Inference, Computation, and Games

In this thesis, we use statistical inference and competitive games to design algorithms for computational mathematics. In the first part, comprising chapters two through six, we use ideas from Gaussian process statistics to obtain fast solvers for differential and integral equations. We begin by observing the equivalence of conditional (near-)independence of Gaussian processes and the (near-)sparsity of the Cholesky factors of its precision and covariance matrices. This implies the existence of a large class of dense matrices with almost sparse Cholesky factors, thereby greatly increasing the scope of application of sparse Cholesky factorization. Using an elimination ordering and sparsity pattern motivated by the screening effect in spatial statistics, we can compute approximate Cholesky factors of the covariance matrices of Gaussian processes admitting a screening effect in near-linear computational complexity. These include many popular smoothness priors such as the Matérn class of covariance functions. In the special case of Green's matrices of elliptic boundary value problems (with possibly unknown elliptic operators of arbitrarily high order, with possibly rough coefficients), we can use tools from numerical homogenization to prove the exponential accuracy of our method. This result improves the state-of-the-art for solving general elliptic integral equations and provides the first proof of an exponential screening effect. We also derive a fast solver for elliptic partial differential equations, with accuracy-vs-complexity guarantees that improve upon the state-of-the-art. Furthermore, the resulting solver is performant in practice, frequently beating established algebraic multigrid libraries such as AMGCL and Trilinos on a series of challenging problems in two and three dimensions. Finally, for any given covariance matrix, we obtain a closed-form expression for its optimal (in terms of Kullback-Leibler divergence) approximate inverse-Cholesky factorization subject to a sparsity constraint, recovering Vecchia approximation and factorized sparse approximate inverses. Our method is highly robust, embarrassingly parallel, and further improves our asymptotic results on the solution of elliptic integral equations. We also provide a way to apply our techniques to sums of independent Gaussian processes, resolving a major limitation of existing methods based on the screening effect. As a result, we obtain fast algorithms for large-scale Gaussian process regression problems with possibly noisy measurements. In the second part of this thesis, comprising chapters seven through nine, we study continuous optimization through the lens of competitive games. In particular, we consider competitive optimization, where multiple agents attempt to minimize conflicting objectives. In the single-agent case, the updates of gradient descent are minimizers of quadratically regularized linearizations of the loss function. We propose to generalize this idea by using the Nash equilibria of quadratically regularized linearizations of the competitive game as updates (linearize the game). We provide fundamental reasons why the natural notion of linearization for competitive optimization problems is given by the multilinear (as opposed to linear) approximation of the agents' loss functions. The resulting algorithm, which we call competitive gradient descent, thus provides a natural generalization of gradient descent to competitive optimization. By using ideas from information geometry, we extend CGD to competitive mirror descent (CMD) that can be applied to a vast range of constrained competitive optimization problems. CGD and CMD resolve the cycling problem of simultaneous gradient descent and show promising results on problems arising in constrained optimization, robust control theory, and generative adversarial networks. Finally, we point out the GAN-dilemma that refutes the common interpretation of GANs as approximate minimizers of a divergence obtained in the limit of a fully trained discriminator. Instead, we argue that GAN performance relies on the implicit competitive regularization (ICR) due to the simultaneous optimization of generator and discriminator and support this hypothesis with results on low-dimensional model problems and GANs on CIFAR10.</p

The C-terminus of p63 contains multiple regulatory elements with different functions

The transcription factor p63 is expressed as at least six different isoforms, of which two have been assigned critical biological roles within ectodermal development and skin stem cell biology on the one hand and supervision of the genetic stability of oocytes on the other hand. These two isoforms contain a C-terminal inhibitory domain that negatively regulates their transcriptional activity. This inhibitory domain contains two individual components: one that uses an internal binding mechanism to interact with and mask the transactivation domain and one that is based on sumoylation. We have carried out an extensive alanine scanning study to identify critical regions within the inhibitory domain. These experiments show that a stretch of ~13 amino acids is crucial for the binding function. Further, investigation of transcriptional activity and the intracellular level of mutants that cannot be sumoylated suggests that sumoylation reduces the concentration of p63. We therefore propose that the inhibitory function of the C-terminal domain is in part due to direct inhibition of the transcriptional activity of the protein and in part due to indirect inhibition by controlling the concentration of p63. Keywords: p63, transcriptional regulation, auto-inhibition, sumoylatio

