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Implementing Bogoliubov Transformations Beyond the Shale-Stinespring Condition
Get PDFWe provide two extensions of a dense subspace of Fock space, such that Bogoliubov transformations become implementable on them, even though they violate the Shale-Stinespring condition, so they are not implementable on Fock space. Both the bosonic and fermionic case are covered. Conditions for implementability in the extended sense are stated and proved. From these, we derive conditions for a quadratic Hamiltonian to be diagonalizable by a Bogoliubov transformation that is implementable in the extended sense. Three examples illustrate situations, in which an implementation in the extended sense is possible although the Shale-Stinespring condition fails to hold.DAAD (Deutscher Akademischer Austauschdienst
Refined isogeometric analysis of quadratic eigenvalue problems
Get PDFCertain applications that analyze damping effects require the solution of quadratic eigenvalue problems (QEPs). We use refined isogeometric analysis (rIGA) to solve quadratic eigenproblems. rIGA discretization, while conserving desirable properties of maximum-continuity isogeometric analysis (IGA), reduces the interconnection between degrees of freedom by adding low-continuity basis functions. This connectivity reduction in rIGA's algebraic system results in faster matrix LU factorizations when using multifrontal direct solvers. We compare computational costs of rIGA versus those of IGA when employing Krylov eigensolvers to solve quadratic eigenproblems arising in 2D vector-valued multifield problems. For large problem sizes, the eigencomputation cost is governed by the cost of LU factorization, followed by costs of several matrix–vector and vector–vector multiplications, which correspond to Krylov projections. We minimize the computational cost by introducing C0 and C1 separators at specific element interfaces for our rIGA generalizations of the curl-conforming Nédélec and divergence-conforming Raviart–Thomas finite elements. Let p be the polynomial degree of basis functions; the LU factorization is up to O((p−1)2) times faster when using rIGA compared to IGA in the asymptotic regime. Thus, rIGA theoretically improves the total eigencomputation cost by O((p−1)2) for sufficiently large problem sizes. Yet, in practical cases of moderate-size eigenproblems, the improvement rate deteriorates as the number of computed eigenvalues increases because of multiple matrix–vector and vector–vector operations. Our numerical tests show that rIGA accelerates the solution of quadratic eigensystems by O(p−1) for moderately sized problems when we seek to compute a reasonable number of eigenvalues
The DPG Method for the Convection-Reaction Problem, Revisited
Get PDFWe study both conforming and non-conforming versions of the practical DPG method for the convection-reaction problem. We determine that the most common approach for DPG stability analysis - construction of a local Fortin operator - is infeasible for the convection-reaction problem. We then develop a line of argument based on a direct proof of discrete stability; we find that employing a polynomial enrichment for the test space does not suffice for this purpose, motivating the introduction of a (two-element) subgrid mesh. The argument combines mathematical analysis with numerical experiments
Learning a Battery of COVID-19 Mortality Prediction Models by Multi-objective Optimization
Get PDFThe COVID-19 pandemic is continuously evolving with drastically changing epidemiological situations which are approached with different decisions: from the reduction of fatalities to even the selection of patients with the highest probability of survival in critical clinical situations. Motivated by this, a battery of mortality prediction models with different performances has been developed to assist physicians and hospital managers. Logistic regression, one of the most popular classifiers within the clinical field, has been chosen as the basis for the generation of our models. Whilst a standard logistic regression only learns a single model focusing on improving accuracy, we propose to extend the possibilities of logistic regression by focusing on sensitivity and specificity. Hence, the log-likelihood function, used to calculate the coefficients in the logistic model, is split into two objective functions: one representing the survivors and the other for the deceased class. A multi-objective optimization process is undertaken on both functions in order to find the Pareto set, composed of models not improved by another model in both objective functions simultaneously. The individual optimization of either sensitivity (deceased patients) or specificity (survivors) criteria may be conflicting objectives because the improvement of one can imply the worsening of the other. Nonetheless, this conflict guarantees the output of a battery of diverse prediction models. Furthermore, a specific methodology for the evaluation of the Pareto models is proposed. As a result, a battery of COVID-19 mortality prediction models is obtained to assist physicians in decision-making for specific epidemiological situations.This research is supported by the Basque Government (IT1504- 22, Elkartek) through the BERC 2022–2025 program and BMTF project, and by the Ministry of Science, Innovation and Universities: BCAM Severo Ochoa accreditation SEV-2017-0718 and PID2019-104966GB-I00. Furthermore, the work is also supported by the AXA Research Fund project “Early prognosis of COVID-19 infections via machine learning”
Notes on : structural properties, dyadic variants, and bilinear - mappings
Get PDFThis article is devoted to a study of the Hardy space introduced by Bonami, Grellier, and Ky. We present an alternative approach to their result relating the product of a function in the real Hardy space and a function in to distributions that belong to based on dyadic paraproducts.
