@article{1681,
  abstract     = {In many social situations, individuals endeavor to find the single best possible partner, but are constrained to evaluate the candidates in sequence. Examples include the search for mates, economic partnerships, or any other long-term ties where the choice to interact involves two parties. Surprisingly, however, previous theoretical work on mutual choice problems focuses on finding equilibrium solutions, while ignoring the evolutionary dynamics of decisions. Empirically, this may be of high importance, as some equilibrium solutions can never be reached unless the population undergoes radical changes and a sufficient number of individuals change their decisions simultaneously. To address this question, we apply a mutual choice sequential search problem in an evolutionary game-theoretical model that allows one to find solutions that are favored by evolution. As an example, we study the influence of sequential search on the evolutionary dynamics of cooperation. For this, we focus on the classic snowdrift game and the prisoner’s dilemma game.},
  author       = {Priklopil, Tadeas and Chatterjee, Krishnendu},
  issn         = {2073-4336},
  journal      = {Games},
  number       = {4},
  pages        = {413 -- 437},
  publisher    = {MDPI},
  title        = {{Evolution of decisions in population games with sequentially searching individuals}},
  doi          = {10.3390/g6040413},
  volume       = {6},
  year         = {2015},
}

@article{1682,
  abstract     = {We study the problem of robust satisfiability of systems of nonlinear equations, namely, whether for a given continuous function f:K→ ℝn on a finite simplicial complex K and α > 0, it holds that each function g: K → ℝn such that ||g - f || ∞ < α, has a root in K. Via a reduction to the extension problem of maps into a sphere, we particularly show that this problem is decidable in polynomial time for every fixed n, assuming dimK ≤ 2n - 3. This is a substantial extension of previous computational applications of topological degree and related concepts in numerical and interval analysis. Via a reverse reduction, we prove that the problem is undecidable when dim K > 2n - 2, where the threshold comes from the stable range in homotopy theory. For the lucidity of our exposition, we focus on the setting when f is simplexwise linear. Such functions can approximate general continuous functions, and thus we get approximation schemes and undecidability of the robust satisfiability in other possible settings.},
  author       = {Franek, Peter and Krcál, Marek},
  journal      = {Journal of the ACM},
  number       = {4},
  publisher    = {ACM},
  title        = {{Robust satisfiability of systems of equations}},
  doi          = {10.1145/2751524},
  volume       = {62},
  year         = {2015},
}

@article{1684,
  abstract     = {Many species groups, including mammals and many insects, determine sex using heteromorphic sex chromosomes. Diptera flies, which include the model Drosophila melanogaster, generally have XY sex chromosomes and a conserved karyotype consisting of six chromosomal arms (five large rods and a small dot), but superficially similar karyotypes may conceal the true extent of sex chromosome variation. Here, we use whole-genome analysis in 37 fly species belonging to 22 different families of Diptera and uncover tremendous hidden diversity in sex chromosome karyotypes among flies. We identify over a dozen different sex chromosome configurations, and the small dot chromosome is repeatedly used as the sex chromosome, which presumably reflects the ancestral karyotype of higher Diptera. However, we identify species with undifferentiated sex chromosomes, others in which a different chromosome replaced the dot as a sex chromosome or in which up to three chromosomal elements became incorporated into the sex chromosomes, and others yet with female heterogamety (ZW sex chromosomes). Transcriptome analysis shows that dosage compensation has evolved multiple times in flies, consistently through up-regulation of the single X in males. However, X chromosomes generally show a deficiency of genes with male-biased expression, possibly reflecting sex-specific selective pressures. These species thus provide a rich resource to study sex chromosome biology in a comparative manner and show that similar selective forces have shaped the unique evolution of sex chromosomes in diverse fly taxa.},
  author       = {Vicoso, Beatriz and Bachtrog, Doris},
  journal      = {PLoS Biology},
  number       = {4},
  publisher    = {Public Library of Science},
  title        = {{Numerous transitions of sex chromosomes in Diptera}},
  doi          = {10.1371/journal.pbio.1002078},
  volume       = {13},
  year         = {2015},
}

