@inproceedings{10748,
  abstract     = {The study of fluxoid states and fluxoid dynamics in mesoscopic iron-based superconducting rings is valuable for characterizing the basic properties of the superconductor, and may also provide important insight into the superconducting paring symmetry. We report the fabrications of micron-sized rings and disks from thin films of Fe(Se, Te) grown by molecular beam epitaxy. In order to study fluxoid states in rings we developed a custom-tailored version of magnetic force microscopy (MFM). This technique has a number of qualitative advantages for working with mesoscopic superconducting samples in comparison to the conventional MFM and other imaging techniques. We observed metastable fluxoid states in rings of different sizes. Thermally activated fluxoid dynamics of these states was studied and modeled. In addition, we found different regimes of interaction between Fe(Se, Te) ring and MFM tip which are explained. Possibilities of the existence of exotic vortex states and proposals for experiments to test the symmetry of the superconducting order parameter in iron based superconductors are analyzed.},
  author       = {Polshyn, Hryhoriy and Zhang, Can and Naibert, Tyler and Eckstein, James and Budakian, Raffi},
  booktitle    = {APS March Meeting 2015},
  issn         = {0003-0503},
  location     = {San Antonio, TX, United States},
  number       = {1},
  publisher    = {American Physical Society},
  title        = {{Study of Fe (Se, Te) micron-sized rings by magnetic force microscopy}},
  volume       = {60},
  year         = {2015},
}

@article{10794,
  abstract     = {Mathematical models are of fundamental importance in the understanding of complex population dynamics. For instance, they can be used to predict the population evolution starting from different initial conditions or to test how a system responds to external perturbations. For this analysis to be meaningful in real applications, however, it is of paramount importance to choose an appropriate model structure and to infer the model parameters from measured data. While many parameter inference methods are available for models based on deterministic ordinary differential equations, the same does not hold for more detailed individual-based models. Here we consider, in particular, stochastic models in which the time evolution of the species abundances is described by a continuous-time Markov chain. These models are governed by a master equation that is typically difficult to solve. Consequently, traditional inference methods that rely on iterative evaluation of parameter likelihoods are computationally intractable. The aim of this paper is to present recent advances in parameter inference for continuous-time Markov chain models, based on a moment closure approximation of the parameter likelihood, and to investigate how these results can help in understanding, and ultimately controlling, complex systems in ecology. Specifically, we illustrate through an agricultural pest case study how parameters of a stochastic individual-based model can be identified from measured data and how the resulting model can be used to solve an optimal control problem in a stochastic setting. In particular, we show how the matter of determining the optimal combination of two different pest control methods can be formulated as a chance constrained optimization problem where the control action is modeled as a state reset, leading to a hybrid system formulation.},
  author       = {Parise, Francesca and Lygeros, John and Ruess, Jakob},
  issn         = {2296-665X},
  journal      = {Frontiers in Environmental Science},
  keywords     = {General Environmental Science},
  publisher    = {Frontiers},
  title        = {{Bayesian inference for stochastic individual-based models of ecological systems: a pest control simulation study}},
  doi          = {10.3389/fenvs.2015.00042},
  volume       = {3},
  year         = {2015},
}

@inproceedings{10796,
  abstract     = {We consider concurrent mean-payoff games, a very well-studied class of two-player (player 1 vs player 2) zero-sum games on finite-state graphs where every transition is assigned a reward between 0 and 1, and the payoff function is the long-run average of the rewards. The value is the maximal expected payoff that player 1 can guarantee against all strategies of player 2. We consider the computation of the set of states with value 1 under finite-memory strategies for player 1, and our main results for the problem are as follows: (1) we present a polynomial-time algorithm; (2) we show that whenever there is a finite-memory strategy, there is a stationary strategy that does not need memory at all; and (3) we present an optimal bound (which is double exponential) on the patience of stationary strategies (where patience of a distribution is the inverse of the smallest positive probability and represents a complexity measure of a stationary strategy).},
  author       = {Chatterjee, Krishnendu and Ibsen-Jensen, Rasmus},
  booktitle    = {Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms},
  isbn         = {978-161197374-7},
  location     = {San Diego, CA, United States},
  number       = {1},
  pages        = {1018--1029},
  publisher    = {SIAM},
  title        = {{The value 1 problem under finite-memory strategies for concurrent mean-payoff games}},
  doi          = {10.1137/1.9781611973730.69},
  volume       = {2015},
  year         = {2015},
}

