@inproceedings{12302, abstract = {We propose a novel algorithm to decide the language inclusion between (nondeterministic) Büchi automata, a PSPACE-complete problem. Our approach, like others before, leverage a notion of quasiorder to prune the search for a counterexample by discarding candidates which are subsumed by others for the quasiorder. Discarded candidates are guaranteed to not compromise the completeness of the algorithm. The novelty of our work lies in the quasiorder used to discard candidates. We introduce FORQs (family of right quasiorders) that we obtain by adapting the notion of family of right congruences put forward by Maler and Staiger in 1993. We define a FORQ-based inclusion algorithm which we prove correct and instantiate it for a specific FORQ, called the structural FORQ, induced by the Büchi automaton to the right of the inclusion sign. The resulting implementation, called FORKLIFT, scales up better than the state-of-the-art on a variety of benchmarks including benchmarks from program verification and theorem proving for word combinatorics. Artifact: https://doi.org/10.5281/zenodo.6552870}, author = {Doveri, Kyveli and Ganty, Pierre and Mazzocchi, Nicolas Adrien}, booktitle = {Computer Aided Verification}, isbn = {9783031131875}, issn = {1611-3349}, location = {Haifa, Israel}, pages = {109--129}, publisher = {Springer Nature}, title = {{FORQ-based language inclusion formal testing}}, doi = {10.1007/978-3-031-13188-2_6}, volume = {13372}, year = {2022}, } @inbook{12303, abstract = {We construct for each choice of a quiver Q, a cohomology theory A, and a poset P a “loop Grassmannian” GP(Q,A). This generalizes loop Grassmannians of semisimple groups and the loop Grassmannians of based quadratic forms. The addition of a “dilation” torus D⊆G2m gives a quantization GPD(Q,A). This construction is motivated by the program of introducing an inner cohomology theory in algebraic geometry adequate for the Geometric Langlands program (Mirković, Some extensions of the notion of loop Grassmannians. Rad Hrvat. Akad. Znan. Umjet. Mat. Znan., the Mardešić issue. No. 532, 53–74, 2017) and on the construction of affine quantum groups from generalized cohomology theories (Yang and Zhao, Quiver varieties and elliptic quantum groups, preprint. arxiv1708.01418).}, author = {Mirković, Ivan and Yang, Yaping and Zhao, Gufang}, booktitle = {Representation Theory and Algebraic Geometry}, editor = {Baranovskky, Vladimir and Guay, Nicolas and Schedler, Travis}, isbn = {9783030820060}, issn = {2297-024X}, pages = {347--392}, publisher = {Springer Nature; Birkhäuser}, title = {{Loop Grassmannians of Quivers and Affine Quantum Groups}}, doi = {10.1007/978-3-030-82007-7_8}, year = {2022}, } @article{12304, abstract = {We establish sharp criteria for the instantaneous propagation of free boundaries in solutions to the thin-film equation. The criteria are formulated in terms of the initial distribution of mass (as opposed to previous almost-optimal results), reflecting the fact that mass is a locally conserved quantity for the thin-film equation. In the regime of weak slippage, our criteria are at the same time necessary and sufficient. The proof of our upper bounds on free boundary propagation is based on a strategy of “propagation of degeneracy” down to arbitrarily small spatial scales: We combine estimates on the local mass and estimates on energies to show that “degeneracy” on a certain space-time cylinder entails “degeneracy” on a spatially smaller space-time cylinder with the same time horizon. The derivation of our lower bounds on free boundary propagation is based on a combination of a monotone quantity and almost optimal estimates established previously by the second author with a new estimate connecting motion of mass to entropy production.}, author = {De Nitti, Nicola and Fischer, Julian L}, issn = {1532-4133}, journal = {Communications in Partial Differential Equations}, keywords = {Applied Mathematics, Analysis}, number = {7}, pages = {1394--1434}, publisher = {Taylor & Francis}, title = {{Sharp criteria for the waiting time phenomenon in solutions to the thin-film equation}}, doi = {10.1080/03605302.2022.2056702}, volume = {47}, year = {2022}, } @article{12305, abstract = {This paper is concerned with the sharp interface limit for the Allen--Cahn equation with a nonlinear Robin boundary condition in a bounded smooth domain Ω⊂\R2. We assume that a diffuse interface already has developed and that it is in contact with the boundary ∂Ω. The boundary condition is designed in such a way that the limit problem is given by the mean curvature flow with constant α-contact angle. For α close to 90° we prove a local in time convergence result for well-prepared initial data for times when a smooth solution to the limit problem exists. Based on the latter we construct a suitable curvilinear coordinate system and carry out a rigorous asymptotic expansion for the Allen--Cahn equation with the nonlinear Robin boundary condition. Moreover, we show a spectral estimate for the corresponding linearized Allen--Cahn operator and with its aid we derive strong norm estimates for the difference of the exact and approximate solutions using a Gronwall-type argument.