@inbook{424, abstract = {We show that very weak topological assumptions are enough to ensure the existence of a Helly-type theorem. More precisely, we show that for any non-negative integers b and d there exists an integer h(b, d) such that the following holds. If F is a finite family of subsets of Rd such that βi(∩G)≤b for any G⊊F and every 0 ≤ i ≤ [d/2]-1 then F has Helly number at most h(b, d). Here βi denotes the reduced Z2-Betti numbers (with singular homology). These topological conditions are sharp: not controlling any of these [d/2] first Betti numbers allow for families with unbounded Helly number. Our proofs combine homological non-embeddability results with a Ramsey-based approach to build, given an arbitrary simplicial complex K, some well-behaved chain map C*(K)→C*(Rd).}, author = {Goaoc, Xavier and Paták, Pavel and Patakova, Zuzana and Tancer, Martin and Wagner, Uli}, booktitle = {A Journey through Discrete Mathematics: A Tribute to Jiri Matousek}, editor = {Loebl, Martin and Nešetřil, Jaroslav and Thomas, Robin}, isbn = {978-331944479-6}, pages = {407 -- 447}, publisher = {Springer}, title = {{Bounding helly numbers via betti numbers}}, doi = {10.1007/978-3-319-44479-6_17}, year = {2017}, } @inproceedings{431, abstract = {Parallel implementations of stochastic gradient descent (SGD) have received significant research attention, thanks to its excellent scalability properties. A fundamental barrier when parallelizing SGD is the high bandwidth cost of communicating gradient updates between nodes; consequently, several lossy compresion heuristics have been proposed, by which nodes only communicate quantized gradients. Although effective in practice, these heuristics do not always converge. In this paper, we propose Quantized SGD (QSGD), a family of compression schemes with convergence guarantees and good practical performance. QSGD allows the user to smoothly trade off communication bandwidth and convergence time: nodes can adjust the number of bits sent per iteration, at the cost of possibly higher variance. We show that this trade-off is inherent, in the sense that improving it past some threshold would violate information-theoretic lower bounds. QSGD guarantees convergence for convex and non-convex objectives, under asynchrony, and can be extended to stochastic variance-reduced techniques. When applied to training deep neural networks for image classification and automated speech recognition, QSGD leads to significant reductions in end-to-end training time. For instance, on 16GPUs, we can train the ResNet-152 network to full accuracy on ImageNet 1.8 × faster than the full-precision variant. }, author = {Alistarh, Dan-Adrian and Grubic, Demjan and Li, Jerry and Tomioka, Ryota and Vojnović, Milan}, issn = {1049-5258}, location = {Long Beach, CA, United States}, pages = {1710--1721}, publisher = {Neural Information Processing Systems Foundation}, title = {{QSGD: Communication-efficient SGD via gradient quantization and encoding}}, volume = {2017}, year = {2017}, } @inproceedings{432, abstract = {Recently there has been significant interest in training machine-learning models at low precision: by reducing precision, one can reduce computation and communication by one order of magnitude. We examine training at reduced precision, both from a theoretical and practical perspective, and ask: is it possible to train models at end-to-end low precision with provable guarantees? Can this lead to consistent order-of-magnitude speedups? We mainly focus on linear models, and the answer is yes for linear models. We develop a simple framework called ZipML based on one simple but novel strategy called double sampling. Our ZipML framework is able to execute training at low precision with no bias, guaranteeing convergence, whereas naive quanti- zation would introduce significant bias. We val- idate our framework across a range of applica- tions, and show that it enables an FPGA proto- type that is up to 6.5 × faster than an implemen- tation using full 32-bit precision. We further de- velop a variance-optimal stochastic quantization strategy and show that it can make a significant difference in a variety of settings. When applied to linear models together with double sampling, we save up to another 1.7 × in data movement compared with uniform quantization. When training deep networks with quantized models, we achieve higher accuracy than the state-of-the- art XNOR-Net. }, author = {Zhang, Hantian and Li, Jerry and Kara, Kaan and Alistarh, Dan-Adrian and Liu, Ji and Zhang, Ce}, booktitle = {Proceedings of Machine Learning Research}, isbn = {978-151085514-4}, location = {Sydney, Australia}, pages = {4035 -- 4043}, publisher = {ML Research Press}, title = {{ZipML: Training linear models with end-to-end low precision, and a little bit of deep learning}}, volume = { 70}, year = {2017}, } @inbook{444, abstract = {Complex I (NADH:ubiquinone oxidoreductase) plays a central role in cellular energy generation, contributing to the proton motive force used to produce ATP. It couples