@inproceedings{1685,
  abstract     = {Given a graph G cellularly embedded on a surface Σ of genus g, a cut graph is a subgraph of G such that cutting Σ along G yields a topological disk. We provide a fixed parameter tractable approximation scheme for the problem of computing the shortest cut graph, that is, for any ε > 0, we show how to compute a (1 + ε) approximation of the shortest cut graph in time f(ε, g)n3.
Our techniques first rely on the computation of a spanner for the problem using the technique of brick decompositions, to reduce the problem to the case of bounded tree-width. Then, to solve the bounded tree-width case, we introduce a variant of the surface-cut decomposition of Rué, Sau and Thilikos, which may be of independent interest.},
  author       = {Cohen Addad, Vincent and De Mesmay, Arnaud N},
  location     = {Patras, Greece},
  pages        = {386 -- 398},
  publisher    = {Springer},
  title        = {{A fixed parameter tractable approximation scheme for the optimal cut graph of a surface}},
  doi          = {10.1007/978-3-662-48350-3_33},
  volume       = {9294},
  year         = {2015},
}

@article{1687,
  abstract     = {Guided cell movement is essential for development and integrity of animals and crucially involved in cellular immune responses. Leukocytes are professional migratory cells that can navigate through most types of tissues and sense a wide range of directional cues. The responses of these cells to attractants have been mainly explored in tissue culture settings. How leukocytes make directional decisions in situ, within the challenging environment of a tissue maze, is less understood. Here we review recent advances in how leukocytes sense chemical cues in complex tissue settings and make links with paradigms of directed migration in development and Dictyostelium discoideum amoebae.},
  author       = {Sarris, Milka and Sixt, Michael K},
  journal      = {Current Opinion in Cell Biology},
  number       = {10},
  pages        = {93 -- 102},
  publisher    = {Elsevier},
  title        = {{Navigating in tissue mazes: Chemoattractant interpretation in complex environments}},
  doi          = {10.1016/j.ceb.2015.08.001},
  volume       = {36},
  year         = {2015},
}

@article{1688,
  abstract     = {We estimate the selection constant in the following geometric selection theorem by Pach: For every positive integer d, there is a constant (Formula presented.) such that whenever (Formula presented.) are n-element subsets of (Formula presented.), we can find a point (Formula presented.) and subsets (Formula presented.) for every i∈[d+1], each of size at least cdn, such that p belongs to all rainbowd-simplices determined by (Formula presented.) simplices with one vertex in each Yi. We show a super-exponentially decreasing upper bound (Formula presented.). The ideas used in the proof of the upper bound also help us to prove Pach’s theorem with (Formula presented.), which is a lower bound doubly exponentially decreasing in d (up to some polynomial in the exponent). For comparison, Pach’s original approach yields a triply exponentially decreasing lower bound. On the other hand, Fox, Pach, and Suk recently obtained a hypergraph density result implying a proof of Pach’s theorem with (Formula presented.). In our construction for the upper bound, we use the fact that the minimum solid angle of every d-simplex is super-exponentially small. This fact was previously unknown and might be of independent interest. For the lower bound, we improve the ‘separation’ part of the argument by showing that in one of the key steps only d+1 separations are necessary, compared to 2d separations in the original proof. We also provide a measure version of Pach’s theorem.},
  author       = {Karasev, Roman and Kynčl, Jan and Paták, Pavel and Patakova, Zuzana and Tancer, Martin},
  journal      = {Discrete & Computational Geometry},
  number       = {3},
  pages        = {610 -- 636},
  publisher    = {Springer},
  title        = {{Bounds for Pach's selection theorem and for the minimum solid angle in a simplex}},
  doi          = {10.1007/s00454-015-9720-z},
  volume       = {54},
  year         = {2015},
}

