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This work introduces a method for preprocessing measurements of electrical impedance tomography to considerably reduce the effect uncertainties in the electrode contacts have on the reconstruction quality, without a need to explicitly estimate the contacts. The idea is to compute the Jacobian matrix of the forward map with respect to the contact strengths and project the electrode measurements and the forward map onto the orthogonal complement of the range of this Jacobian. Using the smoothened complete electrode model as the forward model, it is demonstrated that inverting the resulting projected equation with respect to only the internal conductivity of the examined body results in good quality reconstructions both when resorting to a single step linearization with a smoothness prior and when combining lagged diffusivity iteration with total variation regularization. The quality of the reconstructions is further improved if the range of the employed projection is also orthogonal to that of the Jacobian with respect to the electrode positions. These results hold even if the projections are formed at internal and contact conductivities that significantly differ from the true ones; it is numerically demonstrated that the orthogonal complement of the range of the contact Jacobian is almost independent of the conductivity parameters at which it is evaluated. In particular, our observations introduce a numerical technique for inferring whether a change in the electrode measurements is caused by a change in the internal conductivity or alterations in the electrode contacts, which has potential applications, e.g., in bedside monitoring of stroke patients. The ideas are tested both on simulated data and on real-world water tank measurements with adjustable contact resistances., Comment: 25 pages, 11 figures

Objective: To develop a fast image reconstruction method for stroke monitoring with electrical impedance tomography with image quality comparable to computationally expensive nonlinear model-based methods. Methods: A post-processing approach with graph convolutional networks is employed. Utilizing the flexibility of the graph setting, a graph U-net is trained on linear difference reconstructions from 2D simulated stroke data and applied to fully 3D images from realistic simulated and experimental data. An additional network, trained on 3D vs. 2D images, is also considered for comparison. Results: Post-processing the linear difference reconstructions through the graph U-net significantly improved the image quality, resulting in images comparable to, or better than, the time-intensive nonlinear reconstruction method (a few minutes vs. several hours). Conclusion: Pairing a fast reconstruction method, such as linear difference imaging, with post-processing through a graph U-net provided significant improvements, at a negligible computational cost. Training in the graph framework vs classic pixel-based setting (CNN) allowed the ability to train on 2D cross-sectional images and process 3D volumes providing a nearly 50x savings in data simulation costs with no noticeable loss in quality. Significance: The proposed approach of post-processing a linear difference reconstruction with the graph U-net could be a feasible approach for on-line monitoring of hemorrhagic stroke., Comment: 11 pages, 8 figures

Let $(F_i)$ be a sequence of sets in a Banach space $X$. For what sequences does the condition $$ \limsup_{i\to \infty} \sup_{f_i\in F_i} \|Tf_i\|_Y=0 $$ hold for every Banach space $Y$ and every compact operator $T:X\to Y$? We answer this question by giving sufficient (and necessary) criteria for such sequences. We illustrate the applicability of the criteria by examples from literature and by characterizing the $L^p\to L^p$ compactness of dyadic paraproducts on general measure spaces., Comment: 20 pages

The global 6G vision has taken its shape after years of international research and development efforts. This work culminated in ITU-R Recommendation on "IMT-2030 Framework". While the definition phase of technological requirements is currently ongoing, 3GPP standardization process on 6G networks is expected to start in 2025 and worldwide commercialization around 2029-2030. This article serves as a comprehensive guide to 6G by providing an overall vision, a contemporary survey of the main literature, and an informative tutorial-type presentation style. In our vision, 6G will be based on three fundamental elements: wireless, artificial intelligence, and Internet of Everything. Consequently, 6G can ultimately become the Intelligent Network of Everything while serving as an enabling platform for the next major disruption in mobile communication, called mobile intelligence. The potential of mobile intelligence is that anything can be made connected, intelligent, and aware of its environment. This will revolutionize the way how devices, systems, and applications are designed; how they operate and interact with humans and each other; and how they can be used for the benefit of people, society, and the world in general. After high-level visioning, the main details of 6G are discussed, including fundamental elements, disruptive applications, key use cases, main performance requirements, potential technologies, and defining features. A special focus is given to a comprehensive set of potential 6G technologies, each of which is introduced in a tutorial manner. Finally, we speculate on what comes after 6G and sketch the first high-level vision of 7G. All in all, the objective of this article is to provide a thorough guide to 6G in order to serve as a source of knowledge and inspiration for further research and development work in academia, industry, and standardization bodies., Comment: Accepted for publication in IEEE Access, 101 pages, 50 figures, 16 tables

