10,259 research outputs found

    Computation of the von Neumann entropy of large matrices via trace estimators and rational Krylov methods

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    We consider the problem of approximating the von Neumann entropy of a large, sparse, symmetric positive semidefinite matrix AA, defined as tr(f(A))\operatorname{tr}(f(A)) where f(x)=xlogxf(x)=-x\log x. After establishing some useful properties of this matrix function, we consider the use of both polynomial and rational Krylov subspace algorithms within two types of approximations methods, namely, randomized trace estimators and probing techniques based on graph colorings. We develop error bounds and heuristics which are employed in the implementation of the algorithms. Numerical experiments on density matrices of different types of networks illustrate the performance of the methods.Comment: 32 pages, 10 figure

    Human gene-engineered calreticulin mutant stem cells recapitulate MPN hallmarks and identify targetable vulnerabilities

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    Calreticulin (CALR) mutations present the main oncogenic drivers in JAK2 wildtype (WT) myeloproliferative neoplasms (MPN), including essential thrombocythemia and myelofibrosis, where mutant (MUT) CALR is increasingly recognized as a suitable mutation-specific drug target. However, our current understanding of its mechanism-of-action is derived from mouse models or immortalized cell lines, where cross-species differences, ectopic over-expression and lack of disease penetrance are hampering translational research. Here, we describe the first human gene-engineered model of CALR MUT MPN using a CRISPR/Cas9 and adeno-associated viral vector-mediated knock-in strategy in primary human hematopoietic stem and progenitor cells (HSPCs) to establish a reproducible and trackable phenotype in vitro and in xenografted mice. Our humanized model recapitulates many disease hallmarks: thrombopoietin-independent megakaryopoiesis, myeloid-lineage skewing, splenomegaly, bone marrow fibrosis, and expansion of megakaryocyte-primed CD41+ progenitors. Strikingly, introduction of CALR mutations enforced early reprogramming of human HSPCs and the induction of an endoplasmic reticulum stress response. The observed compensatory upregulation of chaperones revealed novel mutation-specific vulnerabilities with preferential sensitivity of CALR mutant cells to inhibition of the BiP chaperone and the proteasome. Overall, our humanized model improves purely murine models and provides a readily usable basis for testing of novel therapeutic strategies in a human setting.Johannes Foßelteder, Gabriel Pabst, Tommaso Sconocchia, Angelika Schlacher, Lisa Auinger, Karl Kashofer, Christine Beham-Schmid, Slave Trajanoski, Claudia Waskow, Wolfgang Schöll, Heinz Sill, Armin Zebisch, Albert Wölfler, Daniel Thomas, and Andreas Reinisc

    Machine Learning for SAT: Restricted Heuristics and New Graph Representations

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    Boolean satisfiability (SAT) is a fundamental NP-complete problem with many applications, including automated planning and scheduling. To solve large instances, SAT solvers have to rely on heuristics, e.g., choosing a branching variable in DPLL and CDCL solvers. Such heuristics can be improved with machine learning (ML) models; they can reduce the number of steps but usually hinder the running time because useful models are relatively large and slow. We suggest the strategy of making a few initial steps with a trained ML model and then releasing control to classical heuristics; this simplifies cold start for SAT solving and can decrease both the number of steps and overall runtime, but requires a separate decision of when to release control to the solver. Moreover, we introduce a modification of Graph-Q-SAT tailored to SAT problems converted from other domains, e.g., open shop scheduling problems. We validate the feasibility of our approach with random and industrial SAT problems

    Current issues of the Russian language teaching XIV

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    Collection of papers “Current issues of the Russian language teaching XIV” is devoted to issues of methodology of teaching Russian as a foreign language, to issues of linguistics and literary science and includes papers related to the use of online tools and resources in teaching Russian. This collection of papers is a result of the international scientific conference “Current issues of the Russian language teaching XIV”, which was scheduled for 8–10 May 2020, but due to the pandemic COVID-19 took place remotely

