TY - JOUR
AB - We classify smooth Brunnian (i.e., unknotted on both components) embeddings (S2 × S1) ⊔ S3 → ℝ6. Any Brunnian embedding (S2 × S1) ⊔ S3 → ℝ6 is isotopic to an explicitly constructed embedding fk,m,n for some integers k, m, n such that m ≡ n (mod 2). Two embeddings fk,m,n and fk′ ,m′,n′ are isotopic if and only if k = k′, m ≡ m′ (mod 2k) and n ≡ n′ (mod 2k). We use Haefliger’s classification of embeddings S3 ⊔ S3 → ℝ6 in our proof. The relation between the embeddings (S2 × S1) ⊔ S3 → ℝ6 and S3 ⊔ S3 → ℝ6 is not trivial, however. For example, we show that there exist embeddings f: (S2 ×S1) ⊔ S3 → ℝ6 and g, g′ : S3 ⊔ S3 → ℝ6 such that the componentwise embedded connected sum f # g is isotopic to f # g′ but g is not isotopic to g′.
AU - Avvakumov, Serhii
ID - 1522
IS - 1
JF - Moscow Mathematical Journal
TI - The classification of certain linked 3-manifolds in 6-space
VL - 16
ER -
TY - JOUR
AB - For random graphs, the containment problem considers the probability that a binomial random graph G(n, p) contains a given graph as a substructure. When asking for the graph as a topological minor, i.e., for a copy of a subdivision of the given graph, it is well known that the (sharp) threshold is at p = 1/n. We consider a natural analogue of this question for higher-dimensional random complexes Xk(n, p), first studied by Cohen, Costa, Farber and Kappeler for k = 2. Improving previous results, we show that p = Θ(1/ √n) is the (coarse) threshold for containing a subdivision of any fixed complete 2-complex. For higher dimensions k > 2, we get that p = O(n−1/k) is an upper bound for the threshold probability of containing a subdivision of a fixed k-dimensional complex.
AU - Gundert, Anna
AU - Wagner, Uli
ID - 1523
IS - 4
JF - Proceedings of the American Mathematical Society
TI - On topological minors in random simplicial complexes
VL - 144
ER -
TY - CONF
AB - When designing genetic circuits, the typical primitives used in major existing modelling formalisms are gene interaction graphs, where edges between genes denote either an activation or inhibition relation. However, when designing experiments, it is important to be precise about the low-level mechanistic details as to how each such relation is implemented. The rule-based modelling language Kappa allows to unambiguously specify mechanistic details such as DNA binding sites, dimerisation of transcription factors, or co-operative interactions. Such a detailed description comes with complexity and computationally costly executions. We propose a general method for automatically transforming a rule-based program, by eliminating intermediate species and adjusting the rate constants accordingly. To the best of our knowledge, we show the first automated reduction of rule-based models based on equilibrium approximations.
Our algorithm is an adaptation of an existing algorithm, which was designed for reducing reaction-based programs; our version of the algorithm scans the rule-based Kappa model in search for those interaction patterns known to be amenable to equilibrium approximations (e.g. Michaelis-Menten scheme). Additional checks are then performed in order to verify if the reduction is meaningful in the context of the full model. The reduced model is efficiently obtained by static inspection over the rule-set. The tool is tested on a detailed rule-based model of a λ-phage switch, which lists 92 rules and 13 agents. The reduced model has 11 rules and 5 agents, and provides a dramatic reduction in simulation time of several orders of magnitude.
AU - Beica, Andreea
AU - Guet, Calin C
AU - Petrov, Tatjana
ID - 1524
TI - Efficient reduction of kappa models by static inspection of the rule-set
VL - 9271
ER -
TY - CONF
AB - We present the first study of robustness of systems that are both timed as well as reactive (I/O). We study the behavior of such timed I/O systems in the presence of uncertain inputs and formalize their robustness using the analytic notion of Lipschitz continuity: a timed I/O system is K-(Lipschitz) robust if the perturbation in its output is at most K times the perturbation in its input. We quantify input and output perturbation using similarity functions over timed words such as the timed version of the Manhattan distance and the Skorokhod distance. We consider two models of timed I/O systems — timed transducers and asynchronous sequential circuits. We show that K-robustness of timed transducers can be decided in polynomial space under certain conditions. For asynchronous sequential circuits, we reduce K-robustness w.r.t. timed Manhattan distances to K-robustness of discrete letter-to-letter transducers and show PSpace-completeness of the problem.
AU - Henzinger, Thomas A
AU - Otop, Jan
AU - Samanta, Roopsha
ID - 1526
TI - Lipschitz robustness of timed I/O systems
VL - 9583
ER -
TY - JOUR
AB - We consider partially observable Markov decision processes (POMDPs) with a set of target states and an integer cost associated with every transition. The optimization objective we study asks to minimize the expected total cost of reaching a state in the target set, while ensuring that the target set is reached almost surely (with probability 1). We show that for integer costs approximating the optimal cost is undecidable. For positive costs, our results are as follows: (i) we establish matching lower and upper bounds for the optimal cost, both double exponential in the POMDP state space size; (ii) we show that the problem of approximating the optimal cost is decidable and present approximation algorithms developing on the existing algorithms for POMDPs with finite-horizon objectives. While the worst-case running time of our algorithm is double exponential, we also present efficient stopping criteria for the algorithm and show experimentally that it performs well in many examples of interest.