We calculate the contribution from the $q \bar q g$ state production to the diffractive cross sections in deep inelastic scattering at high energy. The obtained cross section is finite by itself, and consists a part of the full next-to-leading order result for the diffractive structure functions. Our calculation for the diffractive structure functions is performed using exact kinematics, under the shockwave approximation of the scattering process. Once the calculation is completed, we show that the previously known behaviour at the high-$Q^2$ and large-$M_X^2$ regime can be extracted from our results by taking the appropriate limits. Furthermore, we discuss the steps required to obtain the complete next-to-leading order results for the structure functions in the color glass condensate (CGC) formalism, and the application of these results to phenomenology., Comment: DIS2023, talk by HH; 5 pages, 3 figures

We predict heavy quark production cross sections in Deep Inelastic Scattering at high energy by applying the CGC effective theory. We demonstrate that when the calculation is performed consistently at next-to-leading order accuracy with massive quarks it becomes possible, for the first time in the dipole picture with perturbatively calculated center-of-mass energy evolution, to simultaneously describe both light and heavy quark production data at small $x$. We furthermore show how the heavy quark cross section data provides additional strong constraints on the extracted non-perturbative initial condition for the small-$x$ evolution equations., Comment: 5 pages, 4 figures. Talk by H.M. at DIS2023

As our main result, we supply the missing characterization of the $L^p(\mu)\to L^q(\lambda)$ boundedness of the commutator of a non-degenerate Calder\'on--Zygmund operator $T$ and pointwise multiplication by $b$ for exponents $1

We calculate the contribution from the $q\bar{q}g$ component of a virtual photon state to the small-$x$ diffractive cross section in deep inelastic scattering in the saturation regime. The obtained cross section is finite by itself and a part of the full next-to-leading order result. We perform the calculation in exact kinematics in the eikonal limit, and show that the previously known high virtuality $Q^2$ and large invariant mass $M_X^2$ results for the structure functions can be extracted. We furthermore discuss the steps required to obtain the full next-to-leading order result., Comment: 6 pages, 1 figure. Presented by T.L. at "Diffraction and Low-x 2022," Corigliano Calabro, Italy, September 24-40, 2022

We predict heavy quark production cross sections in Deep Inelastic Scattering at high energy by applying the Color Glass Condensate effective theory. We demonstrate that when the calculation is performed consistently at next-to-leading order accuracy with massive quarks it becomes possible, for the first time in the dipole picture with perturbatively calculated center-of-mass energy evolution, to simultaneously describe both light and heavy quark production data at small $x_\mathrm{Bj}$. We furthermore show how the heavy quark cross section data provides additional strong constraints on the extracted non-perturbative initial condition for the small-$x_\mathrm{Bj}$ evolution equations., Comment: 7 pages, 3 figures, v2 matches published version

An additive autoencoder for dimension reduction, which is composed of a serially performed bias estimation, linear trend estimation, and nonlinear residual estimation, is proposed and analyzed. Computational experiments confirm that an autoencoder of this form, with only a shallow network to encapsulate the nonlinear behavior, is able to identify an intrinsic dimension of a dataset with a low autoencoding error. This observation leads to an investigation in which shallow and deep network structures, and how they are trained, are compared. We conclude that the deeper network structures obtain lower autoencoding errors during the identification of the intrinsic dimension. However, the detected dimension does not change compared to a shallow network., Comment: Manuscript submitted to review

We calculate the contribution from the $q \bar q g$ state production to the diffractive cross sections in deep inelastic scattering at high energy. The obtained cross section is finite by itself and a part of the full next-to-leading order result for the diffractive structure functions. We perform the calculation in exact kinematics in the eikonal limit, and show that the previously known high-$Q^2$ and large $M_X^2$ results for the structure functions can be extracted from our results in the appropriate limits. We furthermore discuss the steps required to obtain the full next-to-leading order results for the structure functions., Comment: 32 pages, 12 figures

Rotating turbulence is ubiquitous in nature. Previous works suggest that such turbulence could be described as an ensemble of interacting inertial waves across a wide range of length scales. For turbulence in macroscopic quantum condensates, the nature of the transition between the quasiclassical dynamics at large scales and the corresponding dynamics at small scales, where the quantization of vorticity is essential, remains an outstanding unresolved question. Here we expand the paradigm of wave-driven turbulence to rotating quantum fluids where the spectrum of waves extends to microscopic scales as Kelvin waves on quantized vortices. We excite inertial waves at the largest scale by periodic modulation of the angular velocity and observe dissipation-independent transfer of energy to smaller scales and the eventual onset of the elusive Kelvin-wave cascade at the lowest temperatures. We further find that energy is pumped to the system through a boundary layer distinct from the classical Ekman layer and support our observations with numerical simulations. Our experiments demonstrate a new regime of turbulent motion in quantum fluids where the role of vortex reconnections can be neglected, thus stripping the transition between the classical and the quantum regimes of turbulence down to its bare bones., Comment: 21 pages, 11 figures

