@inproceedings{14203, abstract = {We propose a conditional gradient framework for a composite convex minimization template with broad applications. Our approach combines smoothing and homotopy techniques under the CGM framework, and provably achieves the optimal O(1/k−−√) convergence rate. We demonstrate that the same rate holds if the linear subproblems are solved approximately with additive or multiplicative error. In contrast with the relevant work, we are able to characterize the convergence when the non-smooth term is an indicator function. Specific applications of our framework include the non-smooth minimization, semidefinite programming, and minimization with linear inclusion constraints over a compact domain. Numerical evidence demonstrates the benefits of our framework.}, author = {Yurtsever, Alp and Fercoq, Olivier and Locatello, Francesco and Cevher, Volkan}, booktitle = {Proceedings of the 35th International Conference on Machine Learning}, location = {Stockholm, Sweden}, pages = {5727--5736}, publisher = {ML Research Press}, title = {{A conditional gradient framework for composite convex minimization with applications to semidefinite programming}}, volume = {80}, year = {2018}, } @inproceedings{14204, abstract = {Two popular examples of first-order optimization methods over linear spaces are coordinate descent and matching pursuit algorithms, with their randomized variants. While the former targets the optimization by moving along coordinates, the latter considers a generalized notion of directions. Exploiting the connection between the two algorithms, we present a unified analysis of both, providing affine invariant sublinear O(1/t) rates on smooth objectives and linear convergence on strongly convex objectives. As a byproduct of our affine invariant analysis of matching pursuit, our rates for steepest coordinate descent are the tightest known. Furthermore, we show the first accelerated convergence rate O(1/t2) for matching pursuit and steepest coordinate descent on convex objectives.}, author = {Locatello, Francesco and Raj, Anant and Karimireddy, Sai Praneeth and Rätsch, Gunnar and Schölkopf, Bernhard and Stich, Sebastian U. and Jaggi, Martin}, booktitle = {Proceedings of the 35th International Conference on Machine Learning}, pages = {3198--3207}, publisher = {ML Research Press}, title = {{On matching pursuit and coordinate descent}}, volume = {80}, year = {2018}, } @inproceedings{14224, abstract = {Clustering is a cornerstone of unsupervised learning which can be thought as disentangling multiple generative mechanisms underlying the data. In this paper we introduce an algorithmic framework to train mixtures of implicit generative models which we particularize for variational autoencoders. Relying on an additional set of discriminators, we propose a competitive procedure in which the models only need to approximate the portion of the data distribution from which they can produce realistic samples. As a byproduct, each model is simpler to train, and a clustering interpretation arises naturally from the partitioning of the training points among the models. We empirically show that our approach splits the training distribution in a reasonable way and increases the quality of the generated samples.}, author = {Locatello, Francesco and Vincent, Damien and Tolstikhin, Ilya and Ratsch, Gunnar and Gelly, Sylvain and Scholkopf, Bernhard}, booktitle = {6th International Conference on Learning Representations}, location = {Vancouver, Canada}, title = {{Clustering meets implicit generative models}}, year = {2018}, } @article{14284, abstract = {Pore-forming toxins (PFT) are virulence factors that transform from soluble to membrane-bound states. The Yersinia YaxAB system represents a family of binary α-PFTs with orthologues in human, insect, and plant pathogens, with unknown structures. YaxAB was shown to be cytotoxic and likely involved in pathogenesis, though the molecular basis for its two-component lytic mechanism remains elusive. Here, we present crystal structures of YaxA and YaxB, together with a cryo-electron microscopy map of the YaxAB complex. Our structures reveal a pore predominantly composed of decamers of YaxA–YaxB heterodimers. Both subunits bear membrane-active moieties, but only YaxA is capable of binding to membranes by itself. YaxB can subsequently be recruited to membrane-associated YaxA and induced to present its lytic transmembrane helices. Pore formation can progress by further oligomerization of YaxA–YaxB dimers. Our results allow for a comparison between pore assemblies belonging to the wider ClyA-like family of α-PFTs, highlighting diverse pore architectures.