}, author = {Abels, Helmut and Moser, Maximilian}, issn = {1095-7154}, journal = {SIAM Journal on Mathematical Analysis}, keywords = {Applied Mathematics, Computational Mathematics, Analysis}, number = {1}, pages = {114--172}, publisher = {Society for Industrial and Applied Mathematics}, title = {{Convergence of the Allen--Cahn equation with a nonlinear Robin boundary condition to mean curvature flow with contact angle close to 90°}}, doi = {10.1137/21m1424925}, volume = {54}, year = {2022}, } @article{12307, abstract = {Point-set topology is among the most abstract branches of mathematics in that it lacks tangible notions of distance, length, magnitude, order, and size. There is no shape, no geometry, no algebra, and no direction. Everything we are used to visualizing is gone. In the teaching and learning of mathematics, this can present a conundrum. Yet, this very property makes point set topology perfect for teaching and learning abstract mathematical concepts. It clears our minds of preconceived intuitions and expectations and forces us to think in new and creative ways. In this paper, we present guided investigations into topology through questions and thinking strategies that open up fascinating problems. They are intended for faculty who already teach or are thinking about teaching a class in topology or abstract mathematical reasoning for undergraduates. They can be used to build simple to challenging projects in topology, proofs, honors programs, and research experiences.}, author = {Shipman, Barbara A. and Stephenson, Elizabeth R}, issn = {1935-4053}, journal = {PRIMUS}, keywords = {Education, General Mathematics}, number = {5}, pages = {593--609}, publisher = {Taylor & Francis}, title = {{Tangible topology through the lens of limits}}, doi = {10.1080/10511970.2021.1872750}, volume = {32}, year = {2022}, } @article{12332, abstract = {Activity of sensory neurons is driven not only by external stimuli but also by feedback signals from higher brain areas. Attention is one particularly important internal signal whose presumed role is to modulate sensory representations such that they only encode information currently relevant to the organism at minimal cost. This hypothesis has, however, not yet been expressed in a normative computational framework. Here, by building on normative principles of probabilistic inference and efficient coding, we developed a model of dynamic population coding in the visual cortex. By continuously adapting the sensory code to changing demands of the perceptual observer, an attention-like modulation emerges. This modulation can dramatically reduce the amount of neural activity without deteriorating the accuracy of task-specific inferences. Our results suggest that a range of seemingly disparate cortical phenomena such as intrinsic gain modulation, attention-related tuning modulation, and response variability could be manifestations of the same underlying principles, which combine efficient sensory coding with optimal probabilistic inference in dynamic environments.}, author = {Mlynarski, Wiktor F and Tkačik, Gašper}, issn = {1545-7885}, journal = {PLoS Biology}, number = {12}, pages = {e3001889}, publisher = {Public Library of Science}, title = {{Efficient coding theory of dynamic attentional modulation}}, doi = {10.1371/journal.pbio.3001889}, volume = {20}, year = {2022}, } @article{12333, abstract = {Together, copy-number and point mutations form the basis for most evolutionary novelty, through the process of gene duplication and divergence. While a plethora of genomic data reveals the long-term fate of diverging coding sequences and their cis-regulatory elements, little is known about the early dynamics around the duplication event itself. In microorganisms, selection for increased gene expression often drives the expansion of gene copy-number mutations, which serves as a crude adaptation, prior to divergence through refining point mutations. Using a simple synthetic genetic reporter system that can distinguish between copy-number and point mutations, we study their early and transient adaptive dynamics in real time in Escherichia coli. We find two qualitatively different routes of adaptation, depending on the level of functional improvement needed. In conditions of high gene expression demand, the two mutation types occur as a combination. However, under low gene expression demand, copy-number and point mutations are mutually exclusive; here, owing to their higher frequency, adaptation is dominated by copy-number mutations, in a process we term amplification hindrance. Ultimately, due to high reversal rates and pleiotropic cost, copy-number mutations may not only serve as a crude and transient adaptation, but also constrain sequence divergence over evolutionary time scales.