the transfer of two electrons between NADH and quinone to translocation of four protons across the membrane. It is the largest protein assembly of bacterial and mitochondrial respiratory chains, composed, in mammals, of up to 45 subunits with a total molecular weight of ∼1 MDa. Bacterial enzyme is about half the size, providing the important “minimal” model of complex I. The l-shaped complex consists of a hydrophilic arm, where electron transfer occurs, and a membrane arm, where proton translocation takes place. Previously, we have solved the crystal structures of the hydrophilic domain of complex I from Thermus thermophilus and of the membrane domain from Escherichia coli, followed by the atomic structure of intact, entire complex I from T. thermophilus. Recently, we have solved by cryo-EM a first complete atomic structure of mammalian (ovine) mitochondrial complex I. Core subunits are well conserved from the bacterial version, whilst supernumerary subunits form an interlinked, stabilizing shell around the core. Subunits containing additional cofactors, including Zn ion, NADPH and phosphopantetheine, probably have regulatory roles. Dysfunction of mitochondrial complex I is implicated in many human neurodegenerative diseases. The structure of mammalian enzyme provides many insights into complex I mechanism, assembly, maturation and dysfunction, allowing detailed molecular analysis of disease-causing mutations.}, author = {Sazanov, Leonid A}, booktitle = {Mechanisms of primary energy transduction in biology }, editor = {Wikström, Mårten}, isbn = {978-1-78262-865-1}, pages = {25 -- 59}, publisher = {Royal Society of Chemistry}, title = {{Structure of respiratory complex I: “Minimal” bacterial and “de luxe” mammalian versions}}, doi = {10.1039/9781788010405-00025}, year = {2017}, } @article{447, abstract = {We consider last passage percolation (LPP) models with exponentially distributed random variables, which are linked to the totally asymmetric simple exclusion process (TASEP). The competition interface for LPP was introduced and studied in Ferrari and Pimentel (2005a) for cases where the corresponding exclusion process had a rarefaction fan. Here we consider situations with a shock and determine the law of the fluctuations of the competition interface around its deter- ministic law of large number position. We also study the multipoint distribution of the LPP around the shock, extending our one-point result of Ferrari and Nejjar (2015).}, author = {Ferrari, Patrik and Nejjar, Peter}, journal = {Revista Latino-Americana de Probabilidade e Estatística}, pages = {299 -- 325}, publisher = {Instituto Nacional de Matematica Pura e Aplicada}, title = {{Fluctuations of the competition interface in presence of shocks}}, doi = {10.30757/ALEA.v14-17}, volume = {9}, year = {2017}, } @article{452, abstract = {Spinning tops and yo-yos have long fascinated cultures around the world with their unexpected, graceful motions that seemingly elude gravity. Yet, due to the exceeding difficulty of creating stably spinning objects of asymmetric shape in a manual trial-and-error process, there has been little departure from rotationally symmetric designs. With modern 3D printing technologies, however, we can manufacture shapes of almost unbounded complexity at the press of a button, shifting this design complexity toward computation. In this article, we describe an algorithm to generate designs for spinning objects by optimizing their mass distribution: as input, the user provides a solid 3D model and a desired axis of rotation. Our approach then modifies the interior mass distribution such that the principal directions of the moment of inertia align with the target rotation frame. To create voids inside the model, we represent its volume with an adaptive multiresolution voxelization and optimize the discrete voxel fill values using a continuous, nonlinear formulation. We further optimize for rotational stability by maximizing the dominant principal moment. Our method is well-suited for a variety of 3D printed models, ranging from characters to abstract shapes. We demonstrate tops and yo-yos that spin surprisingly stably despite their asymmetric appearance.}, author = {Bächer, Moritz and Bickel, Bernd and Whiting, Emily and Sorkine Hornung, Olga}, journal = {Communications of the ACM}, number = {8}, pages = {92 -- 99}, publisher = {ACM}, title = {{Spin it: Optimizing moment of inertia for spinnable objects}}, doi = {10.1145/3068766}, volume = {60}, year = {2017}, } @article{453, abstract = {Most kinesin motors move in only one direction along microtubules. Members of the kinesin-5 subfamily were initially described as unidirectional plus-end-directed motors and shown to produce piconewton forces. However, some fungal kinesin-5 motors are bidirectional. The force production of a bidirectional kinesin-5 has not yet been measured. Therefore, it remains unknown whether the mechanism of the unconventional minus-end-directed motility differs fundamentally from that of plus-end-directed