}, author = {Bräuning, Bastian and Bertosin, Eva and Praetorius, Florian M and Ihling, Christian and Schatt, Alexandra and Adler, Agnes and Richter, Klaus and Sinz, Andrea and Dietz, Hendrik and Groll, Michael}, issn = {2041-1723}, journal = {Nature Communications}, keywords = {General Physics and Astronomy, General Biochemistry, Genetics and Molecular Biology, General Chemistry, Multidisciplinary}, publisher = {Springer Nature}, title = {{Structure and mechanism of the two-component α-helical pore-forming toxin YaxAB}}, doi = {10.1038/s41467-018-04139-2}, volume = {9}, year = {2018}, } @inproceedings{143, abstract = {Vector Addition Systems with States (VASS) provide a well-known and fundamental model for the analysis of concurrent processes, parameterized systems, and are also used as abstract models of programs in resource bound analysis. In this paper we study the problem of obtaining asymptotic bounds on the termination time of a given VASS. In particular, we focus on the practically important case of obtaining polynomial bounds on termination time. Our main contributions are as follows: First, we present a polynomial-time algorithm for deciding whether a given VASS has a linear asymptotic complexity. We also show that if the complexity of a VASS is not linear, it is at least quadratic. Second, we classify VASS according to quantitative properties of their cycles. We show that certain singularities in these properties are the key reason for non-polynomial asymptotic complexity of VASS. In absence of singularities, we show that the asymptotic complexity is always polynomial and of the form Θ(nk), for some integer k d, where d is the dimension of the VASS. We present a polynomial-time algorithm computing the optimal k. For general VASS, the same algorithm, which is based on a complete technique for the construction of ranking functions in VASS, produces a valid lower bound, i.e., a k such that the termination complexity is (nk). Our results are based on new insights into the geometry of VASS dynamics, which hold the potential for further applicability to VASS analysis.}, author = {Brázdil, Tomáš and Chatterjee, Krishnendu and Kučera, Antonín and Novotny, Petr and Velan, Dominik and Zuleger, Florian}, isbn = {978-1-4503-5583-4}, location = {Oxford, United Kingdom}, pages = {185 -- 194}, publisher = {IEEE}, title = {{Efficient algorithms for asymptotic bounds on termination time in VASS}}, doi = {10.1145/3209108.3209191}, volume = {F138033}, year = {2018}, } @phdthesis{14306, abstract = {Function and activity of biomolecules often depend on their spatial arrangement. The method introduced here allows genetically encoding the spatial arrangement of proteins and DNA. The approach relies on staple proteins that fold double-stranded DNA into user-defined shapes. This thesis describes the development of staple proteins based on the DNA recognition of TAL effectors and presents experimentally derived rules for designing a variety of self-assembling nanoscale shapes featuring structural motifs such as curvature, vertices, corners, and multilayer helix packing. }, author = {Praetorius, Florian M}, publisher = {Technische Universität München}, title = {{Genetically encoding the spatial arrangement of DNA and proteins in self-assembling nanostructures}}, year = {2018}, } @article{9053, abstract = {The development of strategies to assemble microscopic machines from dissipative building blocks are essential on the route to novel active materials. We recently demonstrated the hierarchical self-assembly of phoretic microswimmers into self-spinning microgears and their synchronization by diffusiophoretic interactions [Aubret et al., Nat. Phys., 2018]. In this paper, we adopt a pedagogical approach and expose our strategy to control self-assembly and build machines using phoretic phenomena. We notably introduce Highly Inclined Laminated Optical sheets microscopy (HILO) to image and characterize anisotropic and dynamic diffusiophoretic interactions, which cannot be performed by conventional fluorescence microscopy. The dynamics of a (haematite) photocatalytic material immersed in (hydrogen peroxide) fuel under various illumination patterns is first described and quantitatively rationalized by a model of diffusiophoresis, the migration of a colloidal particle in a concentration gradient. It is further exploited to design phototactic microswimmers that direct towards the high intensity of light, as a result of the reorientation of the haematite in a light gradient. We finally show the assembly of self-spinning microgears from colloidal microswimmers and carefully characterize the interactions using HILO techniques. The results are compared with analytical and numerical predictions and agree quantitatively, stressing the important role played by concentration gradients induced by chemical activity to control and design interactions. Because the approach described hereby is generic, this works paves the way for the rational design of machines by controlling phoretic phenomena.