This thesis studies gluon saturation in hadronic matter at high energy by calculating next-to-leading order (NLO) corrections to inclusive and diffractive deep inelastic scattering cross sections in the Color Glass Condensate (CGC) effective field theory. We demonstrate that the large soft gluon logarithm is correctly factorized into the Balitsky-Kovchegov (BK) renormalization group equation by accurately connecting the NLO scattering kinematics to the rapidity scale of the dipole amplitude in the scattering. This brings the perturbative expansion under control and enables us to do precision comparisons between theory and data. We fit the initial condition of the BK evolution equation to HERA inclusive deep inelastic scattering data by combining the NLO accuracy inclusive cross sections with beyond leading order BK evolution prescriptions. This results in the state-of-the-art accuracy comparison between CGC theory and HERA data, and determination of the dipole amplitude initial shape which is a necessary input for all NLO CGC phenomenology. In this introductory part, the effect of the NLO BK equation on the fits is assessed, and an alternative form for the NLO loop correction to the inclusive cross sections is derived which enables the consistent setting of the dipole amplitude rapidity scale in the NLO corrections. Diffraction is studied in this thesis in the CGC formalism, and we calculate the tree-level $q \bar q g$ NLO contribution to the diffractive deep inelastic scattering structure functions where the $q \bar q g$ Fock state scatters off the target and becomes the diffractively produced system. This contribution has previously been known in the literature only in leading $\log(Q^2)$ accuracy valid at large $Q^2$, and only for the structure function $F^D_T$. The $q \bar q g$ contribution to both structure functions $F^D_T$ and $F^D_L$ are presented in full NLO accuracy., Comment: PhD thesis, introductory part

The basic disentanglement theorem established by the present authors states that estimates on a weighted geometric mean over (convex) families of functions can be disentangled into quantitatively linked estimates on each family separately. On the one hand, the theorem gives a uniform approach to classical results including Maurey's factorisation theorem and Lozanovski\u{\i}'s factorisation theorem, and, on the other hand, it underpins the duality theory for multilinear norm inequalities developed in our previous two papers. In this paper we give a simple proof of this basic disentanglement theorem. Whereas the approach of our previous paper was rather involved - it relied on the use of minimax theory together with weak*-compactness arguments in the space of finitely additive measures, and an application of the Yosida-Hewitt theory of such measures - the alternate approach of this paper is rather straightforward: it instead depends upon elementary perturbation and compactness arguments., Comment: Abstract and introduction revised. 16 pages, 1 diagram

Deep inelastic scattering (DIS) total cross section data at small-x as measured by the HERA experiments is well described by Balitsky-Kovchegov (BK) evolution in the leading order dipole picture. Recently the full Next-to-Leading Order (NLO) dipole picture total cross sections have become available for DIS, and a working factorization scheme has been devised which subtracts the soft gluon divergence present at NLO. We report our recently published work in which we make the first comparisons of the NLO DIS total cross sections to HERA data. The non-perturbative initial condition to BK evolution is fixed by fitting the HERA reduced cross section data. As the NLO results for the DIS total cross section are currently available only in the massless quark limit, we also fit a light-quark-only cross section constructed with a parametrization of published total and heavy quark data. We find an excellent description of the HERA data. Since the full NLO BK equation is computationally expensive, we use a number of beyond LO prescriptions for the evolution that include most important higher order corrections enhanced by large transverse logarithms, including the recent version of the equation formulated in terms of the target momentum fraction., Comment: 5 pages, 4 figures. Prepared for the proceedings of the Hard Probes 2020: 10th International Conference on Hard and Electromagnetic Probes of High-Energy Nuclear Collisions

We perform the first dipole picture fit to HERA inclusive cross section data using the full next-to-leading order (NLO) impact factor combined with an improved Balitsky-Kovchegov evolution including the dominant effects beyond leading logarithmic accuracy at low $x$. We find that three different formulations of the evolution equation that have been proposed in the recent literature result in a very similar description of HERA data, and robust predictions for future deep inelastic scattering experiments. We find evidence pointing towards a significant nonperturbative contribution to the structure function for light quarks, which stresses the need to extend the NLO impact factor calculation to massive quarks., Comment: 20 pages, 9 figures. v2: matches published version. Fit results available at https://doi.org/10.5281/zenodo.4229269