@article{1106,
  abstract     = {Circumferential skin creases Kunze type (CSC-KT) is a specific congenital entity with an unknown genetic cause. The disease phenotype comprises characteristic circumferential skin creases accompanied by intellectual disability, a cleft palate, short stature, and dysmorphic features. Here, we report that mutations in either MAPRE2 or TUBB underlie the genetic origin of this syndrome. MAPRE2 encodes a member of the microtubule end-binding family of proteins that bind to the guanosine triphosphate cap at growing microtubule plus ends, and TUBB encodes a β-tubulin isotype that is expressed abundantly in the developing brain. Functional analyses of the TUBB mutants show multiple defects in the chaperone-dependent tubulin heterodimer folding and assembly pathway that leads to a compromised yield of native heterodimers. The TUBB mutations also have an impact on microtubule dynamics. For MAPRE2, we show that the mutations result in enhanced MAPRE2 binding to microtubules, implying an increased dwell time at microtubule plus ends. Further, in vivo analysis of MAPRE2 mutations in a zebrafish model of craniofacial development shows that the variants most likely perturb the patterning of branchial arches, either through excessive activity (under a recessive paradigm) or through haploinsufficiency (dominant de novo paradigm). Taken together, our data add CSC-KT to the growing list of tubulinopathies and highlight how multiple inheritance paradigms can affect dosage-sensitive biological systems so as to result in the same clinical defect.},
  author       = {Isrie, Mala and Breuss, Martin and Tian, Guoling and Hansen, Andi H and Cristofoli, Francesca and Morandell, Jasmin and Kupchinsky, Zachari A and Sifrim, Alejandro and Rodriguez Rodriguez, Celia and Dapena, Elena P and Doonanco, Kurston and Leonard, Norma and Tinsa, Faten and Moortgat, Stéphanie and Ulucan, Hakan and Koparir, Erkan and Karaca, Ender and Katsanis, Nicholas and Marton, Valeria and Vermeesch, Joris R and Davis, Erica E and Cowan, Nicholas J and Keays, David and Van Esch, Hilde},
  journal      = {The American Journal of Human Genetics},
  number       = {6},
  pages        = {790 -- 800},
  publisher    = {Cell Press},
  title        = {{Mutations in either TUBB or MAPRE2 cause circumferential skin creases Kunze type}},
  doi          = {10.1016/j.ajhg.2015.10.014},
  volume       = {97},
  year         = {2015},
}

@article{11073,
  abstract     = {Human cancer cells bear complex chromosome rearrangements that can be potential drivers of cancer development. However, the molecular mechanisms underlying these rearrangements have been unclear. Zhang et al. use a new technique combining live-cell imaging and single-cell sequencing to demonstrate that chromosomes mis-segregated to micronuclei frequently undergo chromothripsis-like rearrangements in the subsequent cell cycle.},
  author       = {Hatch, Emily M. and HETZER, Martin W},
  issn         = {0092-8674},
  journal      = {Cell},
  keywords     = {General Biochemistry, Genetics and Molecular Biology},
  number       = {7},
  pages        = {1502--1504},
  publisher    = {Elsevier},
  title        = {{Linking micronuclei to chromosome fragmentation}},
  doi          = {10.1016/j.cell.2015.06.005},
  volume       = {161},
  year         = {2015},
}

@article{11074,
  author       = {Hatch, Emily M. and HETZER, Martin W},
  issn         = {0960-9822},
  journal      = {Current Biology},
  keywords     = {General Agricultural and Biological Sciences, General Biochemistry, Genetics and Molecular Biology},
  number       = {10},
  pages        = {PR397--R399},
  publisher    = {Elsevier},
  title        = {{Chromothripsis}},
  doi          = {10.1016/j.cub.2015.02.033},
  volume       = {25},
  year         = {2015},
}