@inproceedings{1689,
  abstract     = {We consider the problem of computing the set of initial states of a dynamical system such that there exists a control strategy to ensure that the trajectories satisfy a temporal logic specification with probability 1 (almost-surely). We focus on discrete-time, stochastic linear dynamics and specifications given as formulas of the Generalized Reactivity(1) fragment of Linear Temporal Logic over linear predicates in the states of the system. We propose a solution based on iterative abstraction-refinement, and turn-based 2-player probabilistic games. While the theoretical guarantee of our algorithm after any finite number of iterations is only a partial solution, we show that if our algorithm terminates, then the result is the set of satisfying initial states. Moreover, for any (partial) solution our algorithm synthesizes witness control strategies to ensure almost-sure satisfaction of the temporal logic specification. We demonstrate our approach on an illustrative case study.},
  author       = {Svoreňová, Mária and Kretinsky, Jan and Chmelik, Martin and Chatterjee, Krishnendu and Cěrná, Ivana and Belta, Cǎlin},
  booktitle    = {Proceedings of the 18th International Conference on Hybrid Systems: Computation and Control},
  location     = {Seattle, WA, United States},
  pages        = {259 -- 268},
  publisher    = {ACM},
  title        = {{Temporal logic control for stochastic linear systems using abstraction refinement of probabilistic games}},
  doi          = {10.1145/2728606.2728608},
  year         = {2015},
}

@article{1693,
  abstract     = {Quantum interference between energetically close states is theoretically investigated, with the state structure being observed via laser spectroscopy. In this work, we focus on hyperfine states of selected hydrogenic muonic isotopes, and on how quantum interference affects the measured Lamb shift. The process of photon excitation and subsequent photon decay is implemented within the framework of nonrelativistic second-order perturbation theory. Due to its experimental interest, calculations are performed for muonic hydrogen, deuterium, and helium-3. We restrict our analysis to the case of photon scattering by incident linear polarized photons and the polarization of the scattered photons not being observed. We conclude that while quantum interference effects can be safely neglected in muonic hydrogen and helium-3, in the case of muonic deuterium there are resonances with close proximity, where quantum interference effects can induce shifts up to a few percent of the linewidth, assuming a pointlike detector. However, by taking into account the geometry of the setup used by the CREMA collaboration, this effect is reduced to less than 0.2% of the linewidth in all possible cases, which makes it irrelevant at the present level of accuracy. © 2015 American Physical Society.},
  author       = {Amaro, Pedro and Franke, Beatrice and Krauth, Julian and Diepold, Marc and Fratini, Filippo and Safari, Laleh and Machado, Jorge and Antognini, Aldo and Kottmann, Franz and Indelicato, Paul and Pohl, Randolf and Santos, José},
  journal      = {Physical Review A},
  number       = {2},
  publisher    = {American Physical Society},
  title        = {{Quantum interference effects in laser spectroscopy of muonic hydrogen, deuterium, and helium-3}},
  doi          = {10.1103/PhysRevA.92.022514},
  volume       = {92},
  year         = {2015},
}

@article{1695,
  abstract     = {We give a comprehensive introduction into a diagrammatic method that allows for the evaluation of Gutzwiller wave functions in finite spatial dimensions. We discuss in detail some numerical schemes that turned out to be useful in the real-space evaluation of the diagrams. The method is applied to the problem of d-wave superconductivity in a two-dimensional single-band Hubbard model. Here, we discuss in particular the role of long-range contributions in our diagrammatic expansion. We further reconsider our previous analysis on the kinetic energy gain in the superconducting state.},
  author       = {Kaczmarczyk, Jan and Schickling, Tobias and Bünemann, Jörg},
  journal      = {Physica Status Solidi (B): Basic Solid State Physics},
  number       = {9},
  pages        = {2059 -- 2071},
  publisher    = {Wiley},
  title        = {{Evaluation techniques for Gutzwiller wave functions in finite dimensions}},
  doi          = {10.1002/pssb.201552082},
  volume       = {252},
  year         = {2015},
}