}, author = {Tomanek, Isabella and Guet, Calin C}, issn = {2050-084X}, journal = {eLife}, publisher = {eLife Sciences Publications}, title = {{Adaptation dynamics between copynumber and point mutations}}, doi = {10.7554/ELIFE.82240}, volume = {11}, year = {2022}, } @misc{12339, abstract = {Copy-number and point mutations form the basis for most evolutionary novelty through the process of gene duplication and divergence. While a plethora of genomic sequence data reveals the long-term fate of diverging coding sequences and their cis-regulatory elements, little is known about the early dynamics around the duplication event itself. In microorganisms, selection for increased gene expression often drives the expansion of gene copy-number mutations, which serves as a crude adaptation, prior to divergence through refining point mutations. Using a simple synthetic genetic system that allows us to distinguish copy-number and point mutations, we study their early and transient adaptive dynamics in real-time in Escherichia coli. We find two qualitatively different routes of adaptation depending on the level of functional improvement selected for: In conditions of high gene expression demand, the two types of mutations occur as a combination. Under low gene expression demand, negative epistasis between the two types of mutations renders them mutually exclusive. Thus, owing to their higher frequency, adaptation is dominated by copy-number mutations. Ultimately, due to high rates of reversal and pleiotropic cost, copy-number mutations may not only serve as a crude and transient adaptation but also constrain sequence divergence over evolutionary time scales.}, author = {Tomanek, Isabella and Guet, Calin C}, publisher = {Dryad}, title = {{Flow cytometry YFP and CFP data and deep sequencing data of populations evolving in galactose}}, doi = {10.5061/dryad.rfj6q57ds}, year = {2022}, } @phdthesis{12358, abstract = {The complex yarn structure of knitted and woven fabrics gives rise to both a mechanical and visual complexity. The small-scale interactions of yarns colliding with and pulling on each other result in drastically different large-scale stretching and bending behavior, introducing anisotropy, curling, and more. While simulating cloth as individual yarns can reproduce this complexity and match the quality of real fabric, it may be too computationally expensive for large fabrics. On the other hand, continuum-based approaches do not need to discretize the cloth at a stitch-level, but it is non-trivial to find a material model that would replicate the large-scale behavior of yarn fabrics, and they discard the intricate visual detail. In this thesis, we discuss three methods to try and bridge the gap between small-scale and large-scale yarn mechanics using numerical homogenization: fitting a continuum model to periodic yarn simulations, adding mechanics-aware yarn detail onto thin-shell simulations, and quantitatively fitting yarn parameters to physical measurements of real fabric. To start, we present a method for animating yarn-level cloth effects using a thin-shell solver. We first use a large number of periodic yarn-level simulations to build a model of the potential energy density of the cloth, and then use it to compute forces in a thin-shell simulator. The resulting simulations faithfully reproduce expected effects like the stiffening of woven fabrics and the highly deformable nature and anisotropy of knitted fabrics at a fraction of the cost of full yarn-level simulation. While our thin-shell simulations are able to capture large-scale yarn mechanics, they lack the rich visual detail of yarn-level simulations. Therefore, we propose a method to animate yarn-level cloth geometry on top of an underlying deforming mesh in a mechanics-aware fashion in real time. Using triangle strains to interpolate precomputed yarn geometry, we are able to reproduce effects such as knit loops tightening under stretching at negligible cost. Finally, we introduce a methodology for inverse-modeling of yarn-level mechanics of cloth, based on the mechanical response of fabrics in the real world. We compile a database from physical tests of several knitted fabrics used in the textile industry