@article{11075,
  abstract     = {Previously, we identified the nucleoporin gp210/Nup210 as a critical regulator of muscle and neuronal differentiation, but how this nucleoporin exerts its function and whether it modulates nuclear pore complex (NPC) activity remain unknown. Here, we show that gp210/Nup210 mediates muscle cell differentiation in vitro via its conserved N-terminal domain that extends into the perinuclear space. Removal of the C-terminal domain, which partially mislocalizes gp210/Nup210 away from NPCs, efficiently rescues the differentiation defect caused by the knockdown of endogenous gp210/Nup210. Unexpectedly, a gp210/Nup210 mutant lacking the NPC-targeting transmembrane and C-terminal domains is sufficient for C2C12 myoblast differentiation. We demonstrate that the endoplasmic reticulum (ER) stress-specific caspase cascade is exacerbated during Nup210 depletion and that blocking ER stress-mediated apoptosis rescues differentiation of Nup210-deficient cells. Our results suggest that the role of gp210/Nup210 in cell differentiation is mediated by its large luminal domain, which can act independently of NPC association and appears to play a pivotal role in the maintenance of nuclear envelope/ER homeostasis.},
  author       = {Gomez-Cavazos, J. Sebastian and HETZER, Martin W},
  issn         = {1540-8140},
  journal      = {Journal of Cell Biology},
  keywords     = {Cell Biology},
  number       = {6},
  pages        = {671--681},
  publisher    = {Rockefeller University Press},
  title        = {{The nucleoporin gp210/Nup210 controls muscle differentiation by regulating nuclear envelope/ER homeostasis}},
  doi          = {10.1083/jcb.201410047},
  volume       = {208},
  year         = {2015},
}

@article{11076,
  abstract     = {Nuclear pore complexes (NPCs) are composed of several copies of ∼30 different proteins called nucleoporins (Nups). NPCs penetrate the nuclear envelope (NE) and regulate the nucleocytoplasmic trafficking of macromolecules. Beyond this vital role, NPC components influence genome functions in a transport-independent manner. Nups play an evolutionarily conserved role in gene expression regulation that, in metazoans, extends into the nuclear interior. Additionally, in proliferative cells, Nups play a crucial role in genome integrity maintenance and mitotic progression. Here we discuss genome-related functions of Nups and their impact on essential DNA metabolism processes such as transcription, chromosome duplication, and segregation.},
  author       = {Ibarra, Arkaitz and HETZER, Martin W},
  issn         = {1549-5477},
  journal      = {Genes & Development},
  keywords     = {Developmental Biology, Genetics},
  number       = {4},
  pages        = {337--349},
  publisher    = {Cold Spring Harbor Laboratory},
  title        = {{Nuclear pore proteins and the control of genome functions}},
  doi          = {10.1101/gad.256495.114},
  volume       = {29},
  year         = {2015},
}

@article{11077,
  abstract     = {Nucleoporins (Nups) are a family of proteins best known as the constituent building blocks of nuclear pore complexes (NPCs), membrane-embedded channels that mediate nuclear transport across the nuclear envelope. Recent evidence suggests that several Nups have additional roles in controlling the activation and silencing of developmental genes; however, the mechanistic details of these functions remain poorly understood. Here, we show that depletion of Nup153 in mouse embryonic stem cells (mESCs) causes the derepression of developmental genes and induction of early differentiation. This loss of stem cell identity is not associated with defects in the nuclear import of key pluripotency factors. Rather, Nup153 binds around the transcriptional start site (TSS) of developmental genes and mediates the recruitment of the polycomb-repressive complex 1 (PRC1) to a subset of its target loci. Our results demonstrate a chromatin-associated role of Nup153 in maintaining stem cell pluripotency by functioning in mammalian epigenetic gene silencing.},
  author       = {Jacinto, Filipe V. and Benner, Chris and HETZER, Martin W},
  issn         = {1549-5477},
  journal      = {Genes & Development},
  keywords     = {Developmental Biology, Genetics},
  number       = {12},
  pages        = {1224--1238},
  publisher    = {Cold Spring Harbor Laboratory},
  title        = {{The nucleoporin Nup153 regulates embryonic stem cell pluripotency through gene silencing}},
  doi          = {10.1101/gad.260919.115},
  volume       = {29},
  year         = {2015},
}

@article{11078,
  abstract     = {Aging is associated with the decline of protein, cell, and organ function. Here, we use an integrated approach to characterize gene expression, bulk translation, and cell biology in the brains and livers of young and old rats. We identify 468 differences in protein abundance between young and old animals. The majority are a consequence of altered translation output, that is, the combined effect of changes in transcript abundance and translation efficiency. In addition, we identify 130 proteins whose overall abundance remains unchanged but whose sub-cellular localization, phosphorylation state, or splice-form varies. While some protein-level differences appear to be a generic property of the rats’ chronological age, the majority are specific to one organ. These may be a consequence of the organ’s physiology or the chronological age of the cells within the tissue. Taken together, our study provides an initial view of the proteome at the molecular, sub-cellular, and organ level in young and old rats.},
  author       = {Ori, Alessandro and Toyama, Brandon H. and Harris, Michael S. and Bock, Thomas and Iskar, Murat and Bork, Peer and Ingolia, Nicholas T. and HETZER, Martin W and Beck, Martin},
  issn         = {2405-4712},
  journal      = {Cell Systems},
  keywords     = {Cell Biology, Histology, Pathology and Forensic Medicine},
  number       = {3},
  pages        = {P224--237},
  publisher    = {Elsevier},
  title        = {{Integrated transcriptome and proteome analyses reveal organ-specific proteome deterioration in old rats}},
  doi          = {10.1016/j.cels.2015.08.012},
  volume       = {1},
  year         = {2015},
}