@article{1696,
  abstract     = {The recently proposed diagrammatic expansion (DE) technique for the full Gutzwiller wave function (GWF) is applied to the Anderson lattice model. This approach allows for a systematic evaluation of the expectation values with full Gutzwiller wave function in finite-dimensional systems. It introduces results extending in an essential manner those obtained by means of the standard Gutzwiller approximation (GA), which is variationally exact only in infinite dimensions. Within the DE-GWF approach we discuss the principal paramagnetic properties and their relevance to heavy-fermion systems. We demonstrate the formation of an effective, narrow f band originating from atomic f-electron states and subsequently interpret this behavior as a direct itineracy of f electrons; it represents a combined effect of both the hybridization and the correlations induced by the Coulomb repulsive interaction. Such a feature is absent on the level of GA, which is equivalent to the zeroth order of our expansion. Formation of the hybridization- and electron-concentration-dependent narrow f band rationalizes the common assumption of such dispersion of f levels in the phenomenological modeling of the band structure of CeCoIn5. Moreover, it is shown that the emerging f-electron direct itineracy leads in a natural manner to three physically distinct regimes within a single model that are frequently discussed for 4f- or 5f-electron compounds as separate model situations. We identify these regimes as (i) the mixed-valence regime, (ii) Kondo/almost-Kondo insulating regime, and (iii) the Kondo-lattice limit when the f-electron occupancy is very close to the f-state half filling, ⟨nˆf⟩→1. The nonstandard features of the emerging correlated quantum liquid state are stressed.},
  author       = {Wysokiński, Marcin and Kaczmarczyk, Jan and Spałek, Jozef},
  journal      = {Physical Review B},
  number       = {12},
  publisher    = {American Physical Society},
  title        = {{Gutzwiller wave function solution for Anderson lattice model: Emerging universal regimes of heavy quasiparticle states}},
  doi          = {10.1103/PhysRevB.92.125135},
  volume       = {92},
  year         = {2015},
}

@article{1697,
  abstract     = {Motion tracking is a challenge the visual system has to solve by reading out the retinal population. It is still unclear how the information from different neurons can be combined together to estimate the position of an object. Here we recorded a large population of ganglion cells in a dense patch of salamander and guinea pig retinas while displaying a bar moving diffusively. We show that the bar’s position can be reconstructed from retinal activity with a precision in the hyperacuity regime using a linear decoder acting on 100+ cells. We then took advantage of this unprecedented precision to explore the spatial structure of the retina’s population code. The classical view would have suggested that the firing rates of the cells form a moving hill of activity tracking the bar’s position. Instead, we found that most ganglion cells in the salamander fired sparsely and idiosyncratically, so that their neural image did not track the bar. Furthermore, ganglion cell activity spanned an area much larger than predicted by their receptive fields, with cells coding for motion far in their surround. As a result, population redundancy was high, and we could find multiple, disjoint subsets of neurons that encoded the trajectory with high precision. This organization allows for diverse collections of ganglion cells to represent high-accuracy motion information in a form easily read out by downstream neural circuits.},
  author       = {Marre, Olivier and Botella Soler, Vicente and Simmons, Kristina and Mora, Thierry and Tkacik, Gasper and Berry, Michael},
  journal      = {PLoS Computational Biology},
  number       = {7},
  publisher    = {Public Library of Science},
  title        = {{High accuracy decoding of dynamical motion from a large retinal population}},
  doi          = {10.1371/journal.pcbi.1004304},
  volume       = {11},
  year         = {2015},
}

