Scientific publications of the Saarland University
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Algorithmic problems for linear recurrence sequences
Get PDFLinear recurrence sequences (LRS) are among the most fundamental and easily definable classes of number sequences, encompassing many classical sequences such as polynomials, powers of two, and the Fibonacci numbers. They also describe the dynamics of iterated linear maps and arise naturally in numerous contexts within computer science, mathematics, and other quantitive sciences. However, despite their simplicity, many easy-to-state decision problems for LRS have stubbornly remained open for decades despite considerable and sustained attention. Chief among these are the Skolem problem and the Positivity problem, which ask to determine, for a given LRS, whether it contains a zero term and whether it contains only positive terms, respectively. For both problems, decidability is currently open, i.e., whether they are algorithmically solvable. In this thesis, we present the following results. For the Skolem problem, we introduce an algorithm for simple LRS whose correctness is unconditional but whose termination relies on two classical, widely-believed number-theoretic conjectures. This algorithm is implementable in practice, and we report on experimental results. For the Positivity problem, we introduce the notion of reversible LRS, which enables us to carve out a large decidable class of sequences. We also examine various expansions of classical logics by predicates obtained from LRS. In particular, we study expansions of monadic second-order logic of the natural numbers with order and present major advances over the seminal results of Büchi, Elgot, and Rabin from the early 1960s. Finally, we investigate fragments of Presburger arithmetic, where, among others, we establish the decidability of the existential fragment of Presburger arithmetic expanded with powers of 2 and 3.Lineare rekursive Folge (LRF) gehören zu den grundlegendsten und am einfachsten zu definierenden Klassen von Zahlenfolgen und umfassen viele klassische Folgen wie Polynome, Zweierpotenzen und die Fibonacci-Zahlen. Sie beschreiben auch die Dynamik iterierter linearer Abbildungen und tauchen in zahlreichen Kontexten der Informatik, Mathematik und anderer quantitativer Wissenschaften auf. Trotz ihrer Einfachheit bleiben jedoch viele leicht zu formulierendes Entscheidungsprobleme für LRF trotz erheblicher und anhaltender Aufmerksamkeit seit Jahrzehnten hartnäckig o en. Dazu gehören vor allem das Skolem-Problem und das Positivitätsproblem, bei denen es darum geht, für eine gegebene LRF zu bestimmen, ob sie einen Nullterm enthält bzw. ob eine LRF nur positive Terme enthält. Für beide Probleme ist die Entscheidbarkeit derzeit o en, d.h., ob sie algorithmisch lösbar sind. In dieser Doktorarbeit präsentieren wir die folgenden Ergebnisse. Für das Skolem- Problem stellen wir einen Algorithmus für einfache LRF vor, dessen Korrektheit nicht an Bedingungen geknüpft ist, dessen Terminerung aber von zwei weithin akzeptierten zahlentheoretischen Vermutungen abhängt. Dieser Algorithmus ist in der Praxis implementierbar, und wir berichten über experimentelle Ergebnisse. Für das Positivitätsproblem führen wir den Begri der umkehrbaren LRF ein, der es uns ermöglicht, eine groÿe, entscheidbare Klasse von Sequenzen zu bestimmen. Wir untersuchen auch verschiedene Erweiterungen klassischer Logiken durch Prädikate, die aus LRF gewonnen werden. Insbesondere untersuchen wir Erweiterungen von monadische Prädikatenlogik zweiter Stufe der natürlichen Zahlen mit Ordnung und präsentieren wichtige Fortschritte gegenüber den bahnbrechenden Ergebnissen von Büchi, Elgot und Rabin aus den frühen 1960er Jahren. Schließlich untersuchen wir Fragmente der Presburger Arithmetik, wo wir unter anderem die Entscheidbarkeit des existentiellen Fragments der Presburger Arithmetik, erweitert mit Potenzen von 2 und 3, beweisen
Efficacy of Electrochemotherapy with Bleomycin, Oxaliplatin, or Oxaliplatin with Bevacizumab in the Treatment of Colorectal Hepatic Metastases in Rats
