A5059450802- Polynomial and algebraic computation
- Numerical Methods and Algorithms
- Advanced Optimization Algorithms Research
- Cultural Heritage Materials Analysis
- X-ray Spectroscopy and Fluorescence Analysis
- Commutative Algebra and Its Applications
- Advanced Numerical Analysis Techniques
- Formal Methods in Verification
- Topological and Geometric Data Analysis
- Advanced Combinatorial Mathematics
- Advanced Graph Theory Research
- Gene Regulatory Network Analysis
- Mathematical Dynamics and Fractals
- Complexity and Algorithms in Graphs
- Advanced X-ray Imaging Techniques
- Conservation Techniques and Studies
- Mathematical and Theoretical Analysis
- Logic, programming, and type systems
- graph theory and CDMA systems
- Advanced Differential Equations and Dynamical Systems
- Building materials and conservation
- Mathematical functions and polynomials
- VLSI and FPGA Design Techniques
- Bioactive Natural Diterpenoids Research
- Computability, Logic, AI Algorithms
Technische Universität Braunschweig
2018-2025
Otto-von-Guericke University Magdeburg
2020
Bruker (Germany)
2018-2020
Goethe University Frankfurt
2011-2020
Gesellschaft Fur Mathematik Und Datenverarbeitung
2020
Technische Universität Berlin
2007-2018
Texas A&M University
2014-2017
Berlin Mathematical School
2016-2017
Saarland University
2011-2014
Federal Institute For Materials Research and Testing
2007-2011
We completely characterize sections of the cones nonnegative polynomials, convex polynomials and sums squares with supported on circuits, a genuine class sparse polynomials. In particular, nonnegativity is characterized by an invariant, which can be immediately derived from initial polynomial. Furthermore, such f coincides solidness amoeba f, i.e., Log-absolute-value image algebraic variety $${\mathcal {V}} (f) \subset (\mathbb {C}^*)^n$$ f. These results generalize earlier works both in...
Recent evidence shows that during slow-wave sleep (SWS), the brain is cleared from potentially toxic metabolites, such as amyloid-beta protein. Poor or elevated cortisol levels can worsen clearance, leading to formation of amyloid plaques, a neuropathological hallmark Alzheimer disease. Here, we explored how nocturnal neural and endocrine activity affects fluctuations in peripheral blood.
Recently, the second and third authors developed sums of nonnegative circuit polynomials (SONC) as a new certificate nonnegativity for real polynomials, which is independent squares. In this paper we show that SONC cone full-dimensional in polynomials. We establish Positivstellensatz guarantees every polynomial positive on given compact, semialgebraic set can be represented by constraints Based Positivstellensatz, provide hierarchy lower bounds converging to minimum compact $K$. Moreover,...
In this article, we explore the connections between nonnegativity, theory of $A$-discriminants, and tropical geometry. For an integral support set $A \subset \mathbb{Z}^n$, cover boundary sonc-cone by semialgebraic sets that are parametrized families hypersurfaces. As application, give sufficient conditions for equality sparse nonnegativity cone generic sets, describe a stratification in univariate case.
Many metals are essential for plants and humans. Knowledge of metal distribution in plant tissues vivo contributes to the understanding physiological mechanisms uptake, accumulation sequestration. For those studies, X-rays a non-destructive tool, especially suited study plants.We present microfluorescence imaging trace elements living using customized benchtop X-ray fluorescence machine. The system was optimized by additional detector shielding minimize stray counts, custom-made measuring...
Understanding quantum phenomena that go beyond classical concepts is a focus of modern physics. Here, we show how the theory non-negative polynomials emerging around Hilbert's 17th problem, can be used to optimally exploit data capturing nonclassical nature light. Specifically, reveal nonclassicality in even when it hidden from standard detection methods up now. Moreover, abstract language also leads unified mathematical approach for light and spin systems, allowing us map one other....