stepping. Using force spectroscopy, we have measured here the forces that ensembles of purified budding yeast kinesin-5 Cin8 produce in microtubule gliding assays in both plus- and minus-end direction. Correlation analysis of pause forces demonstrated that individual Cin8 molecules produce additive forces in both directions of movement. In ensembles, Cin8 motors were able to produce single-motor forces up to a magnitude of ∼1.5 pN. Hence, these properties appear to be conserved within the kinesin-5 subfamily. Force production was largely independent of the directionality of movement, indicating similarities between the motility mechanisms for both directions. These results provide constraints for the development of models for the bidirectional motility mechanism of fission yeast kinesin-5 and provide insight into the function of this mitotic motor.}, author = {Fallesen, Todd and Roostalu, Johanna and Düllberg, Christian F and Pruessner, Gunnar and Surrey, Thomas}, issn = {1542-0086}, journal = {Biophysical Journal}, number = {9}, pages = {2055 -- 2067}, publisher = {Biophysical Society}, title = {{Ensembles of bidirectional kinesin Cin8 produce additive forces in both directions of movement}}, doi = {10.1016/j.bpj.2017.09.006}, volume = {113}, year = {2017}, } @article{459, abstract = {The social insects bees, wasps, ants, and termites are species-rich, occur in many habitats, and often constitute a large part of the biomass. Many are also invasive, including species of termites, the red imported fire ant, and the Argentine ant. While invasive social insects have been a problem in Southern Europe for some time, Central Europa was free of invasive ant species until recently because most ants are adapted to warmer climates. Only in the 1990s, did Lasius neglectus, a close relative of the common black garden ant, arrive in Germany. First described in 1990 based on individuals collected in Budapest, the species has since been detected for example in France, Germany, Spain, England, and Kyrgyzstan. The species is spread with soil during construction work or plantings, and L. neglectus therefore is often found in parks and botanical gardens. Another invasive ant now spreading in southern Germany is Formica fuscocinerea, which occurs along rivers, including in the sandy floodplains of the river Isar. As is typical of pioneer species, F. fuscocinerea quickly becomes extremely abundant and therefore causes problems for example on playgrounds in Munich. All invasive ant species are characterized by cooperation across nests, leading to strongly interconnected, very large super-colonies. The resulting dominance results in the extinction of native ant species as well as other arthropod species and thus in the reduction of biodiversity.}, author = {Cremer, Sylvia}, issn = {2366-2875}, journal = {Rundgespräche Forum Ökologie}, pages = {105 -- 116}, publisher = {Verlag Dr. Friedrich Pfeil}, title = {{Invasive Ameisen in Europa: Wie sie sich ausbreiten und die heimische Fauna verändern}}, volume = {46}, year = {2017}, } @article{12193, abstract = {DNA methylation regulates eukaryotic gene expression and is extensively reprogrammed during animal development. However, whether developmental methylation reprogramming during the sporophytic life cycle of flowering plants regulates genes is presently unknown. Here we report a distinctive gene-targeted RNA-directed DNA methylation (RdDM) activity in the Arabidopsis thaliana male sexual lineage that regulates gene expression in meiocytes. Loss of sexual-lineage-specific RdDM causes mis-splicing of the MPS1 gene (also known as PRD2), thereby disrupting meiosis. Our results establish a regulatory paradigm in which de novo methylation creates a cell-lineage-specific epigenetic signature that controls gene expression and contributes to cellular function in flowering plants.}, author = {Walker, James and Gao, Hongbo and Zhang, Jingyi and Aldridge, Billy and Vickers, Martin and Higgins, James D. and Feng, Xiaoqi}, issn = {1546-1718}, journal = {Nature Genetics}, keywords = {Genetics}, number = {1}, pages = {130--137}, publisher = {Nature Research}, title = {{Sexual-lineage-specific DNA methylation regulates meiosis in Arabidopsis}}, doi = {10.1038/s41588-017-0008-5}, volume = {50}, year = {2017}, } @proceedings{638, abstract = {This book constitutes the refereed proceedings of the 9th InternationalWorkshop on Numerical Software Verification, NSV 2016, held in Toronto, ON, Canada in July 2011 - colocated with CAV 2016, the 28th International Conference on Computer Aided Verification. The NSV workshop is dedicated to the development of logical and mathematical techniques for the reasoning about programmability and reliability.