    Random graph matching at Otter's threshold via counting chandeliers

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    We propose an efficient algorithm for graph matching based on similarity scores constructed from counting a certain family of weighted trees rooted at each vertex. For two Erd\H{o}s-R\'enyi graphs G(n,q)\mathcal{G}(n,q) whose edges are correlated through a latent vertex correspondence, we show that this algorithm correctly matches all but a vanishing fraction of the vertices with high probability, provided that nqnq\to\infty and the edge correlation coefficient ρ\rho satisfies ρ2>α0.338\rho^2>\alpha \approx 0.338, where α\alpha is Otter's tree-counting constant. Moreover, this almost exact matching can be made exact under an extra condition that is information-theoretically necessary. This is the first polynomial-time graph matching algorithm that succeeds at an explicit constant correlation and applies to both sparse and dense graphs. In comparison, previous methods either require ρ=1o(1)\rho=1-o(1) or are restricted to sparse graphs. The crux of the algorithm is a carefully curated family of rooted trees called chandeliers, which allows effective extraction of the graph correlation from the counts of the same tree while suppressing the undesirable correlation between those of different trees

    PatchGT: Transformer over Non-trainable Clusters for Learning Graph Representations

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    Recently the Transformer structure has shown good performances in graph learning tasks. However, these Transformer models directly work on graph nodes and may have difficulties learning high-level information. Inspired by the vision transformer, which applies to image patches, we propose a new Transformer-based graph neural network: Patch Graph Transformer (PatchGT). Unlike previous transformer-based models for learning graph representations, PatchGT learns from non-trainable graph patches, not from nodes directly. It can help save computation and improve the model performance. The key idea is to segment a graph into patches based on spectral clustering without any trainable parameters, with which the model can first use GNN layers to learn patch-level representations and then use Transformer to obtain graph-level representations. The architecture leverages the spectral information of graphs and combines the strengths of GNNs and Transformers. Further, we show the limitations of previous hierarchical trainable clusters theoretically and empirically. We also prove the proposed non-trainable spectral clustering method is permutation invariant and can help address the information bottlenecks in the graph. PatchGT achieves higher expressiveness than 1-WL-type GNNs, and the empirical study shows that PatchGT achieves competitive performances on benchmark datasets and provides interpretability to its predictions. The implementation of our algorithm is released at our Github repo: https://github.com/tufts-ml/PatchGT.Comment: 25 pages, 10 figure

    Efficient Distributed Decomposition and Routing Algorithms in Minor-Free Networks and Their Applications

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    In the LOCAL model, low-diameter decomposition is a useful tool in designing algorithms, as it allows us to shift from the general graph setting to the low-diameter graph setting, where brute-force information gathering can be done efficiently. Recently, Chang and Su [PODC 2022] showed that any high-conductance network excluding a fixed minor contains a high-degree vertex, so the entire graph topology can be gathered to one vertex efficiently in the CONGEST model using expander routing. Therefore, in networks excluding a fixed minor, many problems that can be solved efficiently in LOCAL via low-diameter decomposition can also be solved efficiently in CONGEST via expander decomposition. In this work, we show improved decomposition and routing algorithms for networks excluding a fixed minor in the CONGEST model. Our algorithms cost poly(logn,1/ϵ)\text{poly}(\log n, 1/\epsilon) rounds deterministically. For bounded-degree graphs, our algorithms finish in O(ϵ1logn)+ϵO(1)O(\epsilon^{-1}\log n) + \epsilon^{-O(1)} rounds. Our algorithms have a wide range of applications, including the following results in CONGEST. 1. A (1ϵ)(1-\epsilon)-approximate maximum independent set in a network excluding a fixed minor can be computed deterministically in O(ϵ1logn)+ϵO(1)O(\epsilon^{-1}\log^\ast n) + \epsilon^{-O(1)} rounds, nearly matching the Ω(ϵ1logn)\Omega(\epsilon^{-1}\log^\ast n) lower bound of Lenzen and Wattenhofer [DISC 2008]. 2. Property testing of any additive minor-closed property can be done deterministically in O(logn)O(\log n) rounds if ϵ\epsilon is a constant or O(ϵ1logn)+ϵO(1)O(\epsilon^{-1}\log n) + \epsilon^{-O(1)} rounds if the maximum degree Δ\Delta is a constant, nearly matching the Ω(ϵ1logn)\Omega(\epsilon^{-1}\log n) lower bound of Levi, Medina, and Ron [PODC 2018].Comment: To appear in PODC 202

    High-throughput Single-Entity Analysis Methods: From Single-Cell Segmentation to Single-Molecule Force Measurements