3D Micro X-ray fluorescence analysis was used for the investigation of reverse-glass paintings. The material-specific combination in paintings leads to damage phenomena reinforced by glass corrosion. To elucidate mechanism corrosion processes taking place object depth profiles mobile elements are interest. In order obtain elemental such kind fragile objects method choice should be non-destructive. Our first results demonstrate usefulness Micro-XRF measurements this investigations. assumption...
In this work, the applicability of a new 3D micro X-ray fluorescence (3D Micro-XRF) laboratory spectrometer for investigation historical glass objects is demonstrated. The non-destructiveness technique and possibility to measure three-dimensionally resolved renders into suitable tool analysis cultural heritage objects. Although absorption resolution effects complicate qualitative data, layered structures can be distinguished from homogeneous samples without need full quantification....
Objective Rapid testing is paramount during a pandemic to prevent continued viral spread and excess morbidity mortality. This study investigates whether strategies based on sample pooling can increase the speed throughput of screening for SARS-CoV-2, especially in resource-limited settings. Methods In mathematical modelling approach conducted May 2020, six different were simulated key input parameters such as infection rate, test characteristics, population size, capacity. The situations...
In this article, we propose a geometric programming method in order to compute lower bounds for real polynomials. We provide new sufficient conditions polynomials be nonnegative as well have sum of binomial squares representation. These criteria rely on the coefficients and support polynomial generalize all previous ones by Lasserre, Ghasemi, Marshall, Fidalgo, Kovacec with arbitrary simplex Newton polytopes. This generalization yields approach computing that significantly extends proposed...
Polycapillary halflenses are widely used to focus X-ray radiation onto a small spot. Additionally they can reduce the field of view semiconductor detector when placed in front one. In 3D micro fluorescence spectroscopy (3D Micro-XRF) with synchrotron radiation, two polycapillary confocal geometry. Up until now, characterization measurements focal plane have only been performed case lens focusing parallel radiation. Assumptions made, that other case, isotropic from spot source is transported...
A combination of 3D micro X-ray fluorescence spectroscopy (3D micro-XRF) and micro-XRF was utilized for the investigation a small collection highly heterogeneous, partly degraded Dead Sea Scroll parchment samples from known excavation sites. The quantitative two techniques proves to be suitable identification reliable marker elements which may used classification provenance studies. With micro-XRF, three-dimensional nature, i.e. depth-resolved elemental composition as well density...
Depth profiling with confocal micro-X-ray fluorescence spectroscopy (confocal micro-XRF) is a nondestructive analytical method for obtaining elemental depth profiles in the micrometer region. Up until now, quantitative reconstruction of thicknesses and concentration stratified samples has been only possible monochromatic, thus, synchrotron radiation. In this work, we present new calibration procedure, which renders quantification laboratory feasible. The proposed model uses approximation an...
Finding the minimum of a multivariate real polynomial is well-known hard problem with various applications. We present time algorithm to approximate such lower bounds via sums nonnegative circuit polynomials (SONC). As main result, we carry out first large-scale comparison SONC, using this and different geometric programming (GP) solvers, classical squares (SOS) approach, several most common semidefinite (SDP) solvers. SONC yields competitive SOS in cases, but significantly less memory. In...
Amoebas and coamoebas are the logarithmic images of algebraic varieties under arg-map, respectively. We present new techniques for computational problems on amoebas coamoebas, thus establishing connections between (co-)amoebas, semialgebraic convex geometry semidefinite programming. Our approach is based formulating membership problem in (respectively coamoebas) as a suitable real feasibility problem. Using Nullstellensatz, this allows us to tackle by sums squares method yields polynomial...
We analyze a chiral periodic tensegrity structure that is auxetic and an exciting model for multifunctional materials.
The amoeba of a Laurent polynomial is the image corresponding hypersurface under coordinatewise log absolute value map. In this article, we demonstrate that theoretical approximation method due to Purbhoo can be used efficiently in practice. To do this, resolve main bottleneck Purbhoo's by exploiting relations between cyclic resultants. We use same approach give an Log preimage using semi-algebraic sets. also provide SINGULAR/Sage implementation these algorithms, which shows significant...