Dithering by Differences of Convex Functions

Motivated by a recent halftoning method which is based on electrostatic principles, we analyse a halftoning framework where one minimizes a functional consisting of the difference of two convex functions (DC). One of them describes attracting forces caused by the image gray values, the other one enforces repulsion between points. In one dimension, the minimizers of our functional can be computed analytically and have the following desired properties: the points are pairwise distinct, lie within the image frame and can be placed at grid points. In the two-dimensional setting, we prove some useful properties of our functional like its coercivity and suggest to compute a minimizer by a forward-backward splitting algorithm. We show that the sequence produced by such an algorithm converges to a critical point of our functional. Furthermore, we suggest to compute the special sums occurring in each iteration step by a fast summation technique based on the fast Fourier transform at non-equispaced knots which requires only Ο(m log(m)) arithmetic operations for m points. Finally, we present numerical results showing the excellent performance of our DC dithering method

Detecting dominant changes in irregularly sampled multivariate water quality data sets

Time series of groundwater and stream water quality often exhibit substantial temporal and spatial variability, whereas typical existing monitoring data sets, e.g. from environmental agencies, are usually characterized by relatively low sampling frequency and irregular sampling in space and/or time. This complicates the differentiation between anthropogenic influence and natural variability as well as the detection of changes in water quality which indicate changes in single drivers. We suggest the new term "dominant changes" for changes in multivariate water quality data which concern (1) multiple variables, (2) multiple sites and (3) long-term patterns and present an exploratory framework for the detection of such dominant changes in data sets with irregular sampling in space and time. Firstly, a non-linear dimension-reduction technique was used to summarize the dominant spatiotemporal dynamics in the multivariate water quality data set in a few components. Those were used to derive hypotheses on the dominant drivers influencing water quality. Secondly, different sampling sites were compared with respect to median component values. Thirdly, time series of the components at single sites were analysed for long-term patterns. We tested the approach with a joint stream water and groundwater data set quality consisting of 1572 samples, each comprising sixteen variables, sampled with a spatially and temporally irregular sampling scheme at 29 sites in northeast Germany from 1998 to 2009. The first four components were interpreted as (1) an agriculturally induced enhancement of the natural background level of solute concentration, (2) a redox sequence from reducing conditions in deep groundwater to post-oxic conditions in shallow groundwater and oxic conditions in stream water, (3) a mixing ratio of deep and shallow groundwater to the streamflow and (4) sporadic events of slurry application in the agricultural practice. Dominant changes were observed for the first two components. The changing intensity of the first component was interpreted as response to the temporal variability of the thickness of the unsaturated zone. A steady increase in the second component at most stream water sites pointed towards progressing depletion of the denitrification capacity of the deep aquifer

Nodular lymphocyte predominant hodgkin lymphoma and T cell/histiocyte rich large B cell lymphoma : endpoints of a spectrum of one disease?

In contrast to the commonly indolent clinical behavior of nodular lymphocyte predominant Hodgkin lymphoma (NLPHL), T cell/histiocyte rich large B cell lymphoma (THRLBCL) is frequently diagnosed in advanced clinical stages and has a poor prognosis. Besides the different clinical presentations of these lymphoma entities, there are variants of NLPHL with considerable histopathologic overlap compared to THRLBCL. Especially THRLBCL-like NLPHL, a diffuse form of NLPHL, often presents a histopathologic pattern similar to THRLBCL, suggesting a close relationship between both lymphoma entities. To corroborate this hypothesis, we performed gene expression profiling of microdissected tumor cells of NLPHL, THRLBCL-like NLPHL and THRLBCL. In unsupervised analyses, the lymphomas did not cluster according to their entity. Moreover, even in supervised analyses, very few consistently differentially expressed transcripts were found, and for these genes the extent of differential expression was only moderate. Hence, there are no clear and consistent differences in the gene expression of the tumor cells of NLPHL, THRLBCL-like NLPHL and THRLBCL. Based on the gene expression studies, we identified BAT3/BAG6, HIGD1A, and FAT10/UBD as immunohistochemical markers expressed in the tumor cells of all three lymphomas. Characterization of the tumor microenvironment for infiltrating T cells and histiocytes revealed significant differences in the cellular composition between typical NLPHL and THRLBCL cases. However, THRLBCL-like NLPHL presented a histopathologic pattern more related to THRLBCL than NLPHL. In conclusion, NLPHL and THRLBCL may represent a spectrum of the same disease. The different clinical behavior of these lymphomas may be strongly influenced by differences in the lymphoma microenvironment, possibly related to the immune status of the patient at the timepoint of diagnosis