}, author = {Aubret, Antoine and Palacci, Jérémie A}, issn = {1744-6848}, journal = {Soft Matter}, keywords = {General Chemistry, Condensed Matter Physics}, number = {47}, pages = {9577--9588}, publisher = {Royal Society of Chemistry }, title = {{Diffusiophoretic design of self-spinning microgears from colloidal microswimmers}}, doi = {10.1039/c8sm01760c}, volume = {14}, year = {2018}, } @article{9062, abstract = {Self-assembly is the autonomous organization of components into patterns or structures: an essential ingredient of biology and a desired route to complex organization1. At equilibrium, the structure is encoded through specific interactions2,3,4,5,6,7,8, at an unfavourable entropic cost for the system. An alternative approach, widely used by nature, uses energy input to bypass the entropy bottleneck and develop features otherwise impossible at equilibrium9. Dissipative building blocks that inject energy locally were made available by recent advances in colloidal science10,11 but have not been used to control self-assembly. Here we show the targeted formation of self-powered microgears from active particles and their autonomous synchronization into dynamical superstructures. We use a photoactive component that consumes fuel, haematite, to devise phototactic microswimmers that form self-spinning microgears following spatiotemporal light patterns. The gears are coupled via their chemical clouds by diffusiophoresis12 and constitute the elementary bricks of synchronized superstructures, which autonomously regulate their dynamics. The results are quantitatively rationalized on the basis of a stochastic description of diffusio-phoretic oscillators dynamically coupled by chemical gradients. Our findings harness non-equilibrium phoretic phenomena to program interactions and direct self-assembly with fidelity and specificity. It lays the groundwork for the autonomous construction of dynamical architectures and functional micro-machinery.}, author = {Aubret, Antoine and Youssef, Mena and Sacanna, Stefano and Palacci, Jérémie A}, issn = {1745-2481}, journal = {Nature Physics}, number = {11}, pages = {1114--1118}, publisher = {Springer Nature}, title = {{Targeted assembly and synchronization of self-spinning microgears}}, doi = {10.1038/s41567-018-0227-4}, volume = {14}, year = {2018}, } @article{9066, abstract = {The novel electronic state of the canted antiferromagnetic (AFM) insulator, strontium iridate (Sr2IrO4) has been well described by the spin-orbit-entangled isospin Jeff = 1/2, but the role of isospin in transport phenomena remains poorly understood. In this study, antiferromagnet-based spintronic functionality is demonstrated by combining unique characteristics of the isospin state in Sr2IrO4. Based on magnetic and transport measurements, large and highly anisotropic magnetoresistance (AMR) is obtained by manipulating the antiferromagnetic isospin domains. First-principles calculations suggest that electrons whose isospin directions are strongly coupled to in-plane net magnetic moment encounter the isospin mismatch when moving across antiferromagnetic domain boundaries, which generates a high resistance state. By rotating a magnetic field that aligns in-plane net moments and removes domain boundaries, the macroscopically-ordered isospins govern dynamic transport through the system, which leads to the extremely angle-sensitive AMR. As with this work that establishes a link between isospins and magnetotransport in strongly spin-orbit-coupled AFM Sr2IrO4, the peculiar AMR effect provides a beneficial foundation for fundamental and applied research on AFM spintronics.