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Michael Reiter

Publications and source records attributed to Michael Reiter.

At least 19 recordsLinked to original sources
arXiv2025

The classification of CR maps from hyperquadrics into tubes over null cones of symmetric forms

We classify CR maps from the hyperquadric of signature $l>0$ in $\mathbb{C}^n$, $n\geq 3$, to the local model for the tube over the null cone of a symmetric form in $\mathbb{C}^{n+1}$, up to CR automorphisms of the source and target. In contrast to the setting of the Heisenberg hypersurface in $\mathbb{C}^3$ (i.e., the case $l=0$), studied earlier in Reiter--Son [27], our analysis uncovers two new equivalence classes of CR maps of geometric rank one and one new class of geometric rank two in the case $n=3$. In the case $n\geq 4$, we establish that all maps extend to local isometries of certain indefinite K\"ahler metrics. We further derive a classification of (local) proper holomorphic maps from the generalized unit ball $\mathbb{B}^n_l$ into a generalized version of the Lie ball $D^{\mathrm{IV}}_{m,l}$ (the generalized classical domain of type~IV).

math.CV↗
arXiv2025

Blocklisted Oblivious Pseudorandom Functions

An oblivious pseudorandom function (OPRF) is a protocol by which a client and server interact to evaluate a pseudorandom function on a key provided by the server and an input provided by the client, without divulging the key or input to the other party. We extend this notion by enabling the server to specify a blocklist, such that OPRF evaluation succeeds only if the client's input is not on the blocklist. More specifically, our design gains performance by embedding the client input into a metric space, where evaluation continues only if this embedding does not cluster with blocklist elements. Our framework exploits this structure to separate the embedding and blocklist check to enable efficient implementations of each, but then must stitch these phases together through cryptographic means. Our framework also supports subsequent evaluation of the OPRF on the same input more efficiently. We demonstrate the use of our design for password blocklisting in augmented password-authenticated key exchange, and to MAC only executables that are not similar to ones on a blocklist of known malware.

cs.CR↗
arXiv2024

On the importance of local and global feature learning for automated measurable residual disease detection in flow cytometry data

This paper evaluates various deep learning methods for measurable residual disease (MRD) detection in flow cytometry (FCM) data, addressing questions regarding the benefits of modeling long-range dependencies, methods of obtaining global information, and the importance of learning local features. Based on our findings, we propose two adaptations to the current state-of-the-art (SOTA) model. Our contributions include an enhanced SOTA model, demonstrating superior performance on publicly available datasets and improved generalization across laboratories, as well as valuable insights for the FCM community, guiding future DL architecture designs for FCM data analysis. The code is available at \url{https://github.com/lisaweijler/flowNetworks}.

cs.CV↗
arXiv2024

Automated Immunophenotyping Assessment for Diagnosing Childhood Acute Leukemia using Set-Transformers

Acute Leukemia is the most common hematologic malignancy in children and adolescents. A key methodology in the diagnostic evaluation of this malignancy is immunophenotyping based on Multiparameter Flow Cytometry (FCM). However, this approach is manual, and thus time-consuming and subjective. To alleviate this situation, we propose in this paper the FCM-Former, a machine learning, self-attention based FCM-diagnostic tool, automating the immunophenotyping assessment in Childhood Acute Leukemia. The FCM-Former is trained in a supervised manner, by directly using flow cytometric data. Our FCM-Former achieves an accuracy of 96.5% assigning lineage to each sample among 960 cases of either acute B-cell, T-cell lymphoblastic, and acute myeloid leukemia (B-ALL, T-ALL, AML). To the best of our knowledge, the FCM-Former is the first work that automates the immunophenotyping assessment with FCM data in diagnosing pediatric Acute Leukemia.

cs.LG↗
arXiv2024

On CR maps from the sphere into the tube over the future light cone II: Higher dimensions

We determine all CR maps from the sphere in $\mathbb{C}^3$ into the tube over the future light cone in $\mathbb{C}^4$. This result leads to a complete characterization of proper holomorphic maps from the three-dimensional unit ball into the classical domain of type IV of four dimension and confirms a conjecture of Reiter - Son in [26] from 2022. Additionally, we prove a boundary characterization of isometric holomorphic embeddings from a ball into a classical domain of type IV in arbitrary dimensions that is similar to the main result in Huang - Lu - Tang - Xiao [16]. The result is then used to treat a special case in the general characterization.

math.CV↗
arXiv2024

On CR maps between hyperquadrics and Winkelmann hypersurfaces

In this paper, we study CR maps between hyperquadrics and Winkelmann hypersurfaces. Based on a previous study on the CR Ahlfors derivative of Lamel-Son and a recent result of Huang-Lu-Tang-Xiao on CR maps between hyperquadrics, we prove that a transversal CR map from a hyperquadric into a hyperquadric or a Winkelmann hypersurface extends to a local holomorphic isometric embedding with respect to certain K\"ahler metrics if and only if the Hermitian part of its CR Ahlfors derivative vanishes on an open set of the source. Our proof is based on relating the geometric rank of a CR map into a hyperquadric and its CR Ahlfors derivative.