spanning diverse physical properties like stiffness, nonlinearity, and anisotropy. We then develop a system for approximating these mechanical responses with yarn-level cloth simulation, using homogenized shell models to speed up computation and adding some small-but-necessary extensions to yarn-level models used in computer graphics. }, author = {Sperl, Georg}, isbn = {978-3-99078-020-6}, issn = {2663-337X}, pages = {138}, publisher = {Institute of Science and Technology Austria}, title = {{Homogenizing yarn simulations: Large-scale mechanics, small-scale detail, and quantitative fitting}}, doi = {10.15479/at:ista:12103}, year = {2022}, } @phdthesis{12364, abstract = {Autism spectrum disorders (ASDs) are a group of neurodevelopmental disorders characterized by behavioral symptoms such as problems in social communication and interaction, as well as repetitive, restricted behaviors and interests. These disorders show a high degree of heritability and hundreds of risk genes have been identifed using high throughput sequencing technologies. This genetic heterogeneity has hampered eforts in understanding the pathogenesis of ASD but at the same time given rise to the concept of convergent mechanisms. Previous studies have identifed that risk genes for ASD broadly converge onto specifc functional categories with transcriptional regulation being one of the biggest groups. In this thesis, I focus on this subgroup of genes and investigate the gene regulatory consequences of some of them in the context of neurodevelopment. First, we showed that mutations in the ASD and intellectual disability risk gene Setd5 lead to perturbations of gene regulatory programs in early cell fate specifcation. In addition, adult animals display abnormal learning behavior which is mirrored at the transcriptional level by altered activity dependent regulation of postsynaptic gene expression. Lastly, we link the regulatory function of Setd5 to its interaction with the Paf1 and the NCoR complex. Second, by modeling the heterozygous loss of the top ASD gene CHD8 in human cerebral organoids we demonstrate profound changes in the developmental trajectories of both inhibitory and excitatory neurons using single cell RNA-sequencing. While the former were generated earlier in CHD8+/- organoids, the generation of the latter was shifted to later times in favor of a prolonged progenitor expansion phase and ultimately increased organoid size. Finally, by modeling heterozygous mutations for four ASD associated chromatin modifers, ASH1L, KDM6B, KMT5B, and SETD5 in human cortical spheroids we show evidence of regulatory convergence across three of those genes. We observe a shift from dorsal cortical excitatory neuron fates towards partially ventralized cell types resembling cells from the lateral ganglionic eminence. As this project is still ongoing at the time of writing, future experiments will aim at elucidating the regulatory mechanisms underlying this shift with the aim of linking these three ASD risk genes through biological convergence.}, author = {Dotter, Christoph}, issn = {2663-337X}, pages = {152}, publisher = {Institute of Science and Technology Austria}, title = {{Transcriptional consequences of mutations in genes associated with Autism Spectrum Disorder}}, doi = {10.15479/at:ista:12094}, year = {2022}, } @phdthesis{12366, abstract = {Recent substantial advances in the feld of superconducting circuits have shown its potential as a leading platform for future quantum computing. In contrast to classical computers based on bits that are represented by a single binary value, 0 or 1, quantum bits (or qubits) can be in a superposition of both. Thus, quantum computers can store and handle more information at the same time and a quantum advantage has already been demonstrated for two types of computational tasks. Rapid progress in academic and industry labs accelerates the development of superconducting processors which may soon fnd applications in complex computations, chemical simulations, cryptography, and optimization. Now that these machines are scaled up to tackle such problems the questions of qubit interconnects and networks becomes very relevant. How to route signals on-chip between diferent processor components? What is the most efcient way to entangle qubits? And how to then send and process entangled signals between distant cryostats hosting superconducting processors? In this thesis, we are looking for solutions to these problems by studying the collective behavior of superconducting qubit ensembles. We frst demonstrate on-demand tunable directional scattering of microwave photons from a pair of qubits in a waveguide. Such a device can route microwave photons on-chip with a high diode efciency. Then