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    This work is focused on the development of new microscopy-based analysis methods with single-entity resolution and high-throughput capabilities from the cellular to the molecular level to study biomembrane-associated interactions. Currently, there is a variety of methods available for obtaining quantitative information on cellular and molecular responses to external stimuli, but many of them lack either high sensitivity or high throughput. Yet, the combination of both aspects is critical for studying the weak but often complex and multivalent interactions at the interface of biological mem-branes. These interactions include binding of pathogens such as some viruses (e.g., influenza A virus, herpes simplex virus, and SARS-CoV-2), transmembrane signaling such as ligand-based oli-gomerization processes, and transduction of mechanical forces acting on cells. The goal of this work was to overcome the shortcomings of current methods by developing and es-tablishing new methods with unprecedented levels of automation, sensitivity, and parallelization. All methods are based on the combination of optical (video) microscopy followed by highly refined data analysis to study single cellular and molecular events, allowing the detection of rare events and the identification and quantification of cellular and molecular populations that would remain hidden in ensemble-averaging approaches. This work comprises four different projects. At the cellular level, two methods have been developed for single-cell segmentation and cell-by-cell readout of fluorescence reporter systems, mainly to study binding and inhibition of binding of viruses to host cells. The method developed in the first pro-ject features a high degree of automation and automatic estimation of sufficient analysis parameters (background threshold, segmentation sensitivity, and fluorescence cutoff) to reduce the manual ef-fort required for the analysis of cell-based infection assays. This method has been used for inhibition potency screening based on the IC50 value of various virus binding inhibitors. With the method used in the second project, the sensitivity of the first method is extended by providing an estimate of the number of fluorescent nanoparticles bound to the cells. The image resolution was chosen to allow many cells to be imaged in parallel. This allowed for the quantification of cell-to-cell heterogeneity of particle binding, at the expense of resolution of the individual fluorescent nanoparticles. To account for this, a new approach was developed and validated by simulations to estimate the number of fluo-rescent nanoparticles below the diffraction limit with an accuracy of about 80 to 100 %. In the third project, an approach for the analysis and refinement of two-dimensional single-particle tracking ex-periments was presented. It focused on the quality assessment of the derived tracks by providing a guide for the selection of an appropriate maximal linking distance. This tracking approach was used in the fourth project to quantify small molecule responses to hydrodynamic shear forces with sub-nm resolution. Here, the combination of TIRF microscopy, microfluidics, and single particle tracking enabled the development of a new single molecule force spectroscopy method with high resolution and parallelization capabilities. This method was validated by quantifying the mechanical response of well-defined PEG linkers and subsequently used to study the energy barriers of dissociation of mul-tivalent biotin-NeutrAvidin complexes under low (~ 1.5 to 12 pN) static forces. In summary, with this work, the repertoire of appropriate methods for high-throughput investigation of the properties and interactions of cells, nanoparticles, and molecules at single resolution is expand-ed. In the future, the methods developed here will be used to screen for additional virus binding inhib-itors, to study the oligomerization of membrane receptors on cells and model membranes, and to quantify the mechanical response of force-bearing proteins and ligand-receptor complexes under low force conditions

    Learning-powered computer-assisted counterexample search

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    Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2023, Director: Kolja Knauer[en] This thesis explores the great potential of computer-assisted proofs in the advancement of mathematical knowledge, with a special focus on using computers to refute conjectures by finding counterexamples, sometimes a humanly impossible task. In recent years, mathematicians have become more aware that machine learning techniques can be extremely helpful for finding counterexamples to conjectures in a more efficient way than by using exhaustive search methods. In this thesis we do not only present the theoretical background behind some of these methods but also implement them to try to refute some graph theory conjectures

    Detection of Common Subtrees with Identical Label Distribution

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    Frequent pattern mining is a relevant method to analyse structured data, like sequences, trees or graphs. It consists in identifying characteristic substructures of a dataset. This paper deals with a new type of patterns for tree data: common subtrees with identical label distribution. Their detection is far from obvious since the underlying isomorphism problem is graph isomorphism complete. An elaborated search algorithm is developed and analysed from both theoretical and numerical perspectives. Based on this, the enumeration of patterns is performed through a new lossless compression scheme for trees, called DAG-RW, whose complexity is investigated as well. The method shows very good properties, both in terms of computation times and analysis of real datasets from the literature. Compared to other substructures like topological subtrees and labelled subtrees for which the isomorphism problem is linear, the patterns found provide a more parsimonious representation of the data.Comment: 40 page
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