math.CV↗
arXiv2023

FATE: Feature-Agnostic Transformer-based Encoder for learning generalized embedding spaces in flow cytometry data

While model architectures and training strategies have become more generic and flexible with respect to different data modalities over the past years, a persistent limitation lies in the assumption of fixed quantities and arrangements of input features. This limitation becomes particularly relevant in scenarios where the attributes captured during data acquisition vary across different samples. In this work, we aim at effectively leveraging data with varying features, without the need to constrain the input space to the intersection of potential feature sets or to expand it to their union. We propose a novel architecture that can directly process data without the necessity of aligned feature modalities by learning a general embedding space that captures the relationship between features across data samples with varying sets of features. This is achieved via a set-transformer architecture augmented by feature-encoder layers, thereby enabling the learning of a shared latent feature space from data originating from heterogeneous feature spaces. The advantages of the model are demonstrated for automatic cancer cell detection in acute myeloid leukemia in flow cytometry data, where the features measured during acquisition often vary between samples. Our proposed architecture's capacity to operate seamlessly across incongruent feature spaces is particularly relevant in this context, where data scarcity arises from the low prevalence of the disease. The code is available for research purposes at https://github.com/lisaweijler/FATE.

eess.IV↗
arXiv2023

Explainable Techniques for Analyzing Flow Cytometry Cell Transformers

Explainability for Deep Learning Models is especially important for clinical applications, where decisions of automated systems have far-reaching consequences. While various post-hoc explainable methods, such as attention visualization and saliency maps, already exist for common data modalities, including natural language and images, little work has been done to adapt them to the modality of Flow CytoMetry (FCM) data. In this work, we evaluate the usage of a transformer architecture called ReluFormer that ease attention visualization as well as we propose a gradient- and an attention-based visualization technique tailored for FCM. We qualitatively evaluate the visualization techniques for cell classification and polygon regression on pediatric Acute Lymphoblastic Leukemia (ALL) FCM samples. The results outline the model's decision process and demonstrate how to utilize the proposed techniques to inspect the trained model. The gradient-based visualization not only identifies cells that are most significant for a particular prediction but also indicates the directions in the FCM feature space in which changes have the most impact on the prediction. The attention visualization provides insights on the transformer's decision process when handling FCM data. We show that different attention heads specialize by attending to different biologically meaningful sub-populations in the data, even though the model retrieved solely supervised binary classification signals during training.

q-bio.QM↗
arXiv2023

What Would Trojans Do? Exploiting Partial-Information Vulnerabilities in Autonomous Vehicle Sensing

Safety-critical sensors in autonomous vehicles (AVs) form an essential part of the vehicle's trusted computing base (TCB), yet they are highly susceptible to attacks. Alarmingly, Tier 1 manufacturers have already exposed vulnerabilities to attacks introducing Trojans that can stealthily alter sensor outputs. We analyze the feasible capability and safety-critical outcomes of an attack on sensing at a cyber level. To further address these threats, we design realistic attacks in AV simulators and real-world datasets under two practical constraints: attackers (1) possess only partial information and (2) are constrained by data structures that maintain sensor integrity.Examining the role of camera and LiDAR in multi-sensor AVs, we find that attacks targeting only the camera have minimal safety impact due to the sensor fusion system's strong reliance on 3D data from LiDAR. This reliance makes LiDAR-based attacks especially detrimental to safety. To mitigate the vulnerabilities, we introduce security-aware sensor fusion incorporating (1) a probabilistic data-asymmetry monitor and (2) a scalable track-to-track fusion of 3D LiDAR and monocular detections (T2T-3DLM). We demonstrate that these methods significantly diminish attack success rate.

cs.CR↗
arXiv2022

On highly degenerate CR maps of spheres

For $N \geq 4$ we classify the $(N-3)$-degenerate smooth CR maps of the three-dimensional unit sphere into the $(2N-1)$-dimensional unit sphere. Each of these maps has image being contained in a five-dimensional complex-linear space and is of degree at most two, or equivalent to one of the four maps into the five-dimensional sphere classified by Faran. As a byproduct of our classification we obtain new examples of rational maps of degree three which are $(N-3)$-degenerate only along a proper real subvariety and are not equivalent to polynomial maps. In particular, by changing the base point, it is possible to construct new families of nondegenerate maps.

math.CV↗
arXiv2021

Automated Identification of Cell Populations in Flow Cytometry Data with Transformers

