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McKay's conjecture (1971) on character degrees was reduced by Isaacs-Malle-Navarro (2007) to a so-called inductive condition on characters of finite quasisimple groups [IMN07], thus opening the way to a proof of McKay's conjecture using the classification of finite simple groups. After [Ma07], [Ma08], [S12], [CS13], [KS16], [MS16], [CS17a], [CS17b], [CS19], [S23a], [S23b], we complete here the last step of a proof with an analysis of the representations of certain normalizers ${\mathrm N}_G({\mathbf S})$ in $G={\mathbf G}^F$ of maximal $d$-tori ${\mathbf S}$ ($d\geq 3$) of the ambient simple simply-connected algebraic group ${\mathbf G}$ of type ${\mathrm D}_l$ ($l\geq 4$) for which $F$ is a Frobenius endomorphism. To establish the so-called local conditions A$(d)$ and B$(d)$, we introduce a certain class of $F$-stable reductive subgroups ${\mathbf M}\leq {\mathbf G}$ of maximal rank where ${\mathbf M}^\circ$ is of type ${\mathrm D}_{l_1}\times {\mathrm D}_{l-l_1}$ with ${\mathbf M}/{\mathbf M}^\circ$ of order 2. They are an efficient substitute for ${\mathrm N}_G({\mathbf S})$ or the local subgroups in non-defining characteristic relevant to McKay's abstract statement. For a general class of those subgroups ${\mathbf M}^F$ we describe their characters and the action of $\operatorname {Aut}({\mathbf G}^F)_{{\mathbf M}^F}$ on them, showing in particular that $\mathrm{Irr}({\mathbf M}^F)$ and $\mathrm {Irr}({\mathbf G}^F)$ share some key features in that regard. With this established, McKay's conjecture is now a theorem stating $\textit{McKay's equality}$: For any prime $\ell$, any finite group has as many irreducible complex characters of degree prime to $\ell$ as the normalizers of its Sylow $\ell$-subgroups.

Several evolved stars have been found to exhibit long-period radial velocity variations that cannot be explained by planetary or brown dwarf companions. Non-radial oscillations caused by oscillatory convective modes have been put forth as an alternative explanation, but no modeling attempt has yet been undertaken. We provide a model of a non-radial oscillation, aiming to explain the observed variations of the cluster giant NGC 4349 No. 127. The star was previously reported to host a brown dwarf companion, but whose existence was later refuted in the literature. We reanalyzed 58 archival HARPS spectra, acquiring additional activity indicators using the SERVAL and RACCOON pipelines. We searched for periodicity in the indicators and correlations between the indicators and radial velocities. We further present a simulation code able to produce synthetic HARPS spectra, incorporating the effect of non-radial oscillations, and compare the simulated results to the observed variations. We find a positive correlation between chromatic index and radial velocity, along with closed-loop Lissajous-like correlations between radial velocity and each of the spectral line shape indicators (full width at half maximum, and contrast of the cross-correlation function and differential line width). Simulations of a low-amplitude, retrograde, dipole (l = 1, m = 1), non-radial oscillation can reproduce the observed behavior and explain the observables. Photometric variations below the detection threshold of the available ASAS-3 photometry are predicted. The oscillation and stellar parameters are largely in agreement with the prediction of oscillatory convective modes. The periodic variations of the radial velocities and activity indicators, along with the respective phase shifts, measured for the intermediate-mass cluster giant NGC 4349 No. 127, can be explained by a non-radial oscillation., Comment: 23 pages, 14 figures. Accepted in A&A. Abstract abridged for arXiv submission