@article{1698,
  abstract     = {In mean-payoff games, the objective of the protagonist is to ensure that the limit average of an infinite sequence of numeric weights is nonnegative. In energy games, the objective is to ensure that the running sum of weights is always nonnegative. Multi-mean-payoff and multi-energy games replace individual weights by tuples, and the limit average (resp., running sum) of each coordinate must be (resp., remain) nonnegative. We prove finite-memory determinacy of multi-energy games and show inter-reducibility of multi-mean-payoff and multi-energy games for finite-memory strategies. We improve the computational complexity for solving both classes with finite-memory strategies: we prove coNP-completeness improving the previous known EXPSPACE bound. For memoryless strategies, we show that deciding the existence of a winning strategy for the protagonist is NP-complete. We present the first solution of multi-mean-payoff games with infinite-memory strategies: we show that mean-payoff-sup objectives can be decided in NP∩coNP, whereas mean-payoff-inf objectives are coNP-complete.},
  author       = {Velner, Yaron and Chatterjee, Krishnendu and Doyen, Laurent and Henzinger, Thomas A and Rabinovich, Alexander and Raskin, Jean},
  journal      = {Information and Computation},
  number       = {4},
  pages        = {177 -- 196},
  publisher    = {Elsevier},
  title        = {{The complexity of multi-mean-payoff and multi-energy games}},
  doi          = {10.1016/j.ic.2015.03.001},
  volume       = {241},
  year         = {2015},
}

@article{1699,
  abstract     = {By hybridization and backcrossing, alleles can surmount species boundaries and be incorporated into the genome of a related species. This introgression of genes is of particular evolutionary relevance if it involves the transfer of adaptations between populations. However, any beneficial allele will typically be associated with other alien alleles that are often deleterious and hamper the introgression process. In order to describe the introgression of an adaptive allele, we set up a stochastic model with an explicit genetic makeup of linked and unlinked deleterious alleles. Based on the theory of reducible multitype branching processes, we derive a recursive expression for the establishment probability of the beneficial allele after a single hybridization event. We furthermore study the probability that slightly deleterious alleles hitchhike to fixation. The key to the analysis is a split of the process into a stochastic phase in which the advantageous alleles establishes and a deterministic phase in which it sweeps to fixation. We thereafter apply the theory to a set of biologically relevant scenarios such as introgression in the presence of many unlinked or few closely linked deleterious alleles. A comparison to computer simulations shows that the approximations work well over a large parameter range.},
  author       = {Uecker, Hildegard and Setter, Derek and Hermisson, Joachim},
  journal      = {Journal of Mathematical Biology},
  number       = {7},
  pages        = {1523 -- 1580},
  publisher    = {Springer},
  title        = {{Adaptive gene introgression after secondary contact}},
  doi          = {10.1007/s00285-014-0802-y},
  volume       = {70},
  year         = {2015},
}

@article{1700,
  abstract     = {We use the dual boson approach to reveal the phase diagram of the Fermi-Hubbard model with long-range dipole-dipole interactions. By using a large-scale finite-temperature calculation on a 64×64 square lattice we demonstrate the existence of a novel phase, possessing an "ultralong-range" order. The fingerprint of this phase - the density correlation function - features a nontrivial behavior on a scale of tens of lattice sites. We study the properties and the stability of the ultralong-range-ordered phase, and show that it is accessible in modern experiments with ultracold polar molecules and magnetic atoms.},
  author       = {Van Loon, Erik and Katsnelson, Mikhail and Lemeshko, Mikhail},
  journal      = {Physical Review B},
  number       = {8},
  publisher    = {American Physical Society},
  title        = {{Ultralong-range order in the Fermi-Hubbard model with long-range interactions}},
  doi          = {10.1103/PhysRevB.92.081106},
  volume       = {92},
  year         = {2015},
}

