@article{2699,
  abstract     = {We prove the universality of the β-ensembles with convex analytic potentials and for any β >
0, i.e. we show that the spacing distributions of log-gases at any inverse temperature β coincide with those of the Gaussian β-ensembles.},
  author       = {Erdös, László and Bourgade, Paul and Yau, Horng},
  journal      = {Duke Mathematical Journal},
  number       = {6},
  pages        = {1127 -- 1190},
  publisher    = {Duke University Press},
  title        = {{Universality of general β-ensembles}},
  doi          = {10.1215/00127094-2649752},
  volume       = {163},
  year         = {2014},
}

@article{2716,
  abstract     = {Multi-dimensional mean-payoff and energy games provide the mathematical foundation for the quantitative study of reactive systems, and play a central role in the emerging quantitative theory of verification and synthesis. In this work, we study the strategy synthesis problem for games with such multi-dimensional objectives along with a parity condition, a canonical way to express ω ω -regular conditions. While in general, the winning strategies in such games may require infinite memory, for synthesis the most relevant problem is the construction of a finite-memory winning strategy (if one exists). Our main contributions are as follows. First, we show a tight exponential bound (matching upper and lower bounds) on the memory required for finite-memory winning strategies in both multi-dimensional mean-payoff and energy games along with parity objectives. This significantly improves the triple exponential upper bound for multi energy games (without parity) that could be derived from results in literature for games on vector addition systems with states. Second, we present an optimal symbolic and incremental algorithm to compute a finite-memory winning strategy (if one exists) in such games. Finally, we give a complete characterization of when finite memory of strategies can be traded off for randomness. In particular, we show that for one-dimension mean-payoff parity games, randomized memoryless strategies are as powerful as their pure finite-memory counterparts.},
  author       = {Chatterjee, Krishnendu and Randour, Mickael and Raskin, Jean},
  journal      = {Acta Informatica},
  number       = {3-4},
  pages        = {129 -- 163},
  publisher    = {Springer},
  title        = {{Strategy synthesis for multi-dimensional quantitative objectives}},
  doi          = {10.1007/s00236-013-0182-6},
  volume       = {51},
  year         = {2014},
}

@inproceedings{2905,
  abstract     = {Persistent homology is a recent grandchild of homology that has found use in
science and engineering as well as in mathematics. This paper surveys the method as well
as the applications, neglecting completeness in favor of highlighting ideas and directions.},
  author       = {Edelsbrunner, Herbert and Morozovy, Dmitriy},
  location     = {Kraków, Poland},
  pages        = {31 -- 50},
  publisher    = {European Mathematical Society Publishing House},
  title        = {{Persistent homology: Theory and practice}},
  doi          = {10.4171/120-1/3},
  year         = {2014},
}

@article{3263,
  abstract     = {Adaptation in the retina is thought to optimize the encoding of natural light signals into sequences of spikes sent to the brain. While adaptive changes in retinal processing to the variations of the mean luminance level and second-order stimulus statistics have been documented before, no such measurements have been performed when higher-order moments of the light distribution change. We therefore measured the ganglion cell responses in the tiger salamander retina to controlled changes in the second (contrast), third (skew) and fourth (kurtosis) moments of the light intensity distribution of spatially uniform temporally independent stimuli. The skew and kurtosis of the stimuli were chosen to cover the range observed in natural scenes. We quantified adaptation in ganglion cells by studying linear-nonlinear models that capture well the retinal encoding properties across all stimuli. We found that the encoding properties of retinal ganglion cells change only marginally when higher-order statistics change, compared to the changes observed in response to the variation in contrast. By analyzing optimal coding in LN-type models, we showed that neurons can maintain a high information rate without large dynamic adaptation to changes in skew or kurtosis. This is because, for uncorrelated stimuli, spatio-temporal summation within the receptive field averages away non-gaussian aspects of the light intensity distribution.},
  author       = {Tkacik, Gasper and Ghosh, Anandamohan and Schneidman, Elad and Segev, Ronen},
  journal      = {PLoS One},
  number       = {1},
  publisher    = {Public Library of Science},
  title        = {{Adaptation to changes in higher-order stimulus statistics in the salamander retina}},
  doi          = {10.1371/journal.pone.0085841},
  volume       = {9},
  year         = {2014},
}

