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Mercyful Fate:
🎵 Evil
#MercyfulFate
https://mercyfulfate.bandcamp.com/album/evil
https://open.spotify.com/track/5pH1BecbNktYDbYw0XCEWn

LA-based MarqVision, which uses AI to monitor marketplaces for counterfeits, raised a $48M Series B led by Peak XV Partners, bringing its total funding to ~$90M (Kate Park/TechCrunch)
https://techcrunch.com/2025/09/15/harvard-law-to-ai-marqvisi…

Harvard Law to AI: MarqVision lands $48M to combat brand abuse | TechCrunch
This LA-based startup raised $48M to tackle brand abuse

Markov dualities via the spectral decompositions of the two Markov generators in their bi-orthogonal basis of right and left eigenvectors
Cecile Monthus
https://arxiv.org/abs/2507.11041

Markov dualities via the spectral decompositions of the two Markov generators in their bi-orthogonal basis of right and left eigenvectors
The notion of Markov duality between two Markov processes that can live in two different configurations spaces $(x,{\tilde x})$ is revisited via the spectral decompositions of the two Markov generators in their bi-orthogonal basis of right and left eigenvectors. In this formulation, the two generators should have the same eigenvalues $(-E)$ that may be complex, while the duality function $Ω(x,{\tilde x})$ can be considered as a mapping between the right and the left eigenvectors of the two mod…

Least squares estimation of the transition density in bifurcating Markov models
S. Val\`ere Bitseki Penda
https://arxiv.org/abs/2509.12906 https://arxiv.or…

Least squares estimation of the transition density in bifurcating Markov models
In this article, we propose a least squares method for the estimation of the transition density in bifurcating Markov models. Unlike the kernel estimation, this method do not use the quotient which can be a source of errors. In order to study the rate of convergence for least squares estimators, we develop exponential inequalities for empirical process of bifurcating Markov chain under bracketing assumption. Unlike the classical processes, we observe that for bifurcating Markov chains, the comp…

Learning non-Markovian Dynamical Systems with Signature-based Encoders
Eliott Pradeleix, R\'emy Hosseinkhan-Boucher, Alena Shilova, Onofrio Semeraro, Lionel Mathelin
https://arxiv.org/abs/2509.12022

Learning non-Markovian Dynamical Systems with Signature-based Encoders
Neural ordinary differential equations offer an effective framework for modeling dynamical systems by learning a continuous-time vector field. However, they rely on the Markovian assumption - that future states depend only on the current state - which is often untrue in real-world scenarios where the dynamics may depend on the history of past states. This limitation becomes especially evident in settings involving the continuous control of complex systems with delays and memory effects. To capt…

Finding the Smallest Possible Exact Aggregation of a Markov Chain
Patrick Sonnentag
https://arxiv.org/abs/2507.11157 https://arxiv.or…

Finding the Smallest Possible Exact Aggregation of a Markov Chain
Markov chains are an important tool for modelling and evaluating systems in computer science, economics, biology and numerous other fields. Thus, approximating Markov chains is a useful tool for decreasing the computational effort needed for analysis by reducing the size of the state space. So far, most approximative algorithms focused on finding approximations, which are, again, Markov chains. We remove this restriction and present an algorithm using the Arnoldi iteration. Further, we show tha…

Multi-Component VAE with Gaussian Markov Random Field
Fouad Oubari, Mohamed El-Baha, Raphael Meunier, Rodrigue D\'ecatoire, Mathilde Mougeot
https://arxiv.org/abs/2507.12165

Multi-Component VAE with Gaussian Markov Random Field
Multi-component datasets with intricate dependencies, like industrial assemblies or multi-modal imaging, challenge current generative modeling techniques. Existing Multi-component Variational AutoEncoders typically rely on simplified aggregation strategies, neglecting critical nuances and consequently compromising structural coherence across generated components. To explicitly address this gap, we introduce the Gaussian Markov Random Field Multi-Component Variational AutoEncoder , a novel gener…

Resetting Induces Memory Loss in Non-Markovian Processes
Debasish Saha, Rati Sharma
https://arxiv.org/abs/2509.11608 https://arxiv.org/pdf/2509.11608

Resetting Induces Memory Loss in Non-Markovian Processes
Stochastic resetting is a powerful strategy known to accelerate the first-passage time statistics of stochastic processes. While its effects on Markovian systems are well understood, a general framework for non-Markovian dynamics is still lacking, mostly due to its mathematical complexity. Here, we present an analytical and numerical framework to study non-Markovian processes under resetting, focusing on the first-passage properties of escape kinetics from metastable states. We show that resett…

Markov approximation for controlled Hawkes Jump-Diffusions with general kernels
Mahmoud Khabou, Mehdi Talbi
https://arxiv.org/abs/2507.11294 https://

Markov approximation for controlled Hawkes Jump-Diffusions with general kernels
We present a Markov approximation for jump-diffusions whose jump part consists in a Hawkes process with intensity driven by a general (possibly non-monotone) kernel. Under minimal integrability conditions, the kernel can be approximated by a linear combination of exponential functions. This implies that Hawkes jump-diffusions can be approximated with Markov jump-diffusions. We illustrate the usefulness of this approximation by applying it to a class of stochastic control problems.