@article{1701,
  abstract     = {The activity of a neural network is defined by patterns of spiking and silence from the individual neurons. Because spikes are (relatively) sparse, patterns of activity with increasing numbers of spikes are less probable, but, with more spikes, the number of possible patterns increases. This tradeoff between probability and numerosity is mathematically equivalent to the relationship between entropy and energy in statistical physics. We construct this relationship for populations of up to N = 160 neurons in a small patch of the vertebrate retina, using a combination of direct and model-based analyses of experiments on the response of this network to naturalistic movies. We see signs of a thermodynamic limit, where the entropy per neuron approaches a smooth function of the energy per neuron as N increases. The form of this function corresponds to the distribution of activity being poised near an unusual kind of critical point. We suggest further tests of criticality, and give a brief discussion of its functional significance. },
  author       = {Tkacik, Gasper and Mora, Thierry and Marre, Olivier and Amodei, Dario and Palmer, Stephanie and Berry Ii, Michael and Bialek, William},
  journal      = {PNAS},
  number       = {37},
  pages        = {11508 -- 11513},
  publisher    = {National Academy of Sciences},
  title        = {{Thermodynamics and signatures of criticality in a network of neurons}},
  doi          = {10.1073/pnas.1514188112},
  volume       = {112},
  year         = {2015},
}

@article{1704,
  abstract     = {Given a convex function (Formula presented.) and two hermitian matrices A and B, Lewin and Sabin study in (Lett Math Phys 104:691–705, 2014) the relative entropy defined by (Formula presented.). Among other things, they prove that the so-defined quantity is monotone if and only if (Formula presented.) is operator monotone. The monotonicity is then used to properly define (Formula presented.) for bounded self-adjoint operators acting on an infinite-dimensional Hilbert space by a limiting procedure. More precisely, for an increasing sequence of finite-dimensional projections (Formula presented.) with (Formula presented.) strongly, the limit (Formula presented.) is shown to exist and to be independent of the sequence of projections (Formula presented.). The question whether this sequence converges to its "obvious" limit, namely (Formula presented.), has been left open. We answer this question in principle affirmatively and show that (Formula presented.). If the operators A and B are regular enough, that is (A − B), (Formula presented.) and (Formula presented.) are trace-class, the identity (Formula presented.) holds.},
  author       = {Deuchert, Andreas and Hainzl, Christian and Seiringer, Robert},
  journal      = {Letters in Mathematical Physics},
  number       = {10},
  pages        = {1449 -- 1466},
  publisher    = {Springer},
  title        = {{Note on a family of monotone quantum relative entropies}},
  doi          = {10.1007/s11005-015-0787-5},
  volume       = {105},
  year         = {2015},
}

@inproceedings{1706,
  abstract     = {We consider a problem of learning kernels for use in SVM classification in the multi-task and lifelong scenarios and provide generalization bounds on the error of a large margin classifier. Our results show that, under mild conditions on the family of kernels used for learning, solving several related tasks simultaneously is beneficial over single task learning. In particular, as the number of observed tasks grows, assuming that in the considered family of kernels there exists one that yields low approximation error on all tasks, the overhead associated with learning such a kernel vanishes and the complexity converges to that of learning when this good kernel is given to the learner.},
  author       = {Pentina, Anastasia and Ben David, Shai},
  location     = {Banff, AB, Canada},
  pages        = {194 -- 208},
  publisher    = {Springer},
  title        = {{Multi-task and lifelong learning of kernels}},
  doi          = {10.1007/978-3-319-24486-0_13},
  volume       = {9355},
  year         = {2015},
}