Get PDFBackground/Objectives: Electrochemotherapy (ECT) has been shown to be effective in
treating colorectal liver metastases when combined with bleomycin (BLM). Based on this
promising finding, we compared in this study the efficacy of BLM with oxaliplatin (OXP)
and bevacizumab (BVZ) in ECT. Methods: WAG/Rij rats were randomized into three
groups and underwent ECT with intravenous injection of BLM, OXP, or OXP with BVZ
for eight days following hepatic tumor cell implantation. Ultrasound and photoacoustic
imaging served to assess oxygen saturation (SO2) and hemoglobin concentration (HbT)
of the developing tumors. Tissue samples were analyzed by histology and immunohis tochemistry. Results: BLM treatment significantly reduced SO2 (33.7%) and HbT (12.7%)
levels compared to pretreatment values. In contrast, the OXP-treated groups exhibited
only modest reductions in both parameters. BLM also induced a markedly higher necrosis
rate (82.6%) compared to OXP and OXP/BVZ (11.0% and 26.3%). Conversely, OXP-treated
tumors exhibited higher apoptosis rates. Furthermore, BLM treatment led to a decrease
in tumor cell proliferation and a reduction in inflammatory response compared to the other treatments. Notably, BLM caused a 26.2% reduction in CD31-positive microvessels,
which was significantly higher than that observed in the OXP group. Conclusions: BLM
showed a more effective anti-tumor activity than OXP, suggesting its preferred use as
chemotherapeutic agent in ECT
A Para-Substituted 2-Phenoxy-1,10-Phenanthroline Ligand for Lanthanide Sensitization: Asymmetric Coordination and Enhanced Emission from Eu3+, Tb3+, Sm3+ and Dy3+ Complexes
Get PDFA para-substituted 1,10-phenanthroline ligand, 2-(4-methylphenoxy)-1,10-phenanthroline
(L24), was synthesized and structurally characterized. Complexes with Eu3+, Tb3+, Sm3+
,
and Dy3+ were obtained in a 2:1 ligand-to-metal ratio and analyzed using single-crystal
x-ray diffraction, photoluminescence spectroscopy, and TD-DFT calculations. Coordination
via the phenanthroline nitrogen atoms, combined with steric asymmetry from the para methylphenoxy group, induces low-symmetry environments favorable for electric-dipole
transitions. Excited-state lifetimes reached 2.12 ms (Eu3+) and 1.12 ms (Tb3+), with quantum
yields of 42% and 68%, respectively. The triplet-state energy of L24 (22,741 cm−1
) aligns
well with emissive levels of Eu3+ and Tb3+, consistent with Latva’s criterion. Fluorescence
titrations indicated positively cooperative complexation, with association constants ranging
from 0.60 to 1.67. Stark splitting and high 5D0 → 7F2/
7F1 intensity ratios (R2 = 6.25) confirm
the asymmetric coordination field. The para-methylphenoxy substituent appears sufficient
to lower coordination symmetry and strengthen electric-dipole transitions, offering a
controlled route to enhance photoluminescence in Eu3+ and Tb3+ complexes
Total Synthesis of Mycoplanecin A
Get PDFThe first total synthesis of mycoplanecin A, a potent
antitubercular macrocyclic depsipeptide natural product targeting the DnaN
sliding clamp, is described. Interesting key steps are the synthesis of the two trans 4-alkylated-L-prolines via an iterative Matteson homologation and an O→N acyl
shift observed during the fragment coupling of the building blocks. The
challenging macrocyclization of the globally deprotected linear precursor was
accomplished under optimized high-temperature, high-dilution conditions. This
work provides chemical access to mycoplanecin A, enabling further biological
investigation and analogue development against the important pathogen
Mycobacterium tuberculosis
Dynamical phases of a Bose-Einstein condensate in a bad optical cavity at optomechanical resonance
Get PDFWe study the emergence of dynamical phases of a Bose-Einstein condensate that is optomechanically coupled
to a dissipative cavity mode and transversally driven by a laser. We focus on the regime close to the optomechani cal resonance, where the atoms’ refractive index shifts the cavity into resonance, assuming fast cavity relaxation.