A Study of Particle Motion in the Presence of Clusters

The motivation for this study came from the task of analysing the kinetic behavior of single molecules in a living cell based on Single Molecule Localization Microscopy. Given measurements of both the motion of clusters and molecules, the main task consists in detecting if a molecule belongs to a cluster. While the exact size of the clusters is usually unknown, upper bounds are available. In this study, we simulate the cluster movement by a Brownian motion and those of the particles by a Gaussian mixture model with two modes depending on the position of the particle within or outside a cluster. We propose various variational models to detect if a particle lies within a cluster based on the Wasserstein and maximum mean discrepancy distances between measures. We compare the performance of the proposed models for simulated data

Organisationsprobleme

1. Einleitung In der vorliegenden Diplomarbeit wird in einem Unternehmen eine Fallstudienuntersuchung durchgeführt. Anhand von Interviews wird hierbei versucht, im Unternehmen aufgetretene Organisationsprobleme darzustellen. „Welche Arten von Organisationsproblemen gibt es im Unternehmen; sind diese über mehrere Probleminstanzen, das heißt die konkreten Fallstudien, konsistent; weisen sie Zusammenhänge untereinander auf?“ 2. Methode Die Theorie, die den Studien zugrunde liegt ergibt sich aus dem Organisationsbegriff, aus dem die beiden Hauptproblemgruppen der Koordinations- und Motivationsprobleme abgeleitet werden. Die Analyseeinheit ist das Unternehmen selbst. Für die Untersuchung werden drei Fälle bewusst ausgewählt. Zur Datenerhebung werden rezeptive Interviews mit mehreren Interviewpartnern pro Fall durchgeführt. Zur Analyse der Daten wird in Anlehnung an entscheidungstheoretische Organisationsliteratur ein Rahmenwerk für die Kategorisierung der aufgetretenen Organisationsprobleme entwickelt. Für die aufgetretenen „Koordinationsprobleme“ ergeben sich dabei die Kategorien „Ressourceneffizienz“, „Prozesseffizienz“, „Delegationseffizienz“ und „Markteffizienz“. Für die Hauptproblemgruppe der „Motivationsprobleme“ ergeben sich die Kategorien „Aufgabengestaltung“, „Planung“, „Führungsverhalten“, „Be-, Entlohnung“ und „Unternehmenskultur“. Diesen Kategorien werden im Zuge der „within case“-Analyse die einzelnen, von den Interviewpartnern dargestellten, Probleme zugeordnet. 3. „cross case“-Analyse und Schlussfolgerung Durch die Kategorisierung der Probleme wird in der „cross case“-Analyse erkennbar, dass sich die Problemschwerpunkte im Unternehmen im Bereich der Motivationsprobleme, genauer gesagt in den Kategorien „Planung“ und „Führungsverhalten“ befinden. Diesen beiden Kategorien können in allen Fällen die meisten, von den Interviewpartnern dargestellten, Probleme zugeordnet werden. Zusammenhänge finden sich zwischen den Kategorien „Planung“ und „Führungsverhalten“ sowie zwischen den Bereichen „Ressourceneffizienz“, „Prozesseffizienz“ und „Aufgabengestaltung“, die jeweils gemeinsam in den Fällen auftreten.1. Introduction In this thesis, case study research is carried out in a company. Organizational problems that occurred in the company are studied and presented on the basis of previously conducted interviews. “Which types of organizational problems can be identified during research; do these problems appear consistently; do correlations exist between particular categories of the framework or between problems that occurred in these particular categories?“ 2. Methodology The theory which underlies the study is derived from the theoretical organizational concept. This concept leads to the definition of the two main problem categories: “coordination problems” and “motivation problems”. The gathered information is analyzed using a framework of systematic evaluation criteria. Therefore the class of “coordination problems” is split up into following categories: “resource efficiency”, “process efficiency”, “delegation efficiency” and “market efficiency”. The class of “motivation problems” contains following categories: “job design“, „planning”, “leadership behavior”, “remuneration” and “corporate culture”. 4. Cross Case Analysis and Conclusion Through the classification of the problems, the identification of critical problem areas within the company is made possible during cross case analysis. These critical problem categories are “planning” and “leadership behavior”, which are found in the class of “motivation problems”. Problems of these two categories were mentioned in all three cases by most interviewees. Correlations could be found between “planning” and “leadership behavior” and between the areas of “resource efficiency”, “process efficiency” and “job design”. Problems of these categories always occurred conjointly