@article{11079,
  abstract     = {Aging is a major risk factor for many human diseases, and in vitro generation of human neurons is an attractive approach for modeling aging-related brain disorders. However, modeling aging in differentiated human neurons has proved challenging. We generated neurons from human donors across a broad range of ages, either by iPSC-based reprogramming and differentiation or by direct conversion into induced neurons (iNs). While iPSCs and derived neurons did not retain aging-associated gene signatures, iNs displayed age-specific transcriptional profiles and revealed age-associated decreases in the nuclear transport receptor RanBP17. We detected an age-dependent loss of nucleocytoplasmic compartmentalization (NCC) in donor fibroblasts and corresponding iNs and found that reduced RanBP17 impaired NCC in young cells, while iPSC rejuvenation restored NCC in aged cells. These results show that iNs retain important aging-related signatures, thus allowing modeling of the aging process in vitro, and they identify impaired NCC as an important factor in human aging.},
  author       = {Mertens, Jerome and Paquola, Apuã C.M. and Ku, Manching and Hatch, Emily and Böhnke, Lena and Ladjevardi, Shauheen and McGrath, Sean and Campbell, Benjamin and Lee, Hyungjun and Herdy, Joseph R. and Gonçalves, J. Tiago and Toda, Tomohisa and Kim, Yongsung and Winkler, Jürgen and Yao, Jun and HETZER, Martin W and Gage, Fred H.},
  issn         = {1934-5909},
  journal      = {Cell Stem Cell},
  keywords     = {Cell Biology, Genetics, Molecular Medicine},
  number       = {6},
  pages        = {705--718},
  publisher    = {Elsevier},
  title        = {{Directly reprogrammed human neurons retain aging-associated transcriptomic signatures and reveal age-related nucleocytoplasmic defects}},
  doi          = {10.1016/j.stem.2015.09.001},
  volume       = {17},
  year         = {2015},
}

@article{2085,
  abstract     = {We study the spectrum of a large system of N identical bosons interacting via a two-body potential with strength 1/N. In this mean-field regime, Bogoliubov's theory predicts that the spectrum of the N-particle Hamiltonian can be approximated by that of an effective quadratic Hamiltonian acting on Fock space, which describes the fluctuations around a condensed state. Recently, Bogoliubov's theory has been justified rigorously in the case that the low-energy eigenvectors of the N-particle Hamiltonian display complete condensation in the unique minimizer of the corresponding Hartree functional. In this paper, we shall justify Bogoliubov's theory for the high-energy part of the spectrum of the N-particle Hamiltonian corresponding to (non-linear) excited states of the Hartree functional. Moreover, we shall extend the existing results on the excitation spectrum to the case of non-uniqueness and/or degeneracy of the Hartree minimizer. In particular, the latter covers the case of rotating Bose gases, when the rotation speed is large enough to break the symmetry and to produce multiple quantized vortices in the Hartree minimizer. },
  author       = {Nam, Phan and Seiringer, Robert},
  journal      = {Archive for Rational Mechanics and Analysis},
  number       = {2},
  pages        = {381 -- 417},
  publisher    = {Springer},
  title        = {{Collective excitations of Bose gases in the mean-field regime}},
  doi          = {10.1007/s00205-014-0781-6},
  volume       = {215},
  year         = {2015},
}

