arXiv subjects

M. Lesch

Publications and source records attributed to M. Lesch.

3 recordsLinked to original sources

arXiv2026

Large-scale real-time signal processing in physics experiments: The ALICE TPC FPGA pipeline

For LHC Run 3, the ALICE Time Projection Chamber was upgraded to operate in continuous readout mode. Interaction rates of up to 50 kHz in Pb-Pb collisions require real-time processing of more than 3 TB/s of raw detector data. This requirement is met by a custom FPGA-based processing pipeline that performs the complete front-end data treatment fully in-stream, including common-mode correction, pedestal subtraction, ion-tail filtering, zero suppression, and dense data packing. A central element of the design is a highly parallel common-mode correction algorithm operating directly on the streaming data. It robustly identifies signal-free readout channels on a time-bin basis and applies pad-dependent scaling to compensate for local variations in capacitive coupling in the GEM readout. In combination with pedestal subtraction and ion-tail filtering, this enables accurate baseline restoration under extreme high-occupancy conditions, preventing signal loss while efficiently suppressing noise prior to zero suppression. The pipeline operates continuously at the full detector bandwidth and reduces the raw input rate to about 900 GB/s for Pb-Pb collisions at the target interaction rate. Overall, it represents a large-scale FPGA-based real-time signal-processing implementation for high-energy physics detector readout.

physics.ins-det↗

arXiv2020

Fredholm conditions and index for restrictions of invariant pseudodifferential operators to isotypical components

Let $\Gamma$ be a compact group acting on a smooth, compact manifold $M$, let $P \in \psi^m(M; E_0, E_1)$ be a $\Gamma$-invariant, classical pseudodifferential operator acting between sections of two equivariant vector bundles $E_i \to M$, $i = 0,1$, and let $\alpha$ be an irreducible representation of the group $\Gamma$. Then $P$ induces a map $\pi_\alpha(P) : H^s(M; E_0)_\alpha \to H^{s-m}(M; E_1)_\alpha$ between the $\alpha$-isotypical components of the corresponding Sobolev spaces of sections. When $\Gamma$ is finite, we explicitly characterize the operators $P$ for which the map $\pi_\alpha(P)$ is Fredholm in terms of the principal symbol of $P$ and the action of $\Gamma$ on the vector bundles $E_i$. When $\Gamma = \{1\}$, that is, when there is no group, our result extends the classical characterization of Fredholm (pseudo)differential operators on compact manifolds. The proof is based on a careful study of the symbol $C^*$-algebra and of the topology of its primitive ideal spectrum. We also obtain several results on the structure of the norm closure of the algebra of invariant pseudodifferential operators and their relation to induced representations. Whenever our results also hold for non-discrete groups, we prove them in this greater generality. As an illustration of the generality of our results, we provide some applications to Hodge theory and to index theory of singular quotient spaces.

math.DG↗

arXiv2002

On the L^2-Stokes theorem and Hodge theory for singular algebraic varieties

For a projective algebraic variety $V$ with isolated singularities, endowed with a metric induced from an embedding, we consider the analysis of the natural partial differential operators on the regular part of $V$. We show that, in the complex case, the Laplacians of the de Rham and Dolbeault complexes are discrete operators except possibly in degrees $n,n\pm 1$, where $n$ is the complex dimension of $V$. We also prove a Hodge theorem on the operator level and the $L^2$--Stokes theorem outside the degrees $n-1,n$. We show that the $L^2$-Stokes theorem may fail to hold in the case of real algebraic varieties, and also discuss the $L^2$-Stokes theorem on more general non-compact spaces.

math.DG↗