Conditional Wasserstein Distances with Applications in Bayesian OT Flow Matching

In inverse problems, many conditional generative models approximate the posterior measure by minimizing a distance between the joint measure and its learned approximation. While this approach also controls the distance between the posterior measures in the case of the Kullback--Leibler divergence, this is in general not hold true for the Wasserstein distance. In this paper, we introduce a conditional Wasserstein distance via a set of restricted couplings that equals the expected Wasserstein distance of the posteriors. Interestingly, the dual formulation of the conditional Wasserstein-1 flow resembles losses in the conditional Wasserstein GAN literature in a quite natural way. We derive theoretical properties of the conditional Wasserstein distance, characterize the corresponding geodesics and velocity fields as well as the flow ODEs. Subsequently, we propose to approximate the velocity fields by relaxing the conditional Wasserstein distance. Based on this, we propose an extension of OT Flow Matching for solving Bayesian inverse problems and demonstrate its numerical advantages on an inverse problem and class-conditional image generation.Comment: This paper supersedes arXiv:2310.1343

Sparse additive function decompositions facing basis transforms

High-dimensional real-world systems can often be well characterized by a small number of simultaneous low-complexity interactions. The analysis of variance (ANOVA) decomposition and the anchored decomposition are typical techniques to find sparse additive decompositions of functions. In this paper, we are interested in a setting, where these decompositions are not directly spare, but become so after an appropriate basis transform. Noting that the sparsity of those additive function decompositions is equivalent to the fact that most of its mixed partial derivatives vanish, we can exploit a connection to the underlying function graphs to determine an orthogonal transform that realizes the appropriate basis change. This is done in three steps: we apply singular value decomposition to minimize the number of vertices of the function graph, and joint block diagonalization techniques of families of matrices followed by sparse minimization based on relaxations of the zero ''norm'' for minimizing the number of edges. For the latter one, we propose and analyze minimization techniques over the manifold of special orthogonal matrices. Various numerical examples illustrate the reliability of our approach for functions having, after a basis transform, a sparse additive decomposition into summands with at most two variables.Comment: 46 pages, 10 figures, 8 table

Effects of synchronous, auditory stimuli on running performance and heart rate

Research has demonstrated that the human being tends to couple body movements and external, acoustic stimuli (metronome or music). This effect is called auditory-motor synchronization. Motivational music possesses qualities which distract from feelings like fatigue and exertion. Combining these two effects may enhance the sports performance even more. Investigations showed that runners can increase their original cadence up to 2%. The purpose of this study was to examine the effects of accelerated, synchronized stimuli on the running performance. Therefore, 28 students (15 ♀, 13 ♂) of the Institute of Sports Science in Innsbruck were asked to do two cooper tests each. After run 1 (no auditory signal), the sample was divided into two groups. In run 2, which took place on a different day, one group listened to music while running; the other group was stimulated by the sound of a metronome. Distance (m) and average heartrate were measured. 75% of the athletes achieved a greater distance under the influence of an acoustic stimulus. In fact, the running distance changed significantly using an acoustic stimulus: +61 m (SD ± 100) or 2.1% (SD ± 3.6). In group 1 (music), the performance improved up to + 3.8% (SD ± 3.3). This difference was significant compared to group 2 (metronome). The average heart rate decreased by 1.5 beats (SD ± 5) from run 1 to run 2. Influenced by music, the average heart rate measured 179 beats (SD ± 8) in contrast to 182 beats (SD ± 10) in run 1 (no acoustic stimulus). If the tempo of the acoustic stimulus is adapted to the accelerated cadence of an athlete (maximum 2%), improved distances due to the synchronization effect can be achieved. In combination with the motivating qualities of music, improved effects in sport performances could be produced

Tumor-microenvironment and molecular biology of classic Hodgkin lymphoma in children, adolescents, and young adults

Classic Hodgkin lymphoma (cHL) exhibits a bimodal age distribution with incidence peaks in adolescents and young adults (AYAs) aged 15-39 years and in older adults over 50 years. The unique biology of cHL, characterized by a tumor microenvironment (TME) composed predominantly of non-malignant immune and stromal cells, plays a pivotal role in supporting Hodgkin and Reed-Sternberg (HRS) cells, the malignant cells of cHL. Understanding the role of the TME in cHL and its age-related differences is crucial for deciphering differential disease etiologies and developing biomarker-driven targeted therapies. Recent technical advances in single-cell sequencing and multiplexed spatial imaging have revealed age-related differences in TME composition and function, including key cellular interactions, leading to the development of age-specific prognostic indicators. In addition, advances in our ability to isolate nucleic acids from HRS cells have accelerated our understanding of the molecular alterations in cHL, many of which drive interactions within the TME. Molecular differences in cHL between pediatric/AYA and older adult patients have also emerged. This review summarizes the unique biology of cHL and its TME in children, adolescents, and young adults, highlighting recent breakthroughs in our understanding of cHL biology, differences across the age spectrum, and advances in biomarker development