@article{10815,
  abstract     = {In the last several decades, developmental biology has clarified the molecular mechanisms of embryogenesis and organogenesis. In particular, it has demonstrated that the “tool-kit genes” essential for regulating developmental processes are not only highly conserved among species, but are also used as systems at various times and places in an organism to control distinct developmental events. Therefore, mutations in many of these tool-kit genes may cause congenital diseases involving morphological abnormalities. This link between genes and abnormal morphological phenotypes underscores the importance of understanding how cells behave and contribute to morphogenesis as a result of gene function. Recent improvements in live imaging and in quantitative analyses of cellular dynamics will advance our understanding of the cellular pathogenesis of congenital diseases associated with aberrant morphologies. In these studies, it is critical to select an appropriate model organism for the particular phenomenon of interest.},
  author       = {Hashimoto, Masakazu and Morita, Hitoshi and Ueno, Naoto},
  issn         = {0914-3505},
  journal      = {Congenital Anomalies},
  keywords     = {Developmental Biology, Embryology, General Medicine, Pediatrics, Perinatology, and Child Health},
  number       = {1},
  pages        = {1--7},
  publisher    = {Wiley},
  title        = {{Molecular and cellular mechanisms of development underlying congenital diseases}},
  doi          = {10.1111/cga.12039},
  volume       = {54},
  year         = {2014},
}

@inproceedings{10884,
  abstract     = {We revisit the parameterized model checking problem for token-passing systems and specifications in indexed CTL  ∗ \X. Emerson and Namjoshi (1995, 2003) have shown that parameterized model checking of indexed CTL  ∗ \X in uni-directional token rings can be reduced to checking rings up to some cutoff size. Clarke et al. (2004) have shown a similar result for general topologies and indexed LTL \X, provided processes cannot choose the directions for sending or receiving the token.
We unify and substantially extend these results by systematically exploring fragments of indexed CTL  ∗ \X with respect to general topologies. For each fragment we establish whether a cutoff exists, and for some concrete topologies, such as rings, cliques and stars, we infer small cutoffs. Finally, we show that the problem becomes undecidable, and thus no cutoffs exist, if processes are allowed to choose the directions in which they send or from which they receive the token.},
  author       = {Aminof, Benjamin and Jacobs, Swen and Khalimov, Ayrat and Rubin, Sasha},
  booktitle    = {Verification, Model Checking, and Abstract Interpretation},
  isbn         = {9783642540127},
  issn         = {1611-3349},
  location     = {San Diego, CA, United States},
  pages        = {262--281},
  publisher    = {Springer Nature},
  title        = {{Parameterized model checking of token-passing systems}},
  doi          = {10.1007/978-3-642-54013-4_15},
  volume       = {8318},
  year         = {2014},
}

@article{11080,
  abstract     = {The spindle assembly checkpoint prevents separation of sister chromatids until each kinetochore is attached to the mitotic spindle. Rodriguez-Bravo et al. report that the nuclear pore complex scaffolds spindle assembly checkpoint signaling in interphase, providing a store of inhibitory signals that limits the speed of the subsequent mitosis.},
  author       = {Buchwalter, Abigail and HETZER, Martin W},
  issn         = {0092-8674},
  journal      = {Cell},
  keywords     = {General Biochemistry, Genetics and Molecular Biology},
  number       = {5},
  pages        = {868--869},
  publisher    = {Elsevier},
  title        = {{Nuclear pores set the speed limit for mitosis}},
  doi          = {10.1016/j.cell.2014.02.004},
  volume       = {156},
  year         = {2014},
}