In previous work we established a multilinear duality and factorisation theory for norm inequalities for pointwise weighted geometric means of positive linear operators defined on normed lattices. In this paper we extend the reach of the theory for the first time to the setting of general linear operators defined on normed spaces. The scope of this theory includes multilinear Fourier restriction-type inequalities. We also sharpen our previous theory of positive operators. Our results all share a common theme: estimates on a weighted geometric mean of linear operators can be disentangled into quantitative estimates on each operator separately. The concept of disentanglement recurs throughout the paper. The methods we used in the previous work - principally convex optimisation - relied strongly on positivity. In contrast, in this paper we use a vector-valued reformulation of disentanglement, geometric properties (Rademacher-type) of the underlying normed spaces, and probabilistic considerations related to p-stable random variables., Comment: 32 pages, 3 diagrams. Final version, incorporating referees' comments, to appear in Analysis & PDE

We report a photoacoustic spectroscopy setup with a high-power mid-infrared frequency comb as the light source. The setup is used in broadband spectroscopy of radiocarbon methane. Due to the high sensitivity of a cantilever-enhanced photoacoustic cell and the high power light source, we can reach a detection limit below 100 ppb in a broadband measurement with a sample volume of only a few milliliters. The first infrared spectrum of $^{14}\text{CH}_4$ is reported and given a preliminary assignment. The results lay a foundation for the development of optical detection systems for radiocarbon methane., Comment: corrected typos, added two references

Objective: To develop, and demonstrate the feasibility of, a novel image reconstruction method for absolute Electrical Impedance Tomography (a-EIT) that pairs deep learning techniques with real-time robust D-bar methods. Approach: A D-bar method is paired with a trained Convolutional Neural Network (CNN) as a post-processing step. Training data is simulated for the network using no knowledge of the boundary shape by using an associated nonphysical Beltrami equation rather than simulating the traditional current and voltage data specific to a given domain. This allows the training data to be boundary shape independent. The method is tested on experimental data from two EIT systems (ACT4 and KIT4). Main Results: Post processing the D-bar images with a CNN produces significant improvements in image quality measured by Structural SIMilarity indices (SSIMs) as well as relative $\ell_2$ and $\ell_1$ image errors. Significance: This work demonstrates that more general networks can be trained without being specific about boundary shape, a key challenge in EIT image reconstruction. The work is promising for future studies involving databases of anatomical atlases., Comment: 15 pages, 8 figures, 3 tables

Let $\sigma$ and $\omega$ be locally finite Borel measures on $\mathbb{R}^d$, and let $p\in(1,\infty)$ and $q\in(0,\infty)$. We study the two-weight norm inequality $$ \lVert T(f\sigma) \rVert_{L^q(\omega)}\leq C \lVert f \rVert_{L^p(\sigma)}, \quad \text{for all} \, \, f \in L^p(\sigma), $$ for both the positive summation operators $T=T_\lambda(\cdot \sigma)$ and positive maximal operators $T=M_\lambda(\cdot \sigma)$. Here, for a family $\{\lambda_Q\}$ of non-negative reals indexed by the dyadic cubes $Q$, these operators are defined by $$ T_\lambda(f\sigma):=\sum_Q \lambda_Q \langle f\rangle^\sigma_Q 1_Q \quad\text{ and } \quad M_\lambda(f\sigma):=\sup_Q \lambda_Q \langle f\rangle^\sigma_Q 1_Q, $$ where $\langle f\rangle^\sigma_Q:=\frac{1}{\sigma(Q)} \int_Q |f| d \sigma.$ We obtain new characterizations of the two-weight norm inequalities in the following cases: 1. For $T=T_\lambda(\cdot\sigma)$ in the subrange $q

We initiate the study of a duality theory which applies to norm inequalities for pointwise weighted geometric means of positive operators. The theory finds its expression in terms of certain pointwise factorisation properties of function spaces which are naturally associated to the norm inequality under consideration. We relate our theory to the Maurey-Nikisin-Stein theory of factorisation of operators, and present a fully multilinear version of Maurey's fundamental theorem on factorisation of operators through $L^1$. The development of the theory involves convex optimisation and minimax theory, functional-analytic considerations concerning the dual of $L^\infty$, and the Yosida-Hewitt theory of finitely additive measures. We consider the connections of the theory with the theory of interpolation of operators. We discuss the ramifications of the theory in the context of concrete families of geometric inequalities, including Loomis-Whitney inequalities, Brascamp-Lieb inequalities and multilinear Kakeya inequalities., Comment: Title shortened. Accepted for publication in Jour. Eur. Math. Soc. Paper streamlined and restructured. Several results now have more succinct and general statements and proofs. References added