@article{21103,
  abstract     = {The structure of the decadeoxyribonucleotide d(GCATGCATGC) is presented at a resolution of 1.8 Å. The decamer adopts a novel double-folded structure in which the direction of progression of the backbone changes at the two thymine residues. Intra-strand stacking interactions (including an interaction between the endocylic O atom of a ribose moiety and the adjacent purine base), hydrogen bonds and cobalt-ion interactions stabilize the double-folded structure of the single strand. Two such double-folded strands come together in the crystal to form a dimer. Inter-strand Watson–Crick hydrogen bonds form four base pairs. This portion of the decamer structure is similar to that observed in other previously reported oligonucleotide structures and has been dubbed a `bi-loop'. Both the double-folded single-strand structure, as well as the dimeric bi-loop structure, serve as starting points to construct models for triplet-repeat DNA sequences, which have been implicated in many human diseases.},
  author       = {Thirugnanasambandam, Arunachalam and Karthik, Selvam and Mandal, Pradeep K and Gautham, Namasivayam},
  issn         = {1399-0047},
  journal      = {Acta Crystallographica Section D Structural Biology},
  number       = {10},
  pages        = {2119--2126},
  publisher    = {International Union of Crystallography},
  title        = {{The novel double-folded structure of d(GCATGCATGC): A possible model for triplet-repeat sequences}},
  doi          = {10.1107/s1399004715013930},
  volume       = {71},
  year         = {2015},
}

@article{2166,
  abstract     = {We consider the spectral statistics of large random band matrices on mesoscopic energy scales. We show that the correlation function of the local eigenvalue density exhibits a universal power law behaviour that differs from the Wigner-Dyson- Mehta statistics. This law had been predicted in the physics literature by Altshuler and Shklovskii in (Zh Eksp Teor Fiz (Sov Phys JETP) 91(64):220(127), 1986); it describes the correlations of the eigenvalue density in general metallic sampleswith weak disorder. Our result rigorously establishes the Altshuler-Shklovskii formulas for band matrices. In two dimensions, where the leading term vanishes owing to an algebraic cancellation, we identify the first non-vanishing term and show that it differs substantially from the prediction of Kravtsov and Lerner in (Phys Rev Lett 74:2563-2566, 1995). The proof is given in the current paper and its companion (Ann. H. Poincaré. arXiv:1309.5107, 2014). },
  author       = {Erdös, László and Knowles, Antti},
  journal      = {Communications in Mathematical Physics},
  number       = {3},
  pages        = {1365 -- 1416},
  publisher    = {Springer},
  title        = {{The Altshuler-Shklovskii formulas for random band matrices I: the unimodular case}},
  doi          = {10.1007/s00220-014-2119-5},
  volume       = {333},
  year         = {2015},
}

@article{2271,
  abstract     = {A class of valued constraint satisfaction problems (VCSPs) is characterised by a valued constraint language, a fixed set of cost functions on a finite domain. Finite-valued constraint languages contain functions that take on rational costs and general-valued constraint languages contain functions that take on rational or infinite costs. An instance of the problem is specified by a sum of functions from the language with the goal to minimise the sum. This framework includes and generalises well-studied constraint satisfaction problems (CSPs) and maximum constraint satisfaction problems (Max-CSPs).
Our main result is a precise algebraic characterisation of valued constraint languages whose instances can be solved exactly by the basic linear programming relaxation (BLP). For a general-valued constraint language Γ, BLP is a decision procedure for Γ if and only if Γ admits a symmetric fractional polymorphism of every arity. For a finite-valued constraint language Γ, BLP is a decision procedure if and only if Γ admits a symmetric fractional polymorphism of some arity, or equivalently, if Γ admits a symmetric fractional polymorphism of arity 2.
Using these results, we obtain tractability of several novel and previously widely-open classes of VCSPs, including problems over valued constraint languages that are: (1) submodular on arbitrary lattices; (2) bisubmodular (also known as k-submodular) on arbitrary finite domains; (3) weakly (and hence strongly) tree-submodular on arbitrary trees. },
  author       = {Kolmogorov, Vladimir and Thapper, Johan and Živný, Stanislav},
  journal      = {SIAM Journal on Computing},
  number       = {1},
  pages        = {1 -- 36},
  publisher    = {SIAM},
  title        = {{The power of linear programming for general-valued CSPs}},
  doi          = {10.1137/130945648},
  volume       = {44},
  year         = {2015},
}

@article{257,
  abstract     = {For suitable pairs of diagonal quadratic forms in eight variables we use the circle method to investigate the density of simultaneous integer solutions and relate this to the problem of estimating linear correlations among sums of two squares.},
  author       = {Timothy Browning and Munshi, Ritabrata},
  journal      = {Forum Mathematicum},
  number       = {4},
  pages        = {2025 -- 2050},
  publisher    = {Walter de Gruyter GmbH},
  title        = {{Pairs of diagonal quadratic forms and linear correlations among sums of two squares}},
  doi          = {10.1515/forum-2013-6024},
  volume       = {27},
  year         = {2015},
}