}, author = {Lee, Nara and Ko, Eunjung and Choi, Hwan Young and Hong, Yun Jeong and Nauman, Muhammad and Kang, Woun and Choi, Hyoung Joon and Choi, Young Jai and Jo, Younjung}, issn = {0935-9648}, journal = {Advanced Materials}, keywords = {Mechanical Engineering, General Materials Science, Mechanics of Materials}, number = {52}, publisher = {Wiley}, title = {{Antiferromagnet‐based spintronic functionality by controlling isospin domains in a layered perovskite iridate}}, doi = {10.1002/adma.201805564}, volume = {30}, year = {2018}, } @article{9068, abstract = {We report the temperature-dependent resistivity ρ(T) of chalcogenide NiS2-xSex (x = 0.1) using hydrostatic pressure as a control parameter in the temperature range of 4–300 K. The insulating behavior of ρ(T) survives at low temperatures in the pressure regime below 7.5 kbar, whereas a clear insulator-to-metallic transition is observed above 7.5 kbar. Two types of magnetic transitions, from the paramagnetic (PM) to the antiferromagnetic (AFM) state and from the AFM state to the weak ferromagnetic (WF) state, were evaluated and confirmed by magnetization measurement. According to the temperature–pressure phase diagram, the WF phase survives up to 7.5 kbar, and the transition temperature of the WF transition decreases as the pressure increases, whereas the metal–insulator transition temperature increases up to 9.4 kbar. We analyzed the metallic behavior and proposed Fermi-liquid behavior of NiS1.9Se0.1.}, author = {Hussain, Tayyaba and Oh, Myeong-jun and Nauman, Muhammad and Jo, Younjung and Han, Garam and Kim, Changyoung and Kang, Woun}, issn = {0921-4526}, journal = {Physica B: Condensed Matter}, pages = {235--238}, publisher = {Elsevier}, title = {{Pressure-induced metal–insulator transitions in chalcogenide NiS2-Se}}, doi = {10.1016/j.physb.2017.11.032}, volume = {536}, year = {2018}, } @article{913, abstract = {Coordinated cell polarization in developing tissues is a recurrent theme in multicellular organisms. In plants, a directional distribution of the plant hormone auxin is at the core of many developmental programs. A feedback regulation of auxin on the polarized localization of PIN auxin transporters in individual cells has been proposed as a self-organizing mechanism for coordinated tissue polarization, but the molecular mechanisms linking auxin signalling to PIN-dependent auxin transport remain unknown. We performed a microarray-based approach to find regulators of the auxin-induced PIN relocation in the Arabidopsis thaliana root. We identified a subset of a family of phosphatidylinositol transfer proteins (PITP), the PATELLINs (PATL). Here, we show that PATLs are expressed in partially overlapping cells types in different tissues going through mitosis or initiating differentiation programs. PATLs are plasma membrane-associated proteins accumulated in Arabidopsis embryos, primary roots, lateral root primordia, and developing stomata. Higher order patl mutants display reduced PIN1 repolarization in response to auxin, shorter root apical meristem, and drastic defects in embryo and seedling development. This suggests PATLs redundantly play a crucial role in polarity and patterning in Arabidopsis.}, author = {Tejos, Ricardo and Rodríguez Furlán, Cecilia and Adamowski, Maciek and Sauer, Michael and Norambuena, Lorena and Friml, Jirí}, issn = {00219533}, journal = {Journal of Cell Science}, number = {2}, publisher = {Company of Biologists}, title = {{PATELLINS are regulators of auxin mediated PIN1 relocation and plant development in Arabidopsis thaliana}}, doi = {10.1242/jcs.204198}, volume = {131}, year = {2018}, } @article{9134, abstract = {Several studies have shown the existence of a critical latitude where the dissipation of internal tides is strongly enhanced. Internal tides are internal waves generated by barotropic tidal currents impinging rough topography at the seafloor. Their dissipation and concomitant diapycnal mixing are believed to be important for water masses and the large‐scale ocean circulation. The purpose of this study is to clarify the physical processes at the origin of this strong latitudinal dependence of tidal energy dissipation. We find that different mechanisms are involved equatorward and poleward of the critical latitude. Triadic resonant instabilities are responsible for the dissipation of internal tides equatorward of the critical latitude. In particular, a dominant triad involving the primary internal tide and near‐inertial waves is key. At the critical latitude, the peak of energy dissipation is explained by both increased instability growth rates, and smaller scales of secondary waves thus more prone to break and dissipate their energy. Surprisingly, poleward of the critical latitude, the generation of evanescent waves appears to be crucial. Triadic instabilities have been widely studied, but the transfer of energy to evanescent waves has received comparatively little attention. Our work suggests that the nonlinear transfer of energy from the internal tide to evanescent waves (corresponding to the 2f‐pump mechanism described by Young et al., 2008, https://doi.org/10.1017/S0022112008001742) is an efficient mechanism to dissipate internal tide energy near and poleward of the critical latitude. The theoretical results are confirmed in idealized high‐resolution numerical simulations of a barotropic M2 tide impinging sinusoidal topography in a linearly stratified fluid.