decomposition (POD). The data are acquired through tomographic reconstruction of X-ray measurements, where holdup, cross-sectional phase distributions and phase interface characteristics are obtained. Instantaneous phase fractions of the flow fields are analyzed and reduced-order descriptions of the flow are achieved. The dispersed flow displays coherent features for the first few modes near the center of the pipe, representing the liquid-liquid interface location while the slug flow case shows coherent features that correspond to the cyclical formation of the slug in the first ten modes. For slug flow, the first two modes capture the liquid-dominated slug body region and the Taylor bubble/liquid film region, respectively. The reconstructions of the fields indicate that main features are observed in the low order descriptions utilizing less than one percent of the degrees of freedom of the full order descriptions. POD temporal coefficients a1, a2 and a3 show interdependence for the slug flow case. The coefficients also describe the phase fraction holdup as a function of time for both dispersed and slug flow.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10852/674132018-01-01T00:00:00ZA proposed tandem mechanism for memory storage in neurons involving magnetite and prions
http://hdl.handle.net/10852/67412
A proposed tandem mechanism for memory storage in neurons involving magnetite and prions
Alfsen, Erik; Størmer, Fredrik; Njå, Arild; Walløe, Lars
Knowledge about how information is stored in neurons of animals and in the human brain is still incomplete. A hypothesis related to long-term changes in synaptic efficiency has strong experimental support, but does not seem to be able to explain all observations. It has recently been proposed that magnetite together with a prionlike protein could be involved in a tandem mechanism for storage of memory in neurons in which electric impulses are received and reshaped by the magnetite to a form which can be accepted by the protein. The magnetite crystals can be magnetized by an electrical impulse, but they cannot hold the magnetism, which drops to zero after each impulse. Therefore, magnetite cannot be the substance in which information is stored. In the present paper we explain how a tandem mechanism could function in a neuron in which magnetite is situated together with a prion-like protein close to the cell surface membrane of the axon. We assume in addition that the information is stored in special storage neurons. With this, we propose a new hypothesis for information storage in neurons which could operate in addition to synaptic plasticity, but perhaps in different neurons.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10852/674122018-01-01T00:00:00Z