Quantitative mass spectrometry has revolutionized proteomics by enabling simultaneous quantification of thousands of proteins. Pooling patient-derived data from multiple institutions enhances statistical power but raises significant privacy concerns. Here we introduce FedProt, the first privacy-preserving tool for collaborative differential protein abundance analysis of distributed data, which utilizes federated learning and additive secret sharing. In the absence of a multicenter patient-derived dataset for evaluation, we created two, one at five centers from LFQ E.coli experiments and one at three centers from TMT human serum. Evaluations using these datasets confirm that FedProt achieves accuracy equivalent to DEqMS applied to pooled data, with completely negligible absolute differences no greater than $\text{$4 \times 10^{-12}$}$. In contrast, -log10(p-values) computed by the most accurate meta-analysis methods diverged from the centralized analysis results by up to 25-27. FedProt is available as a web tool with detailed documentation as a FeatureCloud App., Comment: 52 pages, 16 figures, 12 tables. Last two authors listed are joint last authors

In this work, we explore the integration of discontinuous Orientation Selection into steering interfaces intending to preserve the seamless sensation of real-world movement, while mitigating the risk of inducing cybersickness. Our implementation encounters conflicts in standard input mappings, prompting us to adopt bimanual interaction as a solution. Recognizing the complexity that may arise from this step, we also develop unimanual alternatives, e.g., utilizing a Human-Joystick, commonly referred to as Leaning interface. The outcomes of an empirical study centered around a primed search task yield unexpected findings. We observed a sample of users spanning multiple levels of gaming experience and a balanced gender distribution exhibit no significant difficulties with the bimanual, asymmetric interfaces. Remarkably, the performance of Orientation Selection is, as in prior work, at least on par with Snap Rotation. Moreover, through a subsequent exploratory analysis, we uncover indications that Pointing-Directed Steering outperforms embodied interfaces in usability and task load in the given setting.

Origami structures have been widely explored in robotics due to their many potential advantages. Origami robots can be very compact, as well as cheap and efficient to produce. In particular, they can be constructed in a flat format using modern manufacturing techniques. Rotational motion is essential for robotics, and a variety of origami rotational joints have been proposed in the literature. However, few of these are even approximately flat-foldable. One potential enabler of flat origami rotational joints is the inclusion of lightweight pneumatic pouches which actuate the origami's folds; however, pouch actuators only enable a relatively small amount of rotational displacement. The previously proposed Four-Vertex Origami is a flat-foldable structure which provides an angular multiplier for a pouch actuator, but suffers from a degenerate state. This paper presents a novel rigid origami, the Self-Lock Origami, which eliminates this degeneracy by slightly relaxing the assumption of flat-foldability. This joint is analysed in terms of a trade-off between the angular multiplier and the mechanical advantage. Furthermore, the Self-Lock Origami is a modular joint which can be connected to similar or different joints to produce complex movements for various applications; three different manipulator designs are introduced as a proof of concept., Comment: 11 pages, 8 figures

We determine the action of the outer automorphism group Out$(G)$ on the set of irreducible characters Irr$(G)$ for all finite quasi-simple groups $G$. For groups of Lie type, this includes the construction of an Out$(G)$-equivariant Jordan decomposition of characters (Theorem B). We also prove an extendibility statement, called condition $A(\infty)$, see Theorem A. Among the methods used here in the case of groups of type D and $^2$D, we blend the Shintani descent ideas introduced in [CS19, \S~3] and an analysis of semisimple classes in the dual group $G^*$ from [CS22]. This enables us to control the action of graph and field automorphisms within Lusztig's rational series of characters and to count extendible characters. Condition $A(\infty)$ originates in the program to prove the McKay conjecture using the classification of finite simple groups, see [IMN07]. Using the local results from [MS16], our main theorem implies the McKay conjecture for the prime 3 and all finite groups.

The Becker DeGroot Marshak method is widely used to elicit the valuation that an individual assigns to an object. Theoretically, the second-price structure of the method gives individuals the incentive to state their true valuation. Yet, the elicitation methods empirical accuracy is subject to debate. With this paper, I provide a clear verification of the qualitative accuracy of the method. Participants of an incentivized laboratory experiment can sell a virtual object. The value of the object is publicly known and experimentally varied in a between-subjects design. Replicating previous findings on the low quantitative accuracy, I observe a very small share of individuals placing a payoff-optimal stated valuation. However, the analysis shows that the stated valuation increases with the value of the object. This result shows the qualitative accuracy of the BDM method and suggests that the method can be applied in comparative studies.