}, author = {Richet, O. and Chomaz, J.-M. and Muller, Caroline J}, issn = {2169-9275}, journal = {Journal of Geophysical Research: Oceans}, number = {9}, pages = {6136--6155}, publisher = {American Geophysical Union}, title = {{Internal tide dissipation at topography: Triadic resonant instability equatorward and evanescent waves poleward of the critical latitude}}, doi = {10.1029/2017jc013591}, volume = {123}, year = {2018}, } @article{9135, abstract = {Idealized simulations of tropical moist convection have revealed that clouds can spontaneously clump together in a process called self-aggregation. This results in a state where a moist cloudy region with intense deep convection is surrounded by extremely dry subsiding air devoid of deep convection. Because of the idealized settings of the simulations where it was discovered, the relevance of self-aggregation to the real world is still debated. Here, we show that self-aggregation feedbacks play a leading-order role in the spontaneous genesis of tropical cyclones in cloud-resolving simulations. Those feedbacks accelerate the cyclogenesis process by a factor of 2, and the feedbacks contributing to the cyclone formation show qualitative and quantitative agreement with the self-aggregation process. Once the cyclone is formed, wind-induced surface heat exchange (WISHE) effects dominate, although we find that self-aggregation feedbacks have a small but nonnegligible contribution to the maintenance of the mature cyclone. Our results suggest that self-aggregation, and the framework developed for its study, can help shed more light into the physical processes leading to cyclogenesis and cyclone intensification. In particular, our results point out the importance of the longwave radiative cooling outside the cyclone.}, author = {Muller, Caroline J and Romps, David M.}, issn = {0027-8424}, journal = {Proceedings of the National Academy of Sciences}, keywords = {Multidisciplinary}, number = {12}, pages = {2930--2935}, publisher = {Proceedings of the National Academy of Sciences}, title = {{Acceleration of tropical cyclogenesis by self-aggregation feedbacks}}, doi = {10.1073/pnas.1719967115}, volume = {115}, year = {2018}, } @article{9136, abstract = {In this study we investigate the scaling of precipitation extremes with temperature in the Mediterranean region by assessing against observations the present day and future regional climate simulations performed in the frame of the HyMeX and MED-CORDEX programs. Over the 1979–2008 period, despite differences in quantitative precipitation simulation across the various models, the change in precipitation extremes with respect to temperature is robust and consistent. The spatial variability of the temperature–precipitation extremes relationship displays a hook shape across the Mediterranean, with negative slope at high temperatures and a slope following Clausius–Clapeyron (CC)-scaling at low temperatures. The temperature at which the slope of the temperature–precipitation extreme relation sharply changes (or temperature break), ranges from about 20 °C in the western Mediterranean to <10 °C in Greece. In addition, this slope is always negative in the arid regions of the Mediterranean. The scaling of the simulated precipitation extremes is insensitive to ocean–atmosphere coupling, while it depends very weakly on the resolution at high temperatures for short precipitation accumulation times. In future climate scenario simulations covering the 2070–2100 period, the temperature break shifts to higher temperatures by a value which is on average the mean regional temperature change due to global warming. The slope of the simulated future temperature–precipitation extremes relationship is close to CC-scaling at temperatures below the temperature break, while at high temperatures, the negative slope is close, but somewhat flatter or steeper, than in the current climate depending on the model. Overall, models predict more intense precipitation extremes in the future. Adjusting the temperature–precipitation extremes relationship in the present climate using the CC law and the temperature shift in the future allows the recovery of the temperature–precipitation extremes relationship in the future climate. This implies negligible regional changes of relative humidity in the future despite the large warming and drying over the Mediterranean. This suggests that the Mediterranean Sea is the primary source of moisture which counteracts the drying and warming impacts on relative humidity in parts of the Mediterranean region.