We also point out analogues of classical results of Hardy-Littlewood, Zygmund, and Stein for and related Musielak-Orlicz spaces.Wallenberg Mathematics Program 2018, grant no. KAW 2017.0425
BERC 2022-2025
RYC2018-025477-I
PID2021-122156NB-I00/AEI/10.13039/501100011033
IJC2020-043082-
Exact calculation of the mean first-passage time of continuous-time random walks by nonhomogeneous Wiener-Hopf integral equations
Get PDFWe study the mean first-passage time (MFPT) for asymmetric continuous-time random walks in continuous-space characterised by waiting-times with finite mean and by jump-sizes with both finite mean and finite variance. In the asymptotic limit, this well-controlled process is governed by an advection-diffusion equation and the MFPT results to be finite when the advecting velocity is in the direction of the boundary. We derive a nonhomogeneous Wiener–Hopf integral equation that allows for the exact calculation of the MFPT by avoiding asymptotic limits and it emerges to depend on the whole distribution of the jump-sizes and on the
mean-value only of the waiting-times, thus it holds for general non-Markovian random walks. Through the case study of a quite general family of asymmetric distributions of the jump-sizes that is exponential towards the boundary and arbitrary in the opposite
direction, we show that the MFPT is indeed independent of the jump-sizes distribution in the opposite direction to the boundary. Moreover, we show also that there exists a length-scale, which depends only on the features of the distribution of jumps in the direction of the boundary, such that for starting points near the boundary the MFPT depends on the specific whole distribution of jump-sizes, in opposition to the universality emerging for starting points far-away from the boundary.PRE2018-084427
2.5-D Deep Learning Inversion of LWD and Deep-Sensing em Measurements Across Formations with Dipping Faults
Get PDFDeep learning (DL) inversion of induction logging measurements is used in well geosteering for real-time imaging of the distribution of subsurface electrical conductivity. We develop a DL inversion workflow to solve 2.5-D inverse problems arising in well geosteering. The inversion workflow employs three DL modules: a 'look-around' fault detection module and two inversion modules for reconstructing anisotropic resistivity models in the presence or absence of fault planes, respectively. Our DL approach is capable of detecting and quantifying arbitrary dipping fault planes in real time. We compare inversion performance considering only short logging-while-drilling (LWD) measurements versus using both short LWD and deep-sensing measurements. The latter measurements provide enhanced depth-of-investigation while minimizing uncertainty. We also obtain improved results when using multidimensional inversion, especially nearby fault planes. This study verifies the applicability of real-time 2.5-D DL inversion across arbitrary faulted formations for well geosteering
Experimental investigation of anomalous molecular probe diffusion in entangled polymer melts
Get PDFInvestigations on the diffusion of small molecules or particles in polymeric materials are important to numerous technologies and can also be used to gain insight on polymer chain dynamics. Systems where the probe size is comparable to (or smaller than) a characteristic length of the polymer chain, the tube diameter for example, are of particular interest because the diffusion coefficient of the probe can be orders of magnitude larger than the value predicted by the Stokes-Einstein relation. In the present study, we employ the optical technique known as forced Rayleigh scattering to study the diffusion of a molecular probe (dye) in several entangled polymer melts over a wide range of length and time scales. The probe size is much smaller than the tube diameter for the systems studied. We find the diffusion coefficient is larger by four to five orders of magnitude than the Stokes-Einstein prediction. More interestingly, we observe anomalous, non-Fickian, diffusion where the value of the measured diffusion coefficient can abruptly change by as much as 50%. We suggest that this unexpected behavior occurs when the time scale for diffusion is larger than the relaxation time associated with the constraint release mechanism for polymer chain dynamics
Modeling secondary infections with temporary immunity and disease enhancement factor: Mechanisms for complex dynamics in simple epidemiological models
Get PDFModeling insights for epidemiological scenarios characterized by chaotic dynamics have been largely unexplored. A rigorous analysis of such systems are essential for a real predictive power and a more accurate disease control decision making. Motivated by dengue fever epidemiology, we study a basic SIR–SIR type model for the host population, capturing differences between primary and secondary infections. This model is the minimalistic version to previously suggested multi-strain models for dengue fever in which deterministic chaos was found in wider parameter regions. Without strain structure of pathogens, we consider temporary immunity after a primary infection and disease enhancement in a subsequent infection to identify to which extent these biological mechanisms can generate complex behavior in simple epidemiological models.
Stability analysis of the system is performed using the classical linearization theory, and the qualitative behavior of the model is investigated with a detailed bifurcation analysis. Rich dynamical structures are identified, including the Bogdanov–Takens, cusp and Bautin bifurcations which has never been described in dengue fever epidemiology. Besides the conventional transcritical bifurcation, a backward bifurcation occurs for higher disease enhancement in secondary infections, exhibiting bi-stability when biological temporary immunity period is assumed. The backward bifurcation is formalized using the center manifold theory. While the Hopf and the global homoclinic bifurcation curves were computed numerically, analytical expressions for the transcritical and tangent bifurcations are obtained. The combination of temporary immunity and disease enhancement play a significant role in the complexity of the system dynamics, with chaotic behavior observed after including seasonal forcing