We analyze the causal impact of positive and negative feedback on professional performance. We exploit a unique data source in which quasi-random, naturally occurring variations within subjective ratings serve as positive and negative feedback. The analysis shows that receiving positive feedback has a favorable impact on subsequent performance, while negative feedback does not have an effect. These main results are found in two different environments and for distinct cultural backgrounds, experiences, and gender of the feedback recipients. The findings imply that managers should focus on giving positive motivational feedback.

Recent work has shown the potential of graph neural networks to efficiently predict material properties, enabling high-throughput screening of materials. Training these models, however, often requires large quantities of labelled data, obtained via costly methods such as ab initio calculations or experimental evaluation. By leveraging a series of material-specific transformations, we introduce CrystalCLR, a framework for constrastive learning of representations with crystal graph neural networks. With the addition of a novel loss function, our framework is able to learn representations competitive with engineered fingerprinting methods. We also demonstrate that via model finetuning, contrastive pretraining can improve the performance of graph neural networks for prediction of material properties and significantly outperform traditional ML models that use engineered fingerprints. Lastly, we observe that CrystalCLR produces material representations that form clusters by compound class., Comment: 7 pages, 3 figures, NeurIPS 2022 AI for Accelerated Materials Design Workshop

Therapeutic antibody development has become an increasingly popular approach for drug development. To date, antibody therapeutics are largely developed using large scale experimental screens of antibody libraries containing hundreds of millions of antibody sequences. The high cost and difficulty of developing therapeutic antibodies create a pressing need for computational methods to predict antibody properties and create bespoke designs. However, the relationship between antibody sequence and activity is a complex physical process and traditional iterative design approaches rely on large scale assays and random mutagenesis. Deep learning methods have emerged as a promising way to learn antibody property predictors, but predicting antibody properties and target-specific activities depends critically on the choice of antibody representations and data linking sequences to properties is often limited. Existing works have not yet investigated the value, limitations and opportunities of these methods in application to antibody-based drug discovery. In this paper, we present results on a novel SARS-CoV-2 antibody binding dataset and an additional benchmark dataset. We compare three classes of models: conventional statistical sequence models, supervised learning on each dataset independently, and fine-tuning an antibody specific pre-trained language model. Experimental results suggest that self-supervised pretraining of feature representation consistently offers significant improvement in over previous approaches. We also investigate the impact of data size on the model performance, and discuss challenges and opportunities that the machine learning community can address to advance in silico engineering and design of therapeutic antibodies.

In adjoint reductive groups $H$ of type $\mathsf{D}$ we show that for every semisimple element $s$, its centralizer splits over its connected component, i.e., $C_H(s) = C_H(s)^\circ \rtimes \check A$ for some complement $\check A$ with strong stability properties. We derive several consequences about the action of automorphisms on semisimple conjugacy classes. This helps to parametrize characters of the finite groups $\mathsf{D}_{l,\text{sc}}(q)$ and $^2\mathsf{D}_{l,\text{sc}}(q)$ and describe the action of automorphisms on them. It is also a contribution to the final proof of the McKay conjecture for the prime 3, see [S21], [S23]., Comment: 11 pages, to appear in Vietnam J. Math

Magnetic nanomaterials record information as fast as picoseconds in computer memories but retain it for millions of years in ancient rocks. This exceedingly broad range of times is covered by hopping over a potential energy barrier through temperature, ultrafast optical excitation for demagnetization or magnetization manipulation, mechanical stress, or microwaves. As switching depends on nanoparticle size, shape, orientation, and material properties, only single-nanoparticle studies can eliminate ensemble heterogeneity. Here, we push the sensitivity of photothermal magnetic circular dichroism down to individual 20-nm magnetite nanoparticles. Single-particle magnetization curves display superparamagnetic to ferromagnetic behaviors, depending on size, shape, and orientation. Some nanoparticles undergo thermally activated switching on time scales of milliseconds to minutes. Surprisingly, the switching barrier appears to vary in time, leading to dynamical heterogeneity. Our observations will help to identify and eventually control the nanoscale parameters influencing the switching of magnetic nanoparticles, an important step for applications in many fields.

