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Accelerated Methods for Riemannian Min-Max Optimization Ensuring Bounded Geometric Penalties
No full textA Case Study of the Use of Logical Data Analysis in the Workmen’s Village in Tell el-Amarna, Egypt
No full textThe search for patterns in archaeological contexts is crucial to understanding ancient
civilizations, including the organization of their societies and economies. This study
focuses on the interdisciplinary application of mathematical logical data analysis to
Egyptology, particularly examining food production in the Workmen’s Village of
Amarna. The introduction provides historical context about Amarna, founded by
Pharaoh Akhenaten, and outlines the settlement structure and excavations of the
Workmen’s Village. The research utilizes archaeobotanical and archaeological data,
along with digital humanities tools, to identify activity areas related to food production.
The findings reveal spatial patterns in the distribution of tools such as mortars, pestles,
and ovens, providing insights into the self-sufficiency and daily life of the villagers.
Logical data analysis helps in finding rules and patterns in a dataset which are not
visible otherwise, predicting the distribution of unexcavated areas and thus in this case
enhancing our understanding of ancient Egyptian food production practices in state-
planned settlements
An efficient first-order conditional gradient algorithm in data-driven sparse identification of nonlinear dynamics to solve sparse recovery problems under noise
No full textOn the split closure of the periodic timetabling polytope
No full textThe Periodic Event Scheduling Problem (PESP) is the central mathematical tool for periodic timetable optimization in public transport. PESP can be formulated in several ways as a mixed-integer linear program with typically general integer variables. We investigate the split closure of these formulations and show that split inequalities are identical with the recently introduced flip inequalities. While split inequalities are a general mixed-integer programming technique, flip inequalities are defined in purely combinatorial terms, namely cycles and arc sets of the digraph underlying the PESP instance. It is known that flip inequalities can be separated in pseudo-polynomial time. We prove that this is best possible unless P = NP, but also observe that the complexity becomes linear-time if the cycle defining the flip inequality is fixed. Moreover, introducing mixed-integer-compatible maps, we compare the split closures of different formulations, and show that reformulation or binarization by subdivision do not lead to stronger split closures. Finally, we estimate computationally how much of the optimality gap of the instances of the benchmark library PESPlib can be closed exclusively by split cuts, and provide better dual bounds for five instances
Dynamic control of X-ray core-exciton resonances by Coulomb screening in photoexcited semiconductors
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Konzeption und Entwicklung einer Plattform zur geographisch verteilten Bereitstellung von latenzkritischen Anwendungen
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Independently engaging protein tethers of different length enhance synaptic vesicle trafficking to the plasma membrane
No full textSynaptic vesicle (SV) trafficking toward the plasma membrane (PM) and subsequent SV maturation are essential for neurotransmitter release. These processes, including SV docking and priming, are coordinated by various proteins, such as SNAREs, Munc13, and Synaptotagmin (Syt), which connect—tether—the SV to the PM. Here, we investigated how tethers of varying lengths mediate SV docking using a simplified mathematical model. The heights of the three tether types—estimated from the structures of the SNARE complex, Munc13, and Syt—defined the SV-to-PM distance ranges for tether formation. Geometric considerations linked SV-to-PM distances to the probability and rate of tether formation. We assumed that SV tethering constrains SV motility and that multiple tethers associate by independent interactions. The model predicted that forming multiple tethers favors shorter SV-to-PM distances. Although tethers acted independently in the model, their geometrical properties often caused sequential assembly, from longer ones (Munc13/Syt), that accelerated SV movement towards the PM, to shorter ones (SNAREs) which stabilized PM-proximal SVs. Modifying tether lengths or numbers affected SV trafficking. The independent implementation of tethering proteins enabled their selective removal to mimic gene knockout situations. This showed that simulated SV-to-PM distance distributions qualitatively aligned with published EM studies upon removal of SNARE and Syt tethers, while Munc13 knockout data were best approximated when assuming additional disruption of SNARE tethers. Thus, while salient features of SV docking can be accounted for by independent tethering alone, our results suggest that functional tether interactions not yet featured in our model are crucial for biological function
Dynamics of systems with varying number of particles: from Liouville equations to general master equations for open systems
No full textA varying number of particles is one of the most relevant characteristics of systems of interest in nature and technology, ranging from the exchange of energy and matter with the surrounding environment to the change of particle number through internal dynamics such as reactions. The physico-mathematical modeling of these systems is extremely challenging, with the major difficulty being the time dependence of the number of degrees of freedom and the additional constraint that the increment or reduction of the number and species of particles must not violate basic physical laws. Theoretical models, in such a case, represent the key tool for the design of computational strategies for numerical studies that deliver trustful results. In this manuscript, we review complementary physico-mathematical approaches of varying number of particles inspired by rather different specific numerical goals. As a result of the analysis on the underlying common structure of these models, we propose a unifying master equation for general dynamical systems with varying number of particles. This equation embeds all the previous models and can potentially model a much larger range of complex systems, ranging from molecular to social agent-based dynamics