@article{11081,
  abstract     = {In eukaryotic cells the nuclear genome is enclosed by the nuclear envelope (NE). In metazoans, the NE breaks down in mitosis and it has been assumed that the physical barrier separating nucleoplasm and cytoplasm remains intact during the rest of the cell cycle and cell differentiation. However, recent studies suggest that nonmitotic NE remodeling plays a critical role in development, virus infection, laminopathies, and cancer. Although the mechanisms underlying these NE restructuring events are currently being defined, one common theme is activation of protein kinase C family members in the interphase nucleus to disrupt the nuclear lamina, demonstrating the importance of the lamina in maintaining nuclear integrity.},
  author       = {Hatch, Emily and HETZER, Martin W},
  issn         = {1540-8140},
  journal      = {Journal of Cell Biology},
  keywords     = {Cell Biology},
  number       = {2},
  pages        = {133--141},
  publisher    = {Rockefeller University Press},
  title        = {{Breaching the nuclear envelope in development and disease}},
  doi          = {10.1083/jcb.201402003},
  volume       = {205},
  year         = {2014},
}

@article{11082,
  abstract     = {The nuclear pore complex (NPC) plays a critical role in gene expression by mediating import of transcription regulators into the nucleus and export of RNA transcripts to the cytoplasm. Emerging evidence suggests that in addition to mediating transport, a subset of nucleoporins (Nups) engage in transcriptional activation and elongation at genomic loci that are not associated with NPCs. The underlying mechanism and regulation of Nup mobility on and off nuclear pores remain unclear. Here we show that Nup50 is a mobile Nup with a pronounced presence both at the NPC and in the nucleoplasm that can move between these different localizations. Strikingly, the dynamic behavior of Nup50 in both locations is dependent on active transcription by RNA polymerase II and requires the N-terminal half of the protein, which contains importin α– and Nup153-binding domains. However, Nup50 dynamics are independent of importin α, Nup153, and Nup98, even though the latter two proteins also exhibit transcription-dependent mobility. Of interest, depletion of Nup50 from C2C12 myoblasts does not affect cell proliferation but inhibits differentiation into myotubes. Taken together, our results suggest a transport-independent role for Nup50 in chromatin biology that occurs away from the NPC.},
  author       = {Buchwalter, Abigail L. and Liang, Yun and HETZER, Martin W},
  issn         = {1059-1524},
  journal      = {Molecular Biology of the Cell},
  keywords     = {Cell Biology, Molecular Biology},
  number       = {16},
  pages        = {2472--2484},
  publisher    = {American Society for Cell Biology},
  title        = {{Nup50 is required for cell differentiation and exhibits transcription-dependent dynamics}},
  doi          = {10.1091/mbc.e14-04-0865},
  volume       = {25},
  year         = {2014},
}

@article{11582,
  abstract     = {We have observed a sample of typical z ∼ 1 star-forming galaxies, selected from the HiZELS survey, with the new K-band Multi-Object Spectrograph (KMOS) near-infrared, multi-integral field unit instrument on the Very Large Telescope (VLT), in order to obtain their dynamics and metallicity gradients. The majority of our galaxies have a metallicity gradient consistent with being flat or negative (i.e. higher metallicity cores than outskirts). Intriguingly, we find a trend between metallicity gradient and specific star formation rate (sSFR), such that galaxies with a high sSFR tend to have relatively metal poor centres, a result which is strengthened when combined with data sets from the literature. This result appears to explain the discrepancies reported between different high-redshift studies and varying claims for evolution. From a galaxy evolution perspective, the trend we see would mean that a galaxy's sSFR is governed by the amount of metal-poor gas that can be funnelled into its core, triggered either by merging or through efficient accretion. In fact, merging may play a significant role as it is the starburst galaxies at all epochs, which have the more positive metallicity gradients. Our results may help to explain the origin of the fundamental metallicity relation, in which galaxies at a fixed mass are observed to have lower metallicities at higher star formation rates, especially if the metallicity is measured in an aperture encompassing only the central regions of the galaxy. Finally, we note that this study demonstrates the power of KMOS as an efficient instrument for large-scale resolved galaxy surveys.},
  author       = {Stott, John P. and Sobral, David and Swinbank, A. M. and Smail, Ian and Bower, Richard and Best, Philip N. and Sharples, Ray M. and Geach, James E. and Matthee, Jorryt J},
  issn         = {1365-2966},
  journal      = {Monthly Notices of the Royal Astronomical Society},
  keywords     = {Space and Planetary Science, Astronomy and Astrophysics, galaxies: abundances, galaxies: evolution, galaxies: kinematics and dynamics},
  number       = {3},
  pages        = {2695--2704},
  publisher    = {Oxford University Press},
  title        = {{A relationship between specific star formation rate and metallicity gradient within z ∼ 1 galaxies from KMOS-HiZELS}},
  doi          = {10.1093/mnras/stu1343},
  volume       = {443},
  year         = {2014},
}