we focus on studying ultra-strong coupling regimes between light (microwave photons) and matter (superconducting qubits), a regime that could be promising for extremely fast multi-qubit entanglement generation. Finally, we show coherent pulse storage and periodic revivals in a fve qubit ensemble strongly coupled to a resonator. Such a reconfgurable storage device could be used as part of a quantum repeater that is needed for longer-distance quantum communication. The achieved high degree of control over multi-qubit ensembles highlights not only the beautiful physics of circuit quantum electrodynamics, it also represents the frst step toward new quantum simulation and communication methods, and certain techniques may also fnd applications in future superconducting quantum computing hardware. }, author = {Redchenko, Elena}, isbn = {978-3-99078-024-4}, issn = {2663-337X}, pages = {168}, publisher = {Institute of Science and Technology Austria}, title = {{Controllable states of superconducting Qubit ensembles}}, doi = {10.15479/at:ista:12132}, year = {2022}, } @phdthesis{12368, abstract = {Metazoan development relies on the formation and remodeling of cell-cell contacts. The binding of adhesion receptors and remodeling of the actomyosin cell cortex at cell-cell interaction sites have been implicated in cell-cell contact formation. Yet, how these two processes functionally interact to drive cell-cell contact expansion and strengthening remains unclear. Here, we study how primary germ layer progenitor cells from zebrafish bind to supported lipid bilayers (SLB) functionalized with E-cadherin ectodomains as an assay system for monitoring cell-cell contact formation at high spatiotemporal resolution. We show that cell-cell contact formation represents a two-tiered process: E-cadherinmediated downregulation of the small GTPase RhoA at the forming contact leads to both depletion of Myosin-2 and decrease of F-actin. This is followed by centrifugal actin network flows at the contact triggered by a sharp gradient of Myosin-2 at the rim of the contact zone, with Myosin-2 displaying higher cortical localization outside than inside of the contact. These centrifugal cortical actin flows, in turn, not only further dilute the actin network at the contact disc, but also lead to an accumulation of both F-actin and Ecadherin at the contact rim. Eventually, this combination of actomyosin downregulation and flows at the contact contribute to the characteristic molecular organization implicated in contact formation and maintenance: depletion of cortical actomyosin at the contact disc, driving contact expansion by lowering interfacial tension at the contact, and accumulation of both E-cadherin and F-actin at the contact rim, mechanically linking the contractile cortices of the adhering cells. Thus, using a biomimetic assay, we exemplify how adhesion signaling and cell mechanics function together to modulate the spatial organization of cell-cell contacts.}, author = {Arslan, Feyza N}, isbn = { 978-3-99078-025-1 }, issn = {2663-337X}, pages = {113}, publisher = {Institute of Science and Technology Austria}, title = {{Remodeling of E-cadherin-mediated contacts via cortical flows}}, doi = {10.15479/at:ista:12153}, year = {2022}, } @phdthesis{12378, abstract = {Environmental cues influence the highly dynamic morphology of microglia. Strategies to characterize these changes usually involve user-selected morphometric features, which preclude the identification of a spectrum of context-dependent morphological phenotypes. Here, we develop MorphOMICs, a topological data analysis approach, which enables semiautomatic mapping of microglial morphology into an atlas of cue-dependent phenotypes, overcomes feature-selection bias and minimizes biological variability. First, with MorphOMICs we derive the morphological spectrum of microglia across seven brain regions during postnatal development and in two distinct Alzheimer’s disease degeneration mouse models. We uncover region-specific and sexually dimorphic morphological trajectories, with females showing an earlier morphological shift than males in the degenerating brain. Overall, we demonstrate that both long primary- and short terminal processes provide distinct insights to morphological phenotypes. Moreover, using machine learning to map novel condition on the spectrum, we observe that microglia morphologies reflect a dose-dependent adaptation upon ketamine anesthesia and do not recover to control morphologies. Next, we took advantage of MorphOMICs to build a high-resolution and layer-specific map of microglial morphological spectrum in the retina, covering postnatal development and rd10 degeneration. Here, following photoreceptor death, microglia assume an early developmentlike morphology. Finally, we map microglial morphology following optic nerve crush on the retinal spectrum and observe a layer- and sex-dependent response. Overall, MorphOMICs opens a new perspective to analyze microglial morphology across multiple conditions, and provides a novel tool to characterize microglial morphology beyond the traditionally dichotomized view of microglia.