We derive an effective model for the atomic motion, where the cavity degrees of freedom are eliminated using
perturbation theory in the atom-cavity coupling and benchmark its predictions using numerical simulations based
on the full model. Away from the optomechanical resonance, perturbation theory in the lowest order (adiabatic
elimination) reliably describes the dynamics and predicts chaotic phases with unstable oscillations. Interestingly,
the dynamics close to the optomechanical resonance are qualitatively captured only by including the corrections
to next order (nonadiabatic corrections). In this regime we find limit-cycle phases that describe stable oscillations
of the density with a well-defined frequency. We further show that such limit-cycle solutions are metastable
configurations of the adiabatic model. Our work sheds light on the mechanisms that are required to observe
dynamical phases and predict their existence in atom-cavity systems where a substantial timescale separation is
present
Physical demands and movement characteristics of veterans football players
Get PDFBackground: This study aimed to investigate physical demands and movement
characteristics of veterans football (VF) players. VF players were recruited from
the West and South London Leagues.
Methods: A 15 m shuttle run test was used to assess maximum heart rate
(HRmax), and continuous heart rate was monitored to evaluate the
cardiocirculatory strain during matches. Video analysis was performed to
analyze movement characteristics, such as step counts, number of passes and
sprints, changes of directions (COD), and standing time.
Results: A total of 91 male VF players (age, 45 ± 6 years; BMI, 26.3 ± 4.0 kg/m2
)
participated in the study. The mean heart rate was 147 ± 14 min−1
corresponding
to 80 ± 8% of HRmax, with 57 ± 14% of match time completed above 80% HRmax.
Midfielders completed more sprints (90 ± 10) compared with forwards (34 ± 6,
p < 0.001) and defenders (50 ± 10, p < 0.01). Standing time was significantly
higher (p < 0.001) in forwards (740 ± 87 s) and defenders (649 ± 111 s) than in
midfielders (181 ± 17 s). During a match time of 86 ± 36 min, players covered
5,790 ± 963 steps, equivalent to approximately 6 km, and made 120 ± 59 COD
and 128 ± 62 passes.
Discussion: The cardiocirculatory strain in VF football seems to be considerably
high. Therefore, one VF match appears to be sufficient to meet the minimum of
current guidelines on health-promoting activities. Position-specific differences
in VF are evident for midfielders, who are potentially exposed to higher
physical demands compared with other field positions
Multimethod assessment of self-regulated learning in primary, secondary, and tertiary education – A meta-analysis
Get PDFSelf-regulated learning (SRL) can be measured in several ways, which can be broadly classified into online and offline instruments. Although both online and offline measurements have advantages and disadvantages, the over-dependence of SRL research on offline measurements has been criticised considerably. Currently, efforts are being made to use multimethod SRL assessments. We examined 20 articles with 351 effect sizes that assessed SRL with at least two instruments on at least two SRL components. Most effect sizes were not statistically significant but descriptively higher than others. Combinations of two online instruments showed the highest effect size (r = 0.24). Overall correlations between instruments were highest for university students (r = 0.21). Additionally, results for cognition showed the highest effect size measured with behavioural traces (r = 0.28), and for metacognition measured with microanalysis (r = 0.35). The component of motivation was best measured using self-report questionnaires (r = 0.29).