Changes of hemodynamic and cerebral oxygenation after exercise in normobaric and hypobaric hypoxia: associations with acute mountain sickness

Objective: Normobaric (NH) and hypobaric hypoxia (HH) are associated with acute mountain sickness (AMS) and cognitive dysfunction. Only few variables, like heart-rate-variability, are correlated with AMS. However, prediction of AMS remains difficult. We therefore designed an expedition-study with healthy volunteers in NH/HH to investigate additional non-invasive hemodynamic variables associated with AMS.Methods: Eleven healthy subjects were examined in NH (FiO(2) 13.1%;equivalent of 3.883m a.s.l;duration 4h) and HH (3.883ma.s.l.;duration 24h) before and after an exercise of 120min. Changes in parameters of electrical cardiometry (cardiac index (CI), left-ventricular ejection time (LVET), stroke volume (SV), index of contractility (ICON)), near-infrared spectroscopy (cerebral oxygenation, rScO(2)), Lake-Louise-Score (LLS) and cognitive function tests were assessed. One-Way-ANOVA, Wilcoxon matched-pairs test, Spearman's-correlation-analysis and Student's t-test were performed.Results: HH increased heart rate (HR), mean arterial pressure (MAP) and CI and decreased LVET, SV and ICON, whereas NH increased HR and decreased LVET. In both NH and HH cerebral oxygenation decreased and LLS increased significantly. After 24h in HH, 6 of 11 subjects (54.6%) developed AMS. LLS remained increased until 24h in HH, whereas cognitive function remained unaltered. In HH, HR and LLS were inversely correlated (r=-0.692;p<0.05). More importantly, the rScO2-decrease after exercise in NH significantly correlated with LLS after 24h in HH (r=-0.971;p<0.01) and rScO2 correlated significantly with HR (r=0.802;p<0.01), CI (r=0.682;p<0.05) and SV (r=0.709;p<0.05) after exercise in HH.Conclusion: sBoth acute NH and HH altered hemodynamic and cerebral oxygenation and induced AMS. Subjects, who adapted their CI had higher rScO2 and lower LLS. Furthermore, rScO2 after exercise under normobaric conditions was associated with AMS at high altitudes

Potenziale der schwachen künstlichen Intelligenz für die betriebliche Ressourceneffizienz

POTENZIALE DER SCHWACHEN KÜNSTLICHEN INTELLIGENZ FÜR DIE BETRIEBLICHE RESSOURCENEFFIZIENZ Potenziale der schwachen künstlichen Intelligenz für die betriebliche Ressourceneffizienz / Friedrich, Robert (Rights reserved) ( -

Hybrid cosmic ray measurements using the IceAct telescopes in coincidence with the IceCube and IceTop detectors

IceAct is a proposed surface array of compact (50 cm diameter) and cost-effective Imaging Air Cherenkov Telescopes installed at the site of the IceCube Neutrino Observatory at the geographic South Pole. Since January 2019, two IceAct telescope demonstrators, featuring 61 silicon photomultiplier (SiPM) pixels have been taking data in the center of the IceTop surface array during the austral winter. We present the first analysis of hybrid cosmic ray events detected by the IceAct imaging air-Cherenkov telescopes in coincidence with the IceCube Neutrino Observatory, including the IceTop surface array and the IceCube in-ice array. By featuring an energy threshold of about 10 TeV and a wide field-of-view, the IceAct telescopes show promising capabilities of improving current cosmic ray composition studies: measuring the Cherenkov light emissions in the atmosphere adds new information about the shower development not accessible with the current detectors, enabling significantly better primary particle type discrimination on a statistical basis. The hybrid measurement also allows for detailed feasibility studies of detector cross-calibration and of cosmic ray veto capabilities for neutrino analyses. We present the performance of the telescopes, the results from the analysis of two years of data, and an outlook of a hybrid simulation for a future telescope array