Acute Lymphoblastic Leukemia (ALL) is the most frequent hematologic malignancy in children and adolescents. A strong prognostic factor in ALL is given by the Minimal Residual Disease (MRD), which is a measure for the number of leukemic cells persistent in a patient. Manual MRD assessment from Multiparameter Flow Cytometry (FCM) data after treatment is time-consuming and subjective. In this work, we present an automated method to compute the MRD value directly from FCM data. We present a novel neural network approach based on the transformer architecture that learns to directly identify blast cells in a sample. We train our method in a supervised manner and evaluate it on publicly available ALL FCM data from three different clinical centers. Our method reaches a median F1 score of ~0.94 when evaluated on 519 B-ALL samples and shows better results than existing methods on 4 different datasets

q-bio.QM↗
arXiv2021

On CR maps from the sphere into the tube over the future light cone

We determine all local smooth or formal CR maps from the unit sphere $\mathbb{S}^3\subset \mathbb{C}^2$ into the tube $\mathcal{T}:= \mathcal{C} \times i\mathbb{R}^3 \subset \mathbb{C}^3$ over the future light cone $\mathcal{C}:= \left\{x\in \mathbb{R}^3\colon x_1^2+x_2^2 = x_3^2, \ x_3 > 0\right\}$. This result leads to a complete classification of proper holomorphic maps from the unit ball in $\mathbb{C}^2$ into Cartan's classical domain of type IV in $\mathbb{C}^3$ that extend smoothly to some boundary point. Up to composing with CR automorphisms of the source and target, the classification consists of four algebraic maps. Two maps among them were known earlier in the literature, which were shown to be ``rigid'' in the higher dimensional case in a recent paper by Xiao and Yuan. Two newly discovered quadratic polynomial maps provide counterexamples to a conjecture appeared in the same paper for the case of dimension two.

math.CV↗
arXiv2019

The reflection map and infinitesimal deformations of sphere mappings

The reflection map introduced by D'Angelo is applied to deduce simpler descriptions of nondegeneracy conditions for sphere maps and to the study of infinitesimal deformations of sphere maps. It is shown that the dimension of the space of infinitesimal deformations of a nondegenerate sphere map is bounded from above by the explicitly computed dimension of the space of infinitesimal deformations of the homogeneous sphere map. Moreover a characterization of the homogeneous sphere map in terms of infinitesimal deformations is provided.

math.CV↗
arXiv2019

Deformations of CR maps and applications

We study the deformation theory of CR maps in the positive codimensional case. In particular, we study structural properties of the {\em mapping locus} $E$ of (germs of nondegenerate) holomorphic maps $H \colon (M,p) \to M'$ between generic real submanifolds $M \subset \mathbb C^N$ and $M' \subset \mathbb C^{N'}$, defined to be the set of points $p' \in M'$ which admit such a map with $H(p) = p'$. We show that this set $E$ is semi-analytic and provide examples for which $E$ posseses (prescribed) singularities.

math.CV↗
arXiv2019

On the Chern-Moser-Weyl tensor of real hypersurfaces

We derive an explicit formula for the well-known Chern-Moser-Weyl tensor for nondegenerate real hypersurfaces in complex space in terms of their defining functions. The formula is considerably simplified when applying to "pluriharmonic perturbations" of the sphere or to a Fefferman approximate solution to the complex Monge-Amp\`ere equation. As an application, we show that the CR invariant one-form $X_{\alpha}$ constructed recently by Case and Gover is nontrivial on each real ellipsoid of revolution in $\mathbb{C}^3$, unless it is equivalent to the sphere. This resolves affirmatively a question posed by these two authors in 2017 regarding the (non-) local CR invariance of the $\mathcal{I}'$-pseudohermitian invariant in dimension five and provides a counterexample to a recent conjecture by Hirachi.

math.CV↗
arXiv2017

Infinitesimal and local rigidity of mappings of CR manifolds

A holomorphic mapping $H$ between two real-analytic CR manifolds $M$ and $M'$ is said to be locally rigid if any other holomorphic map $F\colon M \to M'$ which is close enough to $H$ is obtained by composing $H$ with suitable automorphisms of $M$ and $M'$. With the aim of reducing the local rigidity problem to a linear one, we provide sufficient infinitesimal conditions. Furthermore we study some topological properties of the action of the automorphism group on the space of nondegenerate mappings from $M$ to $M'$.

math.CV↗
arXiv2015

Local and infinitesimal rigidity of hypersurface embeddings

We study local rigidity properties of holomorphic embeddings of real hypersurfaces in $\mathbb C^2$ into real hypersurfaces in $\mathbb C^3$ and show that infinitesimal conditions imply actual local rigidity in a number of (important) cases. We use this to show that generic embeddings into a hyperquadric in $\mathbb C^3$ are locally rigid.

math.CV↗