Educational relevance statement
Self-regulated learning is an important predictor of academical success. It is therefore necessary to measure it as precise and comprehensive as possible. Knowing which instruments are best suited for each age group, SRL component, or reliably predict a specific achievement variable can help educators pick the best instrument for their needs
Radiochemistry of cyclen-derived chelators comprising five-membered azaheterocyclic arms with 212Pb2+, 213Bi3+, and 225Ac3+☆,☆☆
Get PDFIn this work, we introduce the cyclen-based metal chelator DOTThia comprising four methylthiazole arms for metal complexation. Together with the recently described congener DOTI-Me bearing four methylimidazole arms, the radiochemistry of these two compounds with 212Pb, 213Bi, and 225Ac was investigated thoroughly. Radiolabeling experiments were performed at various pH values and temperatures to determine the optimal conditions for quantitative radiochemical conversions. Experiments revealed excellent complexation properties of DOTThia for 212Pb at room temperature, comparable to those of the current gold standard for Pb complexation, TCMC, while it was not well suited for 213Bi. Contrarily, DOTI-Me exhibited quantitative radiochemical conversions for 213Bi at pH 5.5 and room temperature, outperforming the metal chelator macropa, but was not able to quantitatively complex 212Pb under any conditions investigated. Of note, both novel chelators were not able to bind 225Ac. In preliminary experiments, we could also show that a functionalized DOTI-Me derivative is capable of complexing 213Bi selectively from 225Ac solutions. This feature may allow the preparation of 213Bi-labeled radiotracers directly from 225Ac solutions without the need for an 225Ac/213Bi generator. However, more detailed studies are needed to fully explore this potential application. Altogether, our results support the future development of 212Pb-labeled radiopharmaceuticals using bifunctional derivatives of DOTThia as well as of 213Bi-labeled radiotracers based on the DOTI-Me scaffold
A useful data presentation tool: Ternary plots in forensic medicine
No full textTernary plots are triangle shaped diagrams which display the proportions of three given categories in an information dense format. This short communication aims at demonstrating ternary plots as a method of data presentation in forensic medicine. In addition, a practical example is given and discussed. They are generally underutilized in medicine and forensic medicine in particular. This method paper describes how to read and design ternary plots. Template files are provided. Example diagrams for “manner of death in custody” are demonstrated and discussed
The power of mathematical modeling and simulation in cardiometabolic disorders: Personalized treatment optimization and disease trajectories
Get PDFThis dissertation investigates the potential of mathematical modeling to enhance the management of cardiometabolic diseases. These conditions represent a major global health challenge due to their high prevalence and the complex nature of underlying metabolic risk factors. Utilizing nonlinear mixed-effects (NLME) modeling, the projects presented in this thesis demonstrate that modeling can (i) improve the accuracy of clinical biomarker data, (ii) incorporate biological rhythms into pharmacokinetic analyses, and (iii) support the development of cost-efficient treatment strategies. The methodological focus includes correcting biases in biomarker measurements, capturing circadian variation in drug exposure, and evaluating flexible dosing regimens that balance therapeutic efficacy with cost-effectiveness. By aligning quantitative insights with clinical practice, this work illustrates how data-driven modeling can personalize treatment and optimize healthcare resource allocation. The findings highlight mathematical modeling as a valuable tool for advancing precision medicine in cardiometabolic care through more adaptive, efficient, and individualized treatment approaches.Diese Dissertation zeigt das Potenzial mathematischer Modellierung zur Verbesserung des Managements kardiometabolischer Erkrankungen auf. Aufgrund der hohen Prävalenz und der komplexen metabolischen Risikofaktoren stellen diese Erkrankungen eine bedeutende globale Gesundheitsherausforderung dar. Diese Arbeit vereint drei Projekte, die jeweils mittels mathematischer Modellierung nichtlinearer gemischter Effekte (NLME) zeigen, wie Modellierungsansätze (i) die Genauigkeit klinischer Messergebnisse von Biomarkern verbessern, (ii) biologische Schwankungen in pharmakokinetische Analysen integrieren und (iii) zur Entwicklung kosteneffizienter Behandlungsstrategien beitragen können. Dabei liegt der methodische Fokus auf der Korrektur von Biomarker-Messungen infolge fehlerhafter Probenlagerung, der Beschreibung und Erklärung von zirkadianen Variationen in der Wirkstoffexposition sowie der Entwicklung flexibler Dosierungsschemata, die therapeutische Wirksamkeit mit ökonomischen Aspekten in Einklang bringen. Durch die Verknüpfung quantitativer Modellierung mit klinischer Anwendung veranschaulicht diese Arbeit, wie datenbasierte Ansätze zur Personalisierung von Therapien und zur effizienteren Nutzung von Gesundheitsressourcen beitragen können. Die Ergebnisse unterstreichen den Mehrwert mathematischer Modellierung als ein Instrument für eine adaptivere, effektivere und individuellere Versorgung von Patienten mit kardiometabolischen Erkrankungen