@article{1709,
  abstract     = {The competition for resources among cells, individuals or species is a fundamental characteristic of evolution. Biological all-pay auctions have been used to model situations where multiple individuals compete for a single resource. However, in many situations multiple resources with various values exist and single reward auctions are not applicable. We generalize the model to multiple rewards and study the evolution of strategies. In biological all-pay auctions the bid of an individual corresponds to its strategy and is equivalent to its payment in the auction. The decreasingly ordered rewards are distributed according to the decreasingly ordered bids of the participating individuals. The reproductive success of an individual is proportional to its fitness given by the sum of the rewards won minus its payments. Hence, successful bidding strategies spread in the population. We find that the results for the multiple reward case are very different from the single reward case. While the mixed strategy equilibrium in the single reward case with more than two players consists of mostly low-bidding individuals, we show that the equilibrium can convert to many high-bidding individuals and a few low-bidding individuals in the multiple reward case. Some reward values lead to a specialization among the individuals where one subpopulation competes for the rewards and the other subpopulation largely avoids costly competitions. Whether the mixed strategy equilibrium is an evolutionarily stable strategy (ESS) depends on the specific values of the rewards.},
  author       = {Reiter, Johannes and Kanodia, Ayush and Gupta, Raghav and Nowak, Martin and Chatterjee, Krishnendu},
  journal      = {Proceedings of the Royal Society of London Series B Biological Sciences},
  number       = {1812},
  publisher    = {Royal Society},
  title        = {{Biological auctions with multiple rewards}},
  doi          = {10.1098/rspb.2015.1041},
  volume       = {282},
  year         = {2015},
}

@article{1710,
  abstract     = {We consider the hollow on the half-plane {(x, y) : y ≤ 0} ⊂ ℝ2 defined by a function u : (-1, 1) → ℝ, u(x) < 0, and a vertical flow of point particles incident on the hollow. It is assumed that u satisfies the so-called single impact condition (SIC): each incident particle is elastically reflected by graph(u) and goes away without hitting the graph of u anymore. We solve the problem: find the function u minimizing the force of resistance created by the flow. We show that the graph of the minimizer is formed by two arcs of parabolas symmetric to each other with respect to the y-axis. Assuming that the resistance of u ≡ 0 equals 1, we show that the minimal resistance equals π/2 - 2arctan(1/2) ≈ 0.6435. This result completes the previously obtained result [SIAM J. Math. Anal., 46 (2014), pp. 2730-2742] stating in particular that the minimal resistance of a hollow in higher dimensions equals 0.5. We additionally consider a similar problem of minimal resistance, where the hollow in the half-space {(x1,...,xd,y) : y ≤ 0} ⊂ ℝd+1 is defined by a radial function U satisfying the SIC, U(x) = u(|x|), with x = (x1,...,xd), u(ξ) < 0 for 0 ≤ ξ < 1, and u(ξ) = 0 for ξ ≥ 1, and the flow is parallel to the y-axis. The minimal resistance is greater than 0.5 (and coincides with 0.6435 when d = 1) and converges to 0.5 as d → ∞.},
  author       = {Akopyan, Arseniy and Plakhov, Alexander},
  journal      = {Society for Industrial and Applied Mathematics},
  number       = {4},
  pages        = {2754 -- 2769},
  publisher    = {SIAM},
  title        = {{Minimal resistance of curves under the single impact assumption}},
  doi          = {10.1137/140993843},
  volume       = {47},
  year         = {2015},
}

@article{1712,
  abstract     = {The majority of immune cells in Drosophila melanogaster are plasmatocytes; they carry out similar functions to vertebrate macrophages, influencing development as well as protecting against infection and cancer. Plasmatocytes, sometimes referred to with the broader term of hemocytes, migrate widely during embryonic development and cycle in the larvae between sessile and circulating positions. Here we discuss the similarities of plasmatocyte developmental migration and its functions to that of vertebrate macrophages, considering the recent controversy regarding the functions of Drosophila PDGF/VEGF related ligands. We also examine recent findings on the significance of adhesion for plasmatocyte migration in the embryo, as well as proliferation, trans-differentiation, and tumor responses in the larva. We spotlight parallels throughout to vertebrate immune responses.},
  author       = {Ratheesh, Aparna and Belyaeva, Vera and Siekhaus, Daria E},
  journal      = {Current Opinion in Cell Biology},
  number       = {10},
  pages        = {71 -- 79},
  publisher    = {Elsevier},
  title        = {{Drosophila immune cell migration and adhesion during embryonic development and larval immune responses}},
  doi          = {10.1016/j.ceb.2015.07.003},
  volume       = {36},
  year         = {2015},
}