Previous work has shown that taint analyses are only useful if correctly customized to the context in which they are used. Existing domain-specific languages (DSLs) allow such customization through the definition of deny-listing data-flow rules that describe potentially vulnerable taint-flows. These languages, however, are designed primarily for security experts who are knowledgeable in taint analysis. Software developers consider these languages to be complex. This paper presents fluentTQL, a query language particularly for taint-flow. fluentTQL is internal Java DSL and uses a fluent-interface design. fluentTQL queries can express various taint-style vulnerability types, e.g. injections, cross-site scripting or path traversal. This paper describes fluentTQL's abstract and concrete syntax and defines its runtime semantics. The semantics are independent of any underlying analysis and allows evaluation of fluentTQL queries by a variety of taint analyses. Instantiations of fluentTQL, on top of two taint analysis solvers, Boomerang and FlowDroid, show and validate fluentTQL expressiveness. Based on existing examples from the literature, we implemented queries for 11 popular security vulnerability types in Java. Using our SQL injection specification, the Boomerang-based taint analysis found all 17 known taint-flows in the OWASP WebGoat application, whereas with FlowDroid 13 taint-flows were found. Similarly, in a vulnerable version of the Java PetClinic application, the Boomerang-based taint analysis found all seven expected taint-flows. In seven real-world Android apps with 25 expected taint-flows, 18 were detected. In a user study with 26 software developers, fluentTQL reached a high usability score. In comparison to CodeQL, the state-of-the-art DSL by Semmle/GitHub, participants found fluentTQL more usable and with it they were able to specify taint analysis queries in shorter time., Comment: 39 pages, Springer Journal on Empirical Software Engineering

The Dynamic State Index is a scalar quantity designed to identify atmospheric developments such as fronts, hurricanes or specific weather pattern. The DSI is defined as Jacobian-determinant of three constitutive quantities that characterize three-dimensional fluid flows: the Bernoulli stream function, the potential vorticity (PV) and the potential temperature. Here, we tackle the questions (i) if the mathematical formulation of the DSI can be reduced, while keeping the main information, and (ii) does the reduction of the DSI depend on the spatial scale? Applying principle component analysis we find that three of six DSI terms that sum up to the Jacobi-determinant are sufficient for future DSI calculations.

We show that the decomposition matrix of a given group $G$ is unitriangular, whenever $G$ has a normal subgroup $N$ such that the decomposition matrix of $N$ is unitriangular, $G/N$ is abelian and certain characters of $N$ extend to their stabilizer in $G$. Using the recent result by Brunat--Dudas--Taylor establishing that unipotent blocks have a unitriangular decomposition matrix, this allows us to prove that blocks of groups of quasi-simple groups of Lie type have a unitriangular decomposition matrix, whenever they are related via Bonnaf\'e--Dat--Rouquier's equivalence to a unipotent block. This is then applied to study the action of automorphisms on Brauer characters of finite quasi-simple groups. We use it to verify the so-called {\it inductive Brauer--Glaubermann condition}, that aims to establish a Glauberman correspondence for Brauer characters, given a coprime action.

This is a contribution to the study of $\operatorname {Irr}(G)$ as an $\operatorname {Aut}(G)$-set for $G$ a finite quasi-simple group. Focusing on the last open case of groups of Lie type $\mathrm D$ and $^2\mathrm D$, a crucial property is the so-called condition $A'(\infty)$ expressing that diagonal automorphisms and graph-field automorphisms of $G$ have transversal orbits in $\operatorname {Irr}(G)$. This is part of the stronger $A(\infty)$ condition introduced in the context of the reduction of the McKay conjecture to a question on quasi-simple groups. Our main theorem is that a minimal counter-example to condition $A(\infty)$ for groups of type $\mathrm D$ would still satisfy $A'(\infty)$. This will be used in a second paper to fully establish $A(\infty)$ for any type and rank. The present paper uses Harish-Chandra induction as a parametrization tool. We give a new, more effective proof of the theorem of Geck and Lusztig ensuring that cuspidal characters of arbitrary standard Levi subgroups of $G={\mathrm D}_{ l,\mathrm{sc}}(q)$ extend to their stabilizers in the normalizer of that Levi subgroup. This allows to control the action of automorphisms on these extensions. From there Harish Chandra theory leads naturally to a detailed study of associated relative Weyl groups and other extendibility problems in that context., Comment: 55 pages, to appear in Nagoya Mathematical Journal