}, editor = {Bogomolov, Sergiy and Martel, Matthieu and Prabhakar, Pavithra}, issn = {0302-9743}, location = {Toronto, ON, Canada}, publisher = {Springer}, title = {{Numerical Software Verification}}, doi = {10.1007/978-3-319-54292-8}, volume = {10152}, year = {2017}, } @inproceedings{1194, abstract = {Termination is one of the basic liveness properties, and we study the termination problem for probabilistic programs with real-valued variables. Previous works focused on the qualitative problem that asks whether an input program terminates with probability~1 (almost-sure termination). A powerful approach for this qualitative problem is the notion of ranking supermartingales with respect to a given set of invariants. The quantitative problem (probabilistic termination) asks for bounds on the termination probability. A fundamental and conceptual drawback of the existing approaches to address probabilistic termination is that even though the supermartingales consider the probabilistic behavior of the programs, the invariants are obtained completely ignoring the probabilistic aspect. In this work we address the probabilistic termination problem for linear-arithmetic probabilistic programs with nondeterminism. We define the notion of {\em stochastic invariants}, which are constraints along with a probability bound that the constraints hold. We introduce a concept of {\em repulsing supermartingales}. First, we show that repulsing supermartingales can be used to obtain bounds on the probability of the stochastic invariants. Second, we show the effectiveness of repulsing supermartingales in the following three ways: (1)~With a combination of ranking and repulsing supermartingales we can compute lower bounds on the probability of termination; (2)~repulsing supermartingales provide witnesses for refutation of almost-sure termination; and (3)~with a combination of ranking and repulsing supermartingales we can establish persistence properties of probabilistic programs. We also present results on related computational problems and an experimental evaluation of our approach on academic examples. }, author = {Chatterjee, Krishnendu and Novotny, Petr and Zikelic, Djordje}, issn = {0730-8566}, location = {Paris, France}, number = {1}, pages = {145 -- 160}, publisher = {ACM}, title = {{Stochastic invariants for probabilistic termination}}, doi = {10.1145/3009837.3009873}, volume = {52}, year = {2017}, } @inproceedings{637, abstract = {For many cryptographic primitives, it is relatively easy to achieve selective security (where the adversary commits a-priori to some of the choices to be made later in the attack) but appears difficult to achieve the more natural notion of adaptive security (where the adversary can make all choices on the go as the attack progresses). A series of several recent works shows how to cleverly achieve adaptive security in several such scenarios including generalized selective decryption (Panjwani, TCC ’07 and Fuchsbauer et al., CRYPTO ’15), constrained PRFs (Fuchsbauer et al., ASIACRYPT ’14), and Yao garbled circuits (Jafargholi and Wichs, TCC ’16b). Although the above works expressed vague intuition that they share a common technique, the connection was never made precise. In this work we present a new framework that connects all of these works and allows us to present them in a unified and simplified fashion. Moreover, we use the framework to derive a new result for adaptively secure secret sharing over access structures defined via monotone circuits. We envision that further applications will follow in the future. Underlying our framework is the following simple idea. It is well known that selective security, where the adversary commits to n-bits of information about his future choices, automatically implies adaptive security at the cost of amplifying the adversary’s advantage by a factor of up to 2n. However, in some cases the proof of selective security proceeds via a sequence of hybrids, where each pair of adjacent hybrids locally only requires some smaller partial information consisting of m ≪ n bits. The partial information needed might be completely different between different pairs of hybrids, and if we look across all the hybrids we might rely on the entire n-bit commitment. Nevertheless, the above is sufficient to prove adaptive security, at the cost of amplifying the adversary’s advantage by a factor of only 2m ≪ 2n. In all of our examples using the above framework, the different hybrids are captured by some sort of a graph pebbling game and the amount of information that the adversary needs to commit to in each pair of hybrids is bounded by the maximum number of pebbles in play at any point in time. Therefore, coming up with better strategies for proving adaptive security translates to various pebbling strategies for different types of graphs.