@inbook{258,
  abstract     = {Given a number field k and a projective algebraic variety X defined over k, the question of whether X contains a k-rational point is both very natural and very difficult. In the event that the set X(k) of k-rational points is not empty, one can also ask how the points of X(k) are distributed. Are they dense in X under the Zariski topology? Are they dense in the set.},
  author       = {Browning, Timothy D},
  booktitle    = {Arithmetic and Geometry},
  pages        = {89 -- 113},
  publisher    = {Cambridge University Press},
  title        = {{A survey of applications of the circle method to rational points}},
  doi          = {10.1017/CBO9781316106877.009},
  year         = {2015},
}

@article{259,
  abstract     = {The Hasse principle and weak approximation is established for non-singular cubic hypersurfaces X over the function field   },
  author       = {Timothy Browning and Vishe, Pankaj},
  journal      = {Geometric and Functional Analysis},
  number       = {3},
  pages        = {671 -- 732},
  publisher    = {Birkhäuser},
  title        = {{Rational points on cubic hypersurfaces over F_q(t) }},
  doi          = {10.1007/s00039-015-0328-5},
  volume       = {25},
  year         = {2015},
}

@article{1546,
  abstract     = {Synaptic efficacy and precision are influenced by the coupling of voltage-gated Ca2+ channels (VGCCs) to vesicles. But because the topography of VGCCs and their proximity to vesicles is unknown, a quantitative understanding of the determinants of vesicular release at nanometer scale is lacking. To investigate this, we combined freeze-fracture replica immunogold labeling of Cav2.1 channels, local [Ca2+] imaging, and patch pipette perfusion of EGTA at the calyx of Held. Between postnatal day 7 and 21, VGCCs formed variable sized clusters and vesicular release became less sensitive to EGTA, whereas fixed Ca2+ buffer properties remained constant. Experimentally constrained reaction-diffusion simulations suggest that Ca2+ sensors for vesicular release are located at the perimeter of VGCC clusters (&lt;30nm) and predict that VGCC number per cluster determines vesicular release probability without altering release time course. This &quot;perimeter release model&quot; provides a unifying framework accounting for developmental changes in both synaptic efficacy and time course.},
  author       = {Nakamura, Yukihiro and Harada, Harumi and Kamasawa, Naomi and Matsui, Ko and Rothman, Jason and Shigemoto, Ryuichi and Silver, R Angus and Digregorio, David and Takahashi, Tomoyuki},
  issn         = {1097-4199},
  journal      = {Neuron},
  number       = {1},
  pages        = {145 -- 158},
  publisher    = {Elsevier},
  title        = {{Nanoscale distribution of presynaptic Ca2+ channels and its impact on vesicular release during development}},
  doi          = {10.1016/j.neuron.2014.11.019},
  volume       = {85},
  year         = {2015},
}

@article{1547,
  abstract     = {Let G be a graph on the vertex set V(G) = {x1,…,xn} with the edge set E(G), and let R = K[x1,…, xn] be the polynomial ring over a field K. Two monomial ideals are associated to G, the edge ideal I(G) generated by all monomials xixj with {xi,xj} ∈ E(G), and the vertex cover ideal IG generated by monomials ∏xi∈Cxi for all minimal vertex covers C of G. A minimal vertex cover of G is a subset C ⊂ V(G) such that each edge has at least one vertex in C and no proper subset of C has the same property. Indeed, the vertex cover ideal of G is the Alexander dual of the edge ideal of G. In this paper, for an unmixed bipartite graph G we consider the lattice of vertex covers LG and we explicitly describe the minimal free resolution of the ideal associated to LG which is exactly the vertex cover ideal of G. Then we compute depth, projective dimension, regularity and extremal Betti numbers of R/I(G) in terms of the associated lattice.},
  author       = {Mohammadi, Fatemeh and Moradi, Somayeh},
  issn         = {2234-3016},
  journal      = {Bulletin of the Korean Mathematical Society},
  number       = {3},
  pages        = {977 -- 986},
  publisher    = {Korean Mathematical Society},
  title        = {{Resolution of unmixed bipartite graphs}},
  doi          = {10.4134/BKMS.2015.52.3.977},
  volume       = {52},
  year         = {2015},
}