@article{11583,
  abstract     = {Candidate galaxies at redshifts of z ∼ 10 are now being found in extremely deep surveys, probing very small areas. As a consequence, candidates are very faint, making spectroscopic confirmation practically impossible. In order to overcome such limitations, we have undertaken the CF-HiZELS survey, which is a large-area, medium-depth near-infrared narrow-band survey targeted at z = 8.8 Lyman α (Lyα) emitters (LAEs) and covering 10 deg2 in part of the SSA22 field with the Canada–France–Hawaii Telescope (CFHT). We surveyed a comoving volume of 4.7 × 106 Mpc3 to a Lyα luminosity limit of 6.3 × 1043舁erg舁s−1. We look for Lyα candidates by applying the following criteria: (i) clear emission-line source, (ii) no optical detections (ugriz from CFHTLS), (iii) no visible detection in the optical stack (ugriz > 27), (iv) visually checked reliable NBJ and J detections and (v) J − K ≤ 0. We compute photometric redshifts and remove a significant amount of dusty lower redshift line-emitters at z ∼ 1.4 or 2.2. A total of 13 Lyα candidates were found, of which two are marked as strong candidates, but the majority have very weak constraints on their spectral energy distributions. Using follow-up observations with SINFONI/VLT, we are able to exclude the most robust candidates as LAEs. We put a strong constraint on the Lyα luminosity function at z ∼ 9 and make realistic predictions for ongoing and future surveys. Our results show that surveys for the highest redshift LAEs are susceptible of multiple contaminations and that spectroscopic follow-up is absolutely necessary.},
  author       = {Matthee, Jorryt J and Sobral, David and Swinbank, A. M. and Smail, Ian and Best, P. N. and Kim, Jae-Woo and Franx, Marijn and Milvang-Jensen, Bo and Fynbo, Johan},
  issn         = {1365-2966},
  journal      = {Monthly Notices of the Royal Astronomical Society},
  keywords     = {Space and Planetary Science, Astronomy and Astrophysics, galaxies: evolution, galaxies: high-redshift, cosmology: observations, dark ages, reionization, first stars},
  number       = {3},
  pages        = {2375--2387},
  publisher    = {Oxford University Press},
  title        = {{A 10 deg2 Lyman α survey at z=8.8 with spectroscopic follow-up: Strong constraints on the luminosity function and implications for other surveys}},
  doi          = {10.1093/mnras/stu392},
  volume       = {440},
  year         = {2014},
}

@inproceedings{11789,
  abstract     = {We study a weighted online bipartite matching problem: G(V 1, V 2, E) is a weighted bipartite graph where V 1 is known beforehand and the vertices of V 2 arrive online. The goal is to match vertices of V 2 as they arrive to vertices in V 1, so as to maximize the sum of weights of edges in the matching. If assignments to V 1 cannot be changed, no bounded competitive ratio is achievable. We study the weighted online matching problem with free disposal, where vertices in V 1 can be assigned multiple times, but only get credit for the maximum weight edge assigned to them over the course of the algorithm. For this problem, the greedy algorithm is 0.5-competitive and determining whether a better competitive ratio is achievable is a well known open problem.

We identify an interesting special case where the edge weights are decomposable as the product of two factors, one corresponding to each end point of the edge. This is analogous to the well studied related machines model in the scheduling literature, although the objective functions are different. For this case of decomposable edge weights, we design a 0.5664 competitive randomized algorithm in complete bipartite graphs. We show that such instances with decomposable weights are non-trivial by establishing upper bounds of 0.618 for deterministic and 0.8 for randomized algorithms.