}, author = {Jafargholi, Zahra and Kamath Hosdurg, Chethan and Klein, Karen and Komargodski, Ilan and Pietrzak, Krzysztof Z and Wichs, Daniel}, editor = {Katz, Jonathan and Shacham, Hovav}, isbn = {978-331963687-0}, location = {Santa Barbara, CA, United States}, pages = {133 -- 163}, publisher = {Springer}, title = {{Be adaptive avoid overcommitting}}, doi = {10.1007/978-3-319-63688-7_5}, volume = {10401}, year = {2017}, } @inproceedings{1001, abstract = {We present a computational approach for designing CurveUps, curvy shells that form from an initially flat state. They consist of small rigid tiles that are tightly held together by two pre-stretched elastic sheets attached to them. Our method allows the realization of smooth, doubly curved surfaces that can be fabricated as a flat piece. Once released, the restoring forces of the pre-stretched sheets support the object to take shape in 3D. CurveUps are structurally stable in their target configuration. The design process starts with a target surface. Our method generates a tile layout in 2D and optimizes the distribution, shape, and attachment areas of the tiles to obtain a configuration that is fabricable and in which the curved up state closely matches the target. Our approach is based on an efficient approximate model and a local optimization strategy for an otherwise intractable nonlinear optimization problem. We demonstrate the effectiveness of our approach for a wide range of shapes, all realized as physical prototypes.}, author = {Guseinov, Ruslan and Miguel, Eder and Bickel, Bernd}, location = {Los Angeles, CA, United States}, number = {4}, publisher = {ACM}, title = {{CurveUps: Shaping objects from flat plates with tension-actuated curvature}}, doi = {10.1145/3072959.3073709}, volume = {36}, year = {2017}, } @article{1120, abstract = {The existence of a self-localization transition in the polaron problem has been under an active debate ever since Landau suggested it 83 years ago. Here we reveal the self-localization transition for the rotational analogue of the polaron -- the angulon quasiparticle. We show that, unlike for the polarons, self-localization of angulons occurs at finite impurity-bath coupling already at the mean-field level. The transition is accompanied by the spherical-symmetry breaking of the angulon ground state and a discontinuity in the first derivative of the ground-state energy. Moreover, the type of the symmetry breaking is dictated by the symmetry of the microscopic impurity-bath interaction, which leads to a number of distinct self-localized states. The predicted effects can potentially be addressed in experiments on cold molecules trapped in superfluid helium droplets and ultracold quantum gases, as well as on electronic excitations in solids and Bose-Einstein condensates. }, author = {Li, Xiang and Seiringer, Robert and Lemeshko, Mikhail}, issn = {2469-9926}, journal = {Physical Review A}, number = {3}, publisher = {American Physical Society}, title = {{Angular self-localization of impurities rotating in a bosonic bath}}, doi = {10.1103/PhysRevA.95.033608}, volume = {95}, year = {2017}, } @inproceedings{911, abstract = {We develop a probabilistic technique for colorizing grayscale natural images. In light of the intrinsic uncertainty of this task, the proposed probabilistic framework has numerous desirable properties. In particular, our model is able to produce multiple plausible and vivid colorizations for a given grayscale image and is one of the first colorization models to provide a proper stochastic sampling scheme. Moreover, our training procedure is supported by a rigorous theoretical framework that does not require any ad hoc heuristics and allows for efficient modeling and learning of the joint pixel color distribution.We demonstrate strong quantitative and qualitative experimental results on the CIFAR-10 dataset and the challenging ILSVRC 2012 dataset.}, author = {Royer, Amélie and Kolesnikov, Alexander and Lampert, Christoph}, location = {London, United Kingdom}, pages = {85.1--85.12}, publisher = {BMVA Press}, title = {{Probabilistic image colorization}}, doi = {10.5244/c.31.85}, year = {2017}, } @inproceedings{647, abstract = {Despite researchers’ efforts in the last couple of decades, reachability analysis is still a challenging problem even for linear hybrid systems. Among the existing approaches, the most practical ones are mainly based on bounded-time reachable set over-approximations. For the purpose of unbounded-time analysis, one important strategy is to abstract the original system and find an invariant for the abstraction. In this paper, we propose an approach to constructing a new kind of abstraction called conic abstraction for affine hybrid systems, and to computing reachable sets based on this abstraction. The essential feature of a conic abstraction is that it partitions the state space of a system into a set of convex polyhedral cones which is derived from a uniform conic partition of the derivative space. Such a set of polyhedral cones is able to cut all trajectories of the system into almost straight segments so that every segment of a reach pipe in a polyhedral cone tends to be straight as well, and hence can be over-approximated tightly by polyhedra using similar techniques as HyTech or PHAVer. In particular, for diagonalizable affine systems, our approach can guarantee to find an invariant for unbounded reachable sets, which is beyond the capability of bounded-time reachability analysis tools. We implemented the approach in a tool and experiments on benchmarks show that our approach is more powerful than SpaceEx and PHAVer in dealing with diagonalizable systems.