}, author = {Colombo, Gloria}, issn = {2663-337X}, pages = {142}, publisher = {Institute of Science and Technology Austria}, title = {{MorphOMICs, a tool for mapping microglial morphology, reveals brain region- and sex-dependent phenotypes}}, doi = {10.15479/at:ista:12378}, year = {2022}, } @phdthesis{12390, abstract = {The scope of this thesis is to study quantum systems exhibiting a continuous symmetry that is broken on the level of the corresponding effective theory. In particular we are going to investigate translation-invariant Bose gases in the mean field limit, effectively described by the Hartree functional, and the Fröhlich Polaron in the regime of strong coupling, effectively described by the Pekar functional. The latter is a model describing the interaction between a charged particle and the optical modes of a polar crystal. Regarding the former, we assume in addition that the particles in the gas are unconfined, and typically we will consider particles that are subject to an attractive interaction. In both cases the ground state energy of the Hamiltonian is not a proper eigenvalue due to the underlying translation-invariance, while on the contrary there exists a whole invariant orbit of minimizers for the corresponding effective functionals. Both, the absence of proper eigenstates and the broken symmetry of the effective theory, make the study significantly more involved and it is the content of this thesis to develop a frameworks which allows for a systematic way to circumvent these issues. It is a well-established result that the ground state energy of Bose gases in the mean field limit, as well as the ground state energy of the Fröhlich Polaron in the regime of strong coupling, is to leading order given by the minimal energy of the corresponding effective theory. As part of this thesis we identify the sub-leading term in the expansion of the ground state energy, which can be interpreted as the quantum correction to the classical energy, since the effective theories under consideration can be seen as classical counterparts. We are further going to establish an asymptotic expression for the energy-momentum relation of the Fröhlich Polaron in the strong coupling limit. In the regime of suitably small momenta, this asymptotic expression agrees with the energy-momentum relation of a free particle having an effectively increased mass, and we find that this effectively increased mass agrees with the conjectured value in the physics literature. In addition we will discuss two unrelated papers written by the author during his stay at ISTA in the appendix. The first one concerns the realization of anyons, which are quasi-particles acquiring a non-trivial phase under the exchange of two particles, as molecular impurities. The second one provides a classification of those vector fields defined on a given manifold that can be written as the gradient of a given functional with respect to a suitable metric, provided that some mild smoothness assumptions hold. This classification is subsequently used to identify those quantum Markov semigroups that can be written as a gradient flow of the relative entropy. }, author = {Brooks, Morris}, issn = {2663-337X}, pages = {196}, publisher = {Institute of Science and Technology Austria}, title = {{Translation-invariant quantum systems with effectively broken symmetry}}, doi = {10.15479/at:ista:12390}, year = {2022}, } @phdthesis{12401, abstract = {Detachment of the cancer cells from the bulk of the tumor is the first step of metastasis, which is the primary cause of cancer related deaths. It is unclear, which factors contribute to this step. Recent studies indicate a crucial role of the tumor microenvironment in malignant transformation and metastasis. Studying cancer cell invasion and detachments quantitatively in the context of its physiological microenvironment is technically challenging. Especially, precise control of microenvironmental properties in vivo is currently not possible. Here, I studied the role of microenvironment geometry in the invasion and detachment of cancer cells from the bulk with a simplistic and reductionist approach. In this approach, I engineered microfluidic devices to mimic a pseudo 3D extracellular matrix environment, where I was able to quantitatively tune the geometrical configuration of the microenvironment