In the early 90s, researchers began to focus on security as an important property to address in combination with safety. Over the years, researchers have proposed approaches to harmonize activities within the safety and security disciplines. Despite the academic efforts to identify interdependencies and to propose combined approaches for safety and security, there is still a lack of integration between safety and security practices in the industrial context, as they have separate standards and independent processes often addressed and assessed by different organizational teams and authorities. Specifically, security concerns are generally not covered in any detail in safety standards potentially resulting in successfully safety-certified systems that still are open for security threats from e.g., malicious intents from internal and external personnel and hackers that may jeopardize safety. In recent years security has again received an increasing attention of being an important issue also in safety assurance, as the open interconnected nature of emerging systems makes them susceptible to security threats at a much higher degree than existing more confined products.This article presents initial ideas on how to extend safety work to include aspects of security during the context establishment and initial risk assessment procedures. The ambition of our proposal is to improve safety and increase efficiency and effectiveness of the safety work within the frames of the current safety standards, i.e., raised security awareness in compliance with the current safety standards. We believe that our proposal is useful to raise the security awareness in industrial contexts, although it is not a complete harmonization of safety and security disciplines, as it merely provides applicable guidance to increase security awareness in a safety context., Comment: *** Publication date: March 2016 ; URL: http://www.es.mdh.se/publications/4623-

We use a factorization scheme analogous to one proposed for single inclusive forward hadron production to factorize the soft gluon divergence present in the deep inelastic scattering cross sections in the dipole picture at next-to-leading order (NLO). We show numerically that in this carefully constructed scheme it is possible to obtain meaningful results for the DIS cross sections at NLO, and so we are able to quantitatively study the recently derived NLO corrections to the DIS cross sections. We find that the NLO corrections can be significant and sensitive to the details of the factorization scheme used for the resummation of the large logarithms into the BK evolution equation. In the case of an approximative factorization scheme we observe a problematic behavior of the DIS cross sections similar to what has been seen with analogously factorized single inclusive cross sections., Comment: 6 pages, 3 figures. Prepared for the proceedings of the DIS2018: XXVI International Workshop on Deep Inelastic Scattering and Related Subjects

We study the domination of the lattice Hardy--Littlewood maximal operator by sparse operators in the setting of general Banach lattices. We prove that the admissible exponents of the dominating sparse operator are determined by the $q$-convexity of the Banach lattice., Comment: 14 pages, improved presentation

We develop methods needed to perform loop calculations in light cone perturbation theory using a helicity basis, refining the method introduced in our earlier work. In particular this includes implementing a consistent way to contract the four-dimensional tensor structures from the helicity vectors with d-dimensional tensors arising from loop integrals, in a way that can be fully automatized. We demonstrate this explicitly by calculating the one-loop correction to the virtual photon to quark-antiquark dipole light cone wave function. This allows us to calculate the deep inelastic scattering cross section in the dipole formalism to next-to-leading order accuracy. Our results, obtained using the four dimensional helicity scheme, agree with the recent calculation by Beuf using conventional dimensional regularization, confirming the regularization scheme independence of this cross section., Comment: v2: Improved version in response to referee's comments, matches the published version; 47 pages, 21 figures

We study quantitatively the importance of the recently derived NLO corrections to the DIS structure functions at small x in the dipole formalism. We show that these corrections can be significant and depend on the factorization scheme used to resum large logarithms of energy into renormalization group evolution with the BK equation. This feature is similar to what has recently been observed for single inclusive forward hadron production. Using a factorization scheme consistent with the one recently proposed for the single inclusive cross section, we show that it is possible to obtain meaningful results for the DIS cross sections., Comment: 8 pages, RevTeX, 5 figures

Let $\sigma$, $\omega$ be measures on $\mathbb{R}^d$, and let $\{\lambda_Q\}_{Q\in\mathcal{D}}$ be a family of non-negative reals indexed by the collection $\mathcal{D}$ of dyadic cubes in $\mathbb{R}^d$. We characterize the two-weight norm inequality, \begin{equation*} \lVert T_\lambda(f\sigma)\rVert_{L^q(\omega)}\le C \, \lVert f \rVert_{L^p(\sigma)}\quad \text{for every $f\in L^p(\sigma)$,} \end{equation*} for the positive dyadic operator \begin{equation*} T_\lambda(f\sigma):= \sum_{Q\in \mathcal{D}} \lambda_Q \, \Big(\frac{1}{\sigma(Q)} \int_Q f\mathrm{d}\sigma\Big) \, 1_Q \end{equation*} in the difficult range $0