}, author = {Bogomolov, Sergiy and Giacobbe, Mirco and Henzinger, Thomas A and Kong, Hui}, isbn = {978-331965764-6}, location = {Berlin, Germany}, pages = {116 -- 132}, publisher = {Springer}, title = {{Conic abstractions for hybrid systems}}, doi = {10.1007/978-3-319-65765-3_7}, volume = {10419 }, year = {2017}, } @inproceedings{631, abstract = {Template polyhedra generalize intervals and octagons to polyhedra whose facets are orthogonal to a given set of arbitrary directions. They have been employed in the abstract interpretation of programs and, with particular success, in the reachability analysis of hybrid automata. While previously, the choice of directions has been left to the user or a heuristic, we present a method for the automatic discovery of directions that generalize and eliminate spurious counterexamples. We show that for the class of convex hybrid automata, i.e., hybrid automata with (possibly nonlinear) convex constraints on derivatives, such directions always exist and can be found using convex optimization. We embed our method inside a CEGAR loop, thus enabling the time-unbounded reachability analysis of an important and richer class of hybrid automata than was previously possible. We evaluate our method on several benchmarks, demonstrating also its superior efficiency for the special case of linear hybrid automata.}, author = {Bogomolov, Sergiy and Frehse, Goran and Giacobbe, Mirco and Henzinger, Thomas A}, isbn = {978-366254576-8}, location = {Uppsala, Sweden}, pages = {589 -- 606}, publisher = {Springer}, title = {{Counterexample guided refinement of template polyhedra}}, doi = {10.1007/978-3-662-54577-5_34}, volume = {10205}, year = {2017}, } @article{955, abstract = {Gene expression is controlled by networks of regulatory proteins that interact specifically with external signals and DNA regulatory sequences. These interactions force the network components to co-evolve so as to continually maintain function. Yet, existing models of evolution mostly focus on isolated genetic elements. In contrast, we study the essential process by which regulatory networks grow: the duplication and subsequent specialization of network components. We synthesize a biophysical model of molecular interactions with the evolutionary framework to find the conditions and pathways by which new regulatory functions emerge. We show that specialization of new network components is usually slow, but can be drastically accelerated in the presence of regulatory crosstalk and mutations that promote promiscuous interactions between network components.}, author = {Friedlander, Tamar and Prizak, Roshan and Barton, Nicholas H and Tkacik, Gasper}, issn = {2041-1723}, journal = {Nature Communications}, number = {1}, publisher = {Nature Publishing Group}, title = {{Evolution of new regulatory functions on biophysically realistic fitness landscapes}}, doi = {10.1038/s41467-017-00238-8}, volume = {8}, year = {2017}, } @article{1144, abstract = {We show that matrix elements of functions of N × N Wigner matrices fluctuate on a scale of order N−1/2 and we identify the limiting fluctuation. Our result holds for any function f of the matrix that has bounded variation thus considerably relaxing the regularity requirement imposed in [7, 11].}, author = {Erdös, László and Schröder, Dominik J}, journal = {Electronic Communications in Probability}, publisher = {Institute of Mathematical Statistics}, title = {{Fluctuations of functions of Wigner matrices}}, doi = {10.1214/16-ECP38}, volume = {21}, year = {2017}, } @article{2016, abstract = {The Ising model is one of the simplest and most famous models of interacting systems. It was originally proposed to model ferromagnetic interactions in statistical physics and is now widely used to model spatial processes in many areas such as ecology, sociology, and genetics, usually without testing its goodness-of-fit. Here, we propose an exact goodness-of-fit test for the finite-lattice Ising model. The theory of Markov bases has been developed in algebraic statistics for exact goodness-of-fit testing using a Monte Carlo approach. However, this beautiful theory has fallen short of its promise for applications, because finding a Markov basis is usually computationally intractable. We develop a Monte Carlo method for exact goodness-of-fit testing for the Ising model which avoids computing a Markov basis and also leads to a better connectivity of the Markov chain and hence to a faster convergence. We show how this method can be applied to analyze the spatial organization of receptors on the cell membrane.}, author = {Martin Del Campo Sanchez, Abraham and Cepeda Humerez, Sarah A and Uhler, Caroline}, issn = {03036898}, journal = {Scandinavian Journal of Statistics}, number = {2}, pages = {285 -- 306}, publisher = {Wiley-Blackwell}, title = {{Exact goodness-of-fit testing for the Ising model}}, doi = {10.1111/sjos.12251}, volume = {44}, year = {2017}, }