and follow tumor cells with fluorescence live imaging. To aid quantitative analysis I developed a widely applicable software application to automatically analyze and visualize particle tracking data. Quantitative analysis of tumor cell invasion in isotropic and anisotropic microenvironments showed that heterogeneity in the microenvironment promotes faster invasion and more frequent detachment of cells. These observations correlated with overall higher speed of cells at the edge of the bulk of the cells. In heterogeneous microenvironments cells preferentially passed through larger pores, thus invading areas of least resistance and generating finger-like invasive structures. The detachments occurred mostly at the tips of these structures. To investigate the potential mechanism, we established a two dimensional model to simulate active Brownian particles representing the cell nuclei dynamics. These simulations backed our in vitro observations without the need of precise fitting the simulation parameters. Our model suggests the importance of the pore heterogeneity in the direction perpendicular to the orientation of bias field (lateral heterogeneity), which causes the interface roughening.}, author = {Tasciyan, Saren}, issn = {2663-337X}, pages = {105}, publisher = {Institute of Science and Technology Austria}, title = {{Role of microenvironment heterogeneity in cancer cell invasion}}, doi = {10.15479/at:ista:12401}, year = {2022}, } @article{12431, abstract = {This paper presents a new representation of curve dynamics, with applications to vortex filaments in fluid dynamics. Instead of representing these filaments with explicit curve geometry and Lagrangian equations of motion, we represent curves implicitly with a new co-dimensional 2 level set description. Our implicit representation admits several redundant mathematical degrees of freedom in both the configuration and the dynamics of the curves, which can be tailored specifically to improve numerical robustness, in contrast to naive approaches for implicit curve dynamics that suffer from overwhelming numerical stability problems. Furthermore, we note how these hidden degrees of freedom perfectly map to a Clebsch representation in fluid dynamics. Motivated by these observations, we introduce untwisted level set functions and non-swirling dynamics which successfully regularize sources of numerical instability, particularly in the twisting modes around curve filaments. A consequence is a novel simulation method which produces stable dynamics for large numbers of interacting vortex filaments and effortlessly handles topological changes and re-connection events.}, author = {Ishida, Sadashige and Wojtan, Christopher J and Chern, Albert}, issn = {1557-7368}, journal = {ACM Transactions on Graphics}, number = {6}, publisher = {Association for Computing Machinery}, title = {{Hidden degrees of freedom in implicit vortex filaments}}, doi = {10.1145/3550454.3555459}, volume = {41}, year = {2022}, } @inproceedings{12432, abstract = {We present CertifyHAM, a deterministic algorithm that takes a graph G as input and either finds a Hamilton cycle of G or outputs that such a cycle does not exist. If G ∼ G(n, p) and p ≥ 100 log n/n then the expected running time of CertifyHAM is O(n/p) which is best possible. This improves upon previous results due to Gurevich and Shelah, Thomason and Alon, and Krivelevich, who proved analogous results for p being constant, p ≥ 12n −1/3 and p ≥ 70n −1/2 respectively.}, author = {Anastos, Michael}, booktitle = {63rd Annual IEEE Symposium on Foundations of Computer Science}, isbn = {9781665455190}, issn = {0272-5428}, location = {Denver, CO, United States}, pages = {919--930}, publisher = {Institute of Electrical and Electronics Engineers}, title = {{Solving the Hamilton cycle problem fast on average}}, doi = {10.1109/FOCS54457.2022.00091}, volume = {2022-October}, year = {2022}, } @inproceedings{12452, abstract = {Portrait viewpoint and illumination editing is an important problem with several applications in VR/AR, movies, and photography. Comprehensive knowledge of geometry and illumination is critical for obtaining photorealistic results. Current methods are unable to explicitly model in 3D while handing both viewpoint and illumination editing from a single image. In this paper, we propose VoRF, a novel approach that can take even a single portrait image as input and relight human heads under novel illuminations that can be viewed from arbitrary viewpoints. VoRF represents a human head as a continuous volumetric field and learns a prior model of human heads using a coordinate-based MLP with separate latent spaces for identity and illumination. The prior model is learnt in an auto-decoder manner over a diverse class of head shapes and appearances, allowing VoRF to generalize to novel test identities from a single input image. Additionally, VoRF has a reflectance MLP that uses the intermediate features of the prior model for rendering One-Light-at-A-Time (OLAT) images under novel views. We synthesize novel illuminations by combining these OLAT images with target environment maps. Qualitative and quantitative evaluations demonstrate the effectiveness of VoRF for relighting and novel view synthesis even when applied to unseen subjects under uncontrolled illuminations.