Optimales Beschaffungsdesign: Ein reduzierter Formansatz
Standard procurement models assume that the buyer knows the quality of the good at the time of procurement; Jedoch, in vielen Umgebungen, the quality is learned only long after the transaction. We study procurement problems in which the buyer’s valuation of the...
Dynamische Mittelfeldanalyse adaptiver Langevin-Diffusionen: Ausbreitung des Chaos und Konvergenz der linearen Reaktion
Motivated by an application to empirical Bayes learning in high-dimensional regression, we study a class of Langevin diffusions in a system with random disorder, where the drift coefficient is driven by a parameter that continuously adapts to the empirical distribution of the...
Dynamische Mittelfeldanalyse adaptiver Langevin-Diffusionen: Replikasymmetrischer Fixpunkt und empirische Bayes
In vielen Anwendungen der statistischen Schätzung durch Stichprobenziehung, one may wish to sample from a high-dimensional target distribution that is adaptively evolving to the samples already seen. Wir untersuchen ein Beispiel einer solchen Dynamik, given by a Langevin diffusion for posterior sampling...
Hochempfindliche und hochauflösende kollaborative Bestimmung von Doppelbrechungskoeffizient mittels schwacher Messung
We present a high-sensitivity and high-resolution birefringence coefficient determination system for nm-level membrane films based on weak measurement, addressing the sensitivity-resolution trade-off. A tunable bandwidth light source is exploited to achieve complementary momentum (P-pointer) and intensity (I-pointer) measurements,enabling calibration-free operation across various...
Globale Lösungen für quadratische 5D-Schrödinger-Gleichungen vierter Ordnung
We prove small data scattering for the fourth-order Schr\”odinger equation with quadratic nonlinearity \begin{Gleichung*} i\partial_t u+\Delta^2 u+\alpha u^2 + \beta \bar{u}^2=0\qquad\text{In }\mathbb{R}^5 \end{Gleichung*} for $\alpha, \beta \in \mathbb{R}$. We extend the space-time resonance method, ursprünglich von Germain eingeführt, Masmoudi, and Shatah, to...
Erkundung der Benutzererfahrung von KI-gestützten Soundsuchsystemen für Kreative Arbeitsabläufe
Locating the right sound effect efficiently is an important yet challenging topic for audio production. Most current sound-searching systems rely on pre-annotated audio labels created by humans, which can be time-consuming to produce and prone to inaccuracies, limiting the efficiency of audio...
Optimale Versuchsplanung in Echtzeit zur Parameteridentifizierung von Elektrochemisches Modell einer Li-Ionen-Zelle
Accurately identifying the parameters of electrochemical models of li-ion battery (LiB) cells is a critical task for enhancing the fidelity and predictive ability. Traditional parameter identification methods often require extensive data collection experiments and lack adaptability in dynamic environments. This paper describes...
A characterization of closed subfunctors through $3\times 3$-lemma property in extriangulated categories
Gegeben sei eine extriangulierte Kategorie $(\mathematisch{C},\mathbb{E},\mathfrak{S})$, we introduce the $3 \times 3$-lemma property for subfunctors of $\mathbb{E}$ and prove that an additive subfunctor $\mathbb{F}$ of $\mathbb{E}$ ist geschlossen, wenn, und nur wenn, es erfüllt diese Bedingung. This characterization extends a well known result...
Zum Preis der differenziellen Privatsphäre für hierarchisches Clustering
Hierarchical clustering is a fundamental unsupervised machine learning task with the aim of organizing data into a hierarchy of clusters. Many applications of hierarchical clustering involve sensitive user information, therefore motivating recent studies on differentially private hierarchical clustering under the rigorous framework...
Zentrale Grenzwertsätze und moderate Abweichungen für additive Funktionale von SSEP auf normalen Bäumen
In diesem Papier, Es geht uns um den symmetrischen einfachen Ausschlussprozess (SSEP) on the regular tree $\mathcal{T}_d$. A central limit theorem and a moderate deviation principle of the additive functional of the process are proved, which include the CLT and the...