Voxel-based structures provide a modular, mechanically flexible periodic lattice which can be used as a soft robot through internal deformations. To engage these structures for robotic tasks, we use a finite element method to characterize the motion caused by deforming single degrees of freedom and develop a reduced kinematic model. We find that node translations propagate periodically along geometric planes within the lattice, and briefly show that translational modes dominate the energy usage of the actuators. The resulting kinematic model frames the structural deformations in terms of user-defined control and end effector nodes, which further reduces the model size. The derived Planes of Motion (POM) model can be equivalently used for forward and inverse kinematics, as demonstrated by the design of a tripod stable gait for a locomotive voxel robot and validation of the quasi-static model through physical experiments., Comment: 10 pages, 7 figures

Machine Learning (ML) and Artificial Intelligence (AI) have shown promising results in many areas and are driven by the increasing amount of available data. However, this data is often distributed across different institutions and cannot be shared due to privacy concerns. Privacy-preserving methods, such as Federated Learning (FL), allow for training ML models without sharing sensitive data, but their implementation is time-consuming and requires advanced programming skills. Here, we present the FeatureCloud AI Store for FL as an all-in-one platform for biomedical research and other applications. It removes large parts of this complexity for developers and end-users by providing an extensible AI Store with a collection of ready-to-use apps. We show that the federated apps produce similar results to centralized ML, scale well for a typical number of collaborators and can be combined with Secure Multiparty Computation (SMPC), thereby making FL algorithms safely and easily applicable in biomedical and clinical environments.

Facilitated meetings are an established practice for the requirements engineering activities elicitation and validation. Focus groups are one well-known technique to implement this practice. Several researchers already reported the successful use of vision videos to stimulate active discussions among the participants of on-site focus groups, e.g., for validating scenarios and eliciting feedback. These vision videos show scenarios of a system vision. In this way, the videos serve all parties involved as a visual reference point to actively disclose, discuss, and align their mental models of the future system to achieve shared understanding. In the joint project TrUSD, we had planned to conduct such an on-site focus group using a vision video to validate a scenario of a future software tool, the so-called Privacy Dashboard. However, the COVID-19 pandemic and its associated measures led to an increase in home and remote working, which also affected us. Therefore, we had to replan and conduct the focus group virtually. In this paper, we report about our experiences and recommendations for the use of vision videos in virtual focus groups., Comment: Gesellschaft f\"ur Informatik, Fachgruppentreffen Requirements Engineering 2020

Aggregating transcriptomics data across hospitals can increase sensitivity and robustness of differential expression analyses, yielding deeper clinical insights. As data exchange is often restricted by privacy legislation, meta-analyses are frequently employed to pool local results. However, if class labels are inhomogeneously distributed between cohorts, their accuracy may drop. Flimma (https://exbio.wzw.tum.de/flimma/) addresses this issue by implementing the state-of-the-art workflow limma voom in a privacy-preserving manner, i.e. patient data never leaves its source site. Flimma results are identical to those generated by limma voom on combined datasets even in imbalanced scenarios where meta-analysis approaches fail., Comment: 27 pages, 7 figures

We give a criterion that simplifies the checking of the inductive Alperin weight condition for the remaining open cases of simple groups of Lie type. It is strongly related in form to the criterion of the second author for the inductive McKay conditions (see [Sp\"a12,2.12]) that has proved very useful. The proof follows from a Clifford theory for weights intrinsically present in the proof of reduction theorems of the Alperin weight conjecture given by Navarro--Tiep and the second author. We also give a related criterion for the inductive blockwise Alperin weight condition.