Combined fit to the spectrum and composition data measured by the Pierre Auger Observatory including magnetic horizon effects

The measurements by the Pierre Auger Observatory of the energy spectrum and mass composition of cosmic rays can be interpreted assuming the presence of two extragalactic source populations, one dominating the flux at energies above a few EeV and the other below. To fit the data ignoring magnetic field effects, the high-energy population needs to accelerate a mixture of nuclei with very hard spectra, at odds with the approximate E$^{-2}$ shape expected from diffusive shock acceleration. The presence of turbulent extragalactic magnetic fields in the region between the closest sources and the Earth can significantly modify the observed CR spectrum with respect to that emitted by the sources, reducing the flux of low-rigidity particles that reach the Earth. We here take into account this magnetic horizon effect in the combined fit of the spectrum and shower depth distributions, exploring the possibility that a spectrum for the high-energy population sources with a shape closer to E$^{-2}$ be able to explain the observations

Studies of the mass composition of cosmic rays and proton-proton interaction cross-sections at ultra-high energies with the Pierre Auger Observatory

In this work, we present an estimate of the cosmic-ray mass composition from the distributions of the depth of the shower maximum (Xmax) measured by the fluorescence detector of the Pierre Auger Observatory. We discuss the sensitivity of the mass composition measurements to the uncertainties in the properties of the hadronic interactions, particularly in the predictions of the particle interaction cross-sections. For this purpose, we adjust the fractions of cosmic-ray mass groups to fit the data with Xmax distributions from air shower simulations. We modify the proton-proton cross-sections at ultra-high energies, and the corresponding air shower simulations with rescaled nucleus-air cross-sections are obtained via Glauber theory. We compare the energy-dependent composition of ultra-high-energy cosmic rays obtained for the different extrapolations of the proton-proton cross-sections from low-energy accelerator data

Study of downward Terrestrial Gamma-ray Flashes with the surface detector of the Pierre Auger Observatory

The surface detector (SD) of the Pierre Auger Observatory, consisting of 1660 water-Cherenkov detectors (WCDs), covers 3000 km2 in the Argentinian pampa. Thanks to the high efficiency of WCDs in detecting gamma rays, it represents a unique instrument for studying downward Terrestrial Gamma-ray Flashes (TGFs) over a large area. Peculiar events, likely related to downward TGFs, were detected at the Auger Observatory. Their experimental signature and time evolution are very different from those of a shower produced by an ultrahigh-energy cosmic ray. They happen in coincidence with low thunderclouds and lightning, and their large deposited energy at the ground is compatible with that of a standard downward TGF with the source a few kilometers above the ground. A new trigger algorithm to increase the TGF-like event statistics was installed in the whole array. The study of the performance of the new trigger system during the lightning season is ongoing and will provide a handle to develop improved algorithms to implement in the Auger upgraded electronic boards. The available data sample, even if small, can give important clues about the TGF production models, in particular, the shape of WCD signals. Moreover, the SD allows us to observe more than one point in the TGF beam, providing information on the emission angle

The dynamic range of the upgraded surface-detector stations of AugerPrime

The detection of ultra-high-energy cosmic rays by means of giant detector arrays is often limited by the saturation of the recorded signals near the impact point of the shower core at the ground, where the particle density dramatically increases. The saturation affects in particular the highest energy events, worsening the systematic uncertainties in the reconstruction of the shower characteristics. The upgrade of the Pierre Auger Observatory, called AugerPrime, includes the installation of an 1-inch Small PhotoMultiplier Tube (SPMT) inside each water-Cherenkov station (WCD) of the surface detector array. The SPMT allows an unambiguous measurement of signals down to about 250m from the shower core, thus reducing the number of events featuring a saturated station to a negligible level. In addition, a 3.8m2 plastic scintillator (Scintillator Surface Detector, SSD) is installed on top of each WCD. The SSD is designed to match the WCD (with SPMT) dynamic range, providing a complementary measurement of the shower components up to the highest energies. In this work, the design and performances of the upgraded AugerPrime surface-detector stations in the extended dynamic range are described, highlighting the accuracy of the measurements. A first analysis employing the unsaturated signals in the event reconstruction is also presented