}, author = {Drobinski, Philippe and Silva, Nicolas Da and Panthou, Gérémy and Bastin, Sophie and Muller, Caroline J and Ahrens, Bodo and Borga, Marco and Conte, Dario and Fosser, Giorgia and Giorgi, Filippo and Güttler, Ivan and Kotroni, Vassiliki and Li, Laurent and Morin, Efrat and Önol, Bariş and Quintana-Segui, Pere and Romera, Raquel and Torma, Csaba Zsolt}, issn = {0930-7575}, journal = {Climate Dynamics}, keywords = {Atmospheric Science}, number = {3}, pages = {1237--1257}, publisher = {Springer Nature}, title = {{Scaling precipitation extremes with temperature in the Mediterranean: Past climate assessment and projection in anthropogenic scenarios}}, doi = {10.1007/s00382-016-3083-x}, volume = {51}, year = {2018}, } @article{9229, author = {Danzl, Johann G}, issn = {2500-2295}, journal = {Opera Medica et Physiologica}, number = {S1}, pages = {11}, publisher = {Lobachevsky State University of Nizhny Novgorod}, title = {{Diffraction-unlimited optical imaging for synaptic physiology}}, doi = {10.20388/omp2018.00s1.001}, volume = {4}, year = {2018}, } @article{9471, abstract = {The DEMETER (DME) DNA glycosylase catalyzes genome-wide DNA demethylation and is required for endosperm genomic imprinting and embryo viability. Targets of DME-mediated DNA demethylation reside in small, euchromatic, AT-rich transposons and at the boundaries of large transposons, but how DME interacts with these diverse chromatin states is unknown. The STRUCTURE SPECIFIC RECOGNITION PROTEIN 1 (SSRP1) subunit of the chromatin remodeler FACT (facilitates chromatin transactions), was previously shown to be involved in the DME-dependent regulation of genomic imprinting in Arabidopsis endosperm. Therefore, to investigate the interaction between DME and chromatin, we focused on the activity of the two FACT subunits, SSRP1 and SUPPRESSOR of TY16 (SPT16), during reproduction in Arabidopsis. We found that FACT colocalizes with nuclear DME in vivo, and that DME has two classes of target sites, the first being euchromatic and accessible to DME, but the second, representing over half of DME targets, requiring the action of FACT for DME-mediated DNA demethylation genome-wide. Our results show that the FACT-dependent DME targets are GC-rich heterochromatin domains with high nucleosome occupancy enriched with H3K9me2 and H3K27me1. Further, we demonstrate that heterochromatin-associated linker histone H1 specifically mediates the requirement for FACT at a subset of DME-target loci. Overall, our results demonstrate that FACT is required for DME targeting by facilitating its access to heterochromatin.}, author = {Frost, Jennifer M. and Kim, M. Yvonne and Park, Guen Tae and Hsieh, Ping-Hung and Nakamura, Miyuki and Lin, Samuel J. H. and Yoo, Hyunjin and Choi, Jaemyung and Ikeda, Yoko and Kinoshita, Tetsu and Choi, Yeonhee and Zilberman, Daniel and Fischer, Robert L.}, issn = {1091-6490}, journal = {Proceedings of the National Academy of Sciences}, keywords = {Multidisciplinary}, number = {20}, pages = {E4720--E4729}, publisher = {National Academy of Sciences}, title = {{FACT complex is required for DNA demethylation at heterochromatin during reproduction in Arabidopsis}}, doi = {10.1073/pnas.1713333115}, volume = {115}, year = {2018}, } @article{95, abstract = {Electrostatic charging of insulating fine particles can be responsible for numerous phenomena ranging from lightning in volcanic plumes to dust explosions. However, even basic aspects of how fine particles become charged are still unclear. Studying particle charging is challenging because it usually involves the complexities associated with many-particle collisions. To address these issues, we introduce a method based on acoustic levitation, which makes it possible to initiate sequences of repeated collisions of a single submillimeter particle with a flat plate, and to precisely measure the