AU - Chatterjee, Krishnendu
AU - Chmelik, Martin
AU - Gupta, Raghav
AU - Kanodia, Ayush
ID - 1529
JF - Artificial Intelligence
TI - Optimal cost almost-sure reachability in POMDPs
VL - 234
ER -
TY - JOUR
AB - We provide general conditions for which bosonic quadratic Hamiltonians on Fock spaces can be diagonalized by Bogoliubov transformations. Our results cover the case when quantum systems have infinite degrees of freedom and the associated one-body kinetic and paring operators are unbounded. Our sufficient conditions are optimal in the sense that they become necessary when the relevant one-body operators commute.
AU - Nam, Phan
AU - Napiórkowski, Marcin M
AU - Solovej, Jan
ID - 1545
IS - 11
JF - Journal of Functional Analysis
TI - Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations
VL - 270
ER -
TY - JOUR
AB - Antibiotic resistance carries a fitness cost that must be overcome in order for resistance to persist over the long term. Compensatory mutations that recover the functional defects associated with resistance mutations have been argued to play a key role in overcoming the cost of resistance, but compensatory mutations are expected to be rare relative to generally beneficial mutations that increase fitness, irrespective of antibiotic resistance. Given this asymmetry, population genetics theory predicts that populations should adapt by compensatory mutations when the cost of resistance is large, whereas generally beneficial mutations should drive adaptation when the cost of resistance is small. We tested this prediction by determining the genomic mechanisms underpinning adaptation to antibiotic-free conditions in populations of the pathogenic bacterium Pseudomonas aeruginosa that carry costly antibiotic resistance mutations. Whole-genome sequencing revealed that populations founded by high-cost rifampicin-resistant mutants adapted via compensatory mutations in three genes of the RNA polymerase core enzyme, whereas populations founded by low-cost mutants adapted by generally beneficial mutations, predominantly in the quorum-sensing transcriptional regulator gene lasR. Even though the importance of compensatory evolution in maintaining resistance has been widely recognized, our study shows that the roles of general adaptation in maintaining resistance should not be underestimated and highlights the need to understand how selection at other sites in the genome influences the dynamics of resistance alleles in clinical settings.
AU - Qi, Qin
AU - Toll Riera, Macarena
AU - Heilbron, Karl
AU - Preston, Gail
AU - Maclean, R Craig
ID - 1552
IS - 1822
JF - Proceedings of the Royal Society of London Series B Biological Sciences
TI - The genomic basis of adaptation to the fitness cost of rifampicin resistance in Pseudomonas aeruginosa
VL - 283
ER -
TY - JOUR
AB - The addition of polysialic acid to N- and/or O-linked glycans, referred to as polysialylation, is a rare posttranslational modification that is mainly known to control the developmental plasticity of the nervous system. Here we show that CCR7, the central chemokine receptor controlling immune cell trafficking to secondary lymphatic organs, carries polysialic acid. This modification is essential for the recognition of the CCR7 ligand CCL21. As a consequence, dendritic cell trafficking is abrogated in polysialyltransferase-deficient mice, manifesting as disturbed lymph node homeostasis and unresponsiveness to inflammatory stimuli. Structure-function analysis of chemokine-receptor interactions reveals that CCL21 adopts an autoinhibited conformation, which is released upon interaction with polysialic acid. Thus, we describe a glycosylation-mediated immune cell trafficking disorder and its mechanistic basis.
AU - Kiermaier, Eva
AU - Moussion, Christine
AU - Veldkamp, Christopher
AU - Gerardy Schahn, Rita
AU - De Vries, Ingrid
AU - Williams, Larry
AU - Chaffee, Gary
AU - Phillips, Andrew
AU - Freiberger, Friedrich
AU - Imre, Richard
AU - Taleski, Deni
AU - Payne, Richard
AU - Braun, Asolina
AU - Förster, Reinhold
AU - Mechtler, Karl
AU - Mühlenhoff, Martina
AU - Volkman, Brian
AU - Sixt, Michael K
ID - 1599
IS - 6269
JF - Science
TI - Polysialylation controls dendritic cell trafficking by regulating chemokine recognition
VL - 351
ER -
TY - JOUR
AB - We show that the Anderson model has a transition from localization to delocalization at exactly 2 dimensional growth rate on antitrees with normalized edge weights which are certain discrete graphs. The kinetic part has a one-dimensional structure allowing a description through transfer matrices which involve some Schur complement. For such operators we introduce the notion of having one propagating channel and extend theorems from the theory of one-dimensional Jacobi operators that relate the behavior of transfer matrices with the spectrum. These theorems are then applied to the considered model. In essence, in a certain energy region the kinetic part averages the random potentials along shells and the transfer matrices behave similar as for a one-dimensional operator with random potential of decaying variance. At d dimensional growth for d>2 this effective decay is strong enough to obtain absolutely continuous spectrum, whereas for some uniform d dimensional growth with d<2 one has pure point spectrum in this energy region. At exactly uniform 2 dimensional growth also some singular continuous spectrum appears, at least at small disorder. As a corollary we also obtain a change from singular spectrum (d≤2) to absolutely continuous spectrum (d≥3) for random operators of the type rΔdr+λ on ℤd, where r is an orthogonal radial projection, Δd the discrete adjacency operator (Laplacian) on ℤd and λ a random potential.
AU - Sadel, Christian
ID - 1608
IS - 7
JF - Annales Henri Poincare
TI - Anderson transition at 2 dimensional growth rate on antitrees and spectral theory for operators with one propagating channel
VL - 17
ER -
TY - JOUR
AB - We prove that whenever A is a 3-conservative relational structure with only binary and unary relations,then the algebra of polymorphisms of A either has no Taylor operation (i.e.,CSP(A)is NP-complete),or it generates an SD(∧) variety (i.e.,CSP(A)has bounded width).
AU - Kazda, Alexandr
ID - 1612
IS - 1
JF - Algebra Universalis
TI - CSP for binary conservative relational structures
VL - 75
ER -