The Alperin-McKay conjecture relates height zero characters of an $\ell$-block with the ones of its Brauer correspondent. This conjecture has been reduced to the so-called inductive Alperin-McKay conditions about quasi-simple groups by the third author. Those conditions are still open for groups of Lie type. The present paper describes characters of height zero in $\ell$-blocks of groups of Lie type over a field with $q$ elements when $\ell$ divides $q-1$. We also give information about $\ell$-blocks and Brauer correspondents. As an application we show that quasi-simple groups of type $C$ over $\mathbb{F}_q$ satisfy the inductive Alperin-McKay conditions for primes $\ell\geq 5$ and dividing $q-1$. Some methods to that end are adapted from the work of Malle--Sp\"ath.

Artificial intelligence (AI) has been successfully applied in numerous scientific domains. In biomedicine, AI has already shown tremendous potential, e.g. in the interpretation of next-generation sequencing data and in the design of clinical decision support systems. However, training an AI model on sensitive data raises concerns about the privacy of individual participants. For example, summary statistics of a genome-wide association study can be used to determine the presence or absence of an individual in a given dataset. This considerable privacy risk has led to restrictions in accessing genomic and other biomedical data, which is detrimental for collaborative research and impedes scientific progress. Hence, there has been a substantial effort to develop AI methods that can learn from sensitive data while protecting individuals' privacy. This paper provides a structured overview of recent advances in privacy-preserving AI techniques in biomedicine. It places the most important state-of-the-art approaches within a unified taxonomy and discusses their strengths, limitations, and open problems. As the most promising direction, we suggest combining federated machine learning as a more scalable approach with other additional privacy preserving techniques. This would allow to merge the advantages to provide privacy guarantees in a distributed way for biomedical applications. Nonetheless, more research is necessary as hybrid approaches pose new challenges such as additional network or computation overhead., Comment: 17 pages, 3 figures, 3 tables. Methods of Information in Medicine (2022)

We propose a modular architecture for neuromorphic closed-loop control based on bistable relaxation oscillator modules consisting of three spiking neurons each. Like its biological prototypes, this basic component is robust to parameter variation but can be modulated by external inputs. By combining these modules, we can construct a neural state machine capable of generating the cyclic or repetitive behaviors necessary for legged locomotion. A concrete case study for the approach is provided by a modular robot constructed from flexible plastic volumetric pixels, in which we produce a forward crawling gait entrained to the natural frequency of the robot by a minimal system of twelve neurons organized into four modules., Comment: 22 pages, 11 figures

Coronavirus Disease-2019 (COVID-19) is an infectious disease caused by the SARS-CoV-2 virus. It was first identified in Wuhan, China, and has since spread causing a global pandemic. Various studies have been performed to understand the molecular mechanisms of viral infection for predicting drug repurposing candidates. However, such information is spread across many publications and it is very time-consuming to access, integrate, explore, and exploit. We developed CoVex, the first interactive online platform for SARS-CoV-2 and SARS-CoV-1 host interactome exploration and drug (target) identification. CoVex integrates 1) experimentally validated virus-human protein interactions, 2) human protein-protein interactions and 3) drug-target interactions. The web interface allows user-friendly visual exploration of the virus-host interactome and implements systems medicine algorithms for network-based prediction of drugs. Thus, CoVex is an important resource, not only to understand the molecular mechanisms involved in SARS-CoV-2 and SARS-CoV-1 pathogenicity, but also in clinical research for the identification and prioritization of candidate therapeutics. We apply CoVex to investigate recent hypotheses on a systems biology level and to systematically explore the molecular mechanisms driving the virus life cycle. Furthermore, we extract and discuss drug repurposing candidates involved in these mechanisms. CoVex renders COVID-19 drug research systems-medicine-ready by giving the scientific community direct access to network medicine algorithms integrating virus-host-drug interactions. It is available at https://exbio.wzw.tum.de/covex/., Comment: 15 pages, 4 figures