particle charge in situ after each collision. We show that collisional charge transfer between insulators is dependent on the hydrophobicity of the contacting surfaces. We use glass, which we modify by attaching nonpolar molecules to the particle, the plate, or both. We find that hydrophilic surfaces develop significant positive charges after contacting hydrophobic surfaces. Moreover, we demonstrate that charging between a hydrophilic and a hydrophobic surface is suppressed in an acidic environment and enhanced in a basic one. Application of an electric field during each collision is found to modify the charge transfer, again depending on surface hydrophobicity. We discuss these results within the context of contact charging due to ion transfer, and we show that they lend strong support to OH− ions as the charge carriers.}, author = {Lee, Victor and James, Nicole and Waitukaitis, Scott R and Jaeger, Heinrich}, journal = {Physical Review Materials}, number = {3}, publisher = {American Physical Society}, title = {{Collisional charging of individual submillimeter particles: Using ultrasonic levitation to initiate and track charge transfer}}, doi = {10.1103/PhysRevMaterials.2.035602}, volume = {2}, year = {2018}, } @article{9565, abstract = {Let D(n,p) be the random directed graph on n vertices where each of the n(n-1) possible arcs is present independently with probability p. A celebrated result of Frieze shows that if p≥(logn+ω(1))/n then D(n,p) typically has a directed Hamilton cycle, and this is best possible. In this paper, we obtain a strengthening of this result, showing that under the same condition, the number of directed Hamilton cycles in D(n,p) is typically n!(p(1+o(1)))n. We also prove a hitting-time version of this statement, showing that in the random directed graph process, as soon as every vertex has in-/out-degrees at least 1, there are typically n!(logn/n(1+o(1)))n directed Hamilton cycles.}, author = {Ferber, Asaf and Kwan, Matthew Alan and Sudakov, Benny}, issn = {1098-2418}, journal = {Random Structures and Algorithms}, number = {4}, pages = {592--603}, publisher = {Wiley}, title = {{Counting Hamilton cycles in sparse random directed graphs}}, doi = {10.1002/rsa.20815}, volume = {53}, year = {2018}, } @article{9567, abstract = {Let P be a graph property which is preserved by removal of edges, and consider the random graph process that starts with the empty n-vertex graph and then adds edges one-by-one, each chosen uniformly at random subject to the constraint that P is not violated. These types of random processes have been the subject of extensive research over the last 20 years, having striking applications in extremal combinatorics, and leading to the discovery of important probabilistic tools. In this paper we consider the k-matching-free process, where P is the property of not containing a matching of size k. We are able to analyse the behaviour of this process for a wide range of values of k; in particular we prove that if k=o(n) or if n−2k=o(n−−√/logn) then this process is likely to terminate in a k-matching-free graph with the maximum possible number of edges, as characterised by Erdős and Gallai. We also show that these bounds on k are essentially best possible, and we make a first step towards understanding the behaviour of the process in the intermediate regime.}, author = {Krivelevich, Michael and Kwan, Matthew Alan and Loh, Po‐Shen and Sudakov, Benny}, issn = {1098-2418}, journal = {Random Structures and Algorithms}, number = {4}, pages = {692--716}, publisher = {Wiley}, title = {{The random k‐matching‐free process}}, doi = {10.1002/rsa.20814}, volume = {53}, year = {2018}, } @article{9568, abstract = {An intercalate in a Latin square is a 2×2 Latin subsquare. Let N be the number of intercalates in a uniformly random n×n Latin square. We prove that asymptotically almost surely N≥(1−o(1))n2/4, and that EN≤(1+o(1))n2/2 (therefore asymptotically almost surely N≤fn2 for any f→∞). This significantly improves the previous best lower and upper bounds. We also give an upper tail bound for the number of intercalates in two fixed rows of a random Latin square. In addition, we discuss a problem of Linial and Luria on low-discrepancy Latin squares.}, author = {Kwan, Matthew Alan and Sudakov, Benny}, issn = {1098-2418}, journal = {Random Structures and Algorithms}, number = {2}, pages = {181--196}, publisher = {Wiley}, title = {{Intercalates and discrepancy in random Latin squares}}, doi = {10.1002/rsa.20742}, volume = {52}, year = {2018}, }