}, author = {Rao, Pramod and B R, Mallikarjun and Fox, Gereon and Weyrich, Tim and Bickel, Bernd and Seidel, Hans-Peter and Pfister, Hanspeter and Matusik, Wojciech and Tewari, Ayush and Theobalt, Christian and Elgharib, Mohamed}, booktitle = {33rd British Machine Vision Conference}, location = {London, United Kingdom}, publisher = {British Machine Vision Association and Society for Pattern Recognition}, title = {{VoRF: Volumetric Relightable Faces}}, year = {2022}, } @article{12480, abstract = {We consider the problem of estimating a signal from measurements obtained via a generalized linear model. We focus on estimators based on approximate message passing (AMP), a family of iterative algorithms with many appealing features: the performance of AMP in the high-dimensional limit can be succinctly characterized under suitable model assumptions; AMP can also be tailored to the empirical distribution of the signal entries, and for a wide class of estimation problems, AMP is conjectured to be optimal among all polynomial-time algorithms. However, a major issue of AMP is that in many models (such as phase retrieval), it requires an initialization correlated with the ground-truth signal and independent from the measurement matrix. Assuming that such an initialization is available is typically not realistic. In this paper, we solve this problem by proposing an AMP algorithm initialized with a spectral estimator. With such an initialization, the standard AMP analysis fails since the spectral estimator depends in a complicated way on the design matrix. Our main contribution is a rigorous characterization of the performance of AMP with spectral initialization in the high-dimensional limit. The key technical idea is to define and analyze a two-phase artificial AMP algorithm that first produces the spectral estimator, and then closely approximates the iterates of the true AMP. We also provide numerical results that demonstrate the validity of the proposed approach.}, author = {Mondelli, Marco and Venkataramanan, Ramji}, issn = {1742-5468}, journal = {Journal of Statistical Mechanics: Theory and Experiment}, keywords = {Statistics, Probability and Uncertainty, Statistics and Probability, Statistical and Nonlinear Physics}, number = {11}, publisher = {IOP Publishing}, title = {{Approximate message passing with spectral initialization for generalized linear models}}, doi = {10.1088/1742-5468/ac9828}, volume = {2022}, year = {2022}, } @article{12495, abstract = {Fairness-aware learning aims at constructing classifiers that not only make accurate predictions, but also do not discriminate against specific groups. It is a fast-growing area of machine learning with far-reaching societal impact. However, existing fair learning methods are vulnerable to accidental or malicious artifacts in the training data, which can cause them to unknowingly produce unfair classifiers. In this work we address the problem of fair learning from unreliable training data in the robust multisource setting, where the available training data comes from multiple sources, a fraction of which might not be representative of the true data distribution. We introduce FLEA, a filtering-based algorithm that identifies and suppresses those data sources that would have a negative impact on fairness or accuracy if they were used for training. As such, FLEA is not a replacement of prior fairness-aware learning methods but rather an augmentation that makes any of them robust against unreliable training data. We show the effectiveness of our approach by a diverse range of experiments on multiple datasets. Additionally, we prove formally that –given enough data– FLEA protects the learner against corruptions as long as the fraction of affected data sources is less than half. Our source code and documentation are available at https://github.com/ISTAustria-CVML/FLEA.}, author = {Iofinova, Eugenia B and Konstantinov, Nikola H and Lampert, Christoph}, issn = {2835-8856}, journal = {Transactions on Machine Learning Research}, publisher = {ML Research Press}, title = {{FLEA: Provably robust fair multisource learning from unreliable training data}}, year = {2022}, }