A tight competitive ratio of 1 − 1/e ≈ 0.632 was known previously for both the 0-1 case as well as the case where edge weights depend on the offline vertices only, but for these cases, reassignments cannot change the quality of the solution. Beating 0.5 for weighted matching where reassignments are necessary has been a significant challenge. We thus give the first online algorithm with competitive ratio strictly better than 0.5 for a non-trivial case of weighted matching with free disposal.},
  author       = {Charikar, Moses and Henzinger, Monika H and Nguyễn, Huy L.},
  booktitle    = {22nd Annual European Symposium on Algorithms},
  isbn         = {978-366244776-5},
  issn         = {0302-9743},
  location     = {Wroclaw, Poland},
  pages        = {260 -- 271},
  publisher    = {Springer Nature},
  title        = {{Online bipartite matching with decomposable weights}},
  doi          = {10.1007/978-3-662-44777-2_22},
  volume       = {8737},
  year         = {2014},
}

@article{7771,
  abstract     = {In their Letter, Schreck, Bertrand, O'Hern and Shattuck [Phys. Rev. Lett. 107, 078301 (2011)] study nonlinearities in jammed particulate systems that arise when contacts are altered. They conclude that there is "no harmonic regime in the large system limit for all compressions" and "at jamming onset for any system size." Their argument rests on the claim that for finite-range repulsive potentials, of the form used in studies of jamming, the breaking or forming of a single contact is sufficient to destroy the linear regime. We dispute these conclusions and argue that linear response is both justified and essential for understanding the nature of the jammed solid. },
  author       = {Goodrich, Carl Peter and Liu, Andrea J. and Nagel, Sidney R.},
  issn         = {0031-9007},
  journal      = {Physical Review Letters},
  number       = {4},
  publisher    = {American Physical Society},
  title        = {{Comment on “Repulsive contact interactions make jammed particulate systems inherently nonharmonic”}},
  doi          = {10.1103/physrevlett.112.049801},
  volume       = {112},
  year         = {2014},
}

@article{8021,
  abstract     = {Most excitatory inputs in the mammalian brain are made on dendritic spines, rather than on dendritic shafts. Spines compartmentalize calcium, and this biochemical isolation can underlie input-specific synaptic plasticity, providing a raison d'etre for spines. However, recent results indicate that the spine can experience a membrane potential different from that in the parent dendrite, as though the spine neck electrically isolated the spine. Here we use two-photon calcium imaging of mouse neocortical pyramidal neurons to analyze the correlation between the morphologies of spines activated under minimal synaptic stimulation and the excitatory postsynaptic potentials they generate. We find that excitatory postsynaptic potential amplitudes are inversely correlated with spine neck lengths. Furthermore, a spike timing-dependent plasticity protocol, in which two-photon glutamate uncaging over a spine is paired with postsynaptic spikes, produces rapid shrinkage of the spine neck and concomitant increases in the amplitude of the evoked spine potentials. Using numerical simulations, we explore the parameter regimes for the spine neck resistance and synaptic conductance changes necessary to explain our observations. Our data, directly correlating synaptic and morphological plasticity, imply that long-necked spines have small or negligible somatic voltage contributions, but that, upon synaptic stimulation paired with postsynaptic activity, they can shorten their necks and increase synaptic efficacy, thus changing the input/output gain of pyramidal neurons. },
  author       = {Araya, R. and Vogels, Tim P and Yuste, R.},
  issn         = {1091-6490},
  journal      = {Proceedings of the National Academy of Sciences},
  number       = {28},
  pages        = {E2895--E2904},
  publisher    = {Proceedings of the National Academy of Sciences},
  title        = {{Activity-dependent dendritic spine neck changes are correlated with synaptic strength}},
  doi          = {10.1073/pnas.1321869111},
  volume       = {111},
  year         = {2014},
}

@article{8022,
  abstract     = {Populations of neurons in motor cortex engage in complex transient dynamics of large amplitude during the execution of limb movements. Traditional network models with stochastically assigned synapses cannot reproduce this behavior. Here we introduce a class of cortical architectures with strong and random excitatory recurrence that is stabilized by intricate, fine-tuned inhibition, optimized from a control theory perspective. Such networks transiently amplify specific activity states and can be used to reliably execute multidimensional movement patterns. Similar to the experimental observations, these transients must be preceded by a steady-state initialization phase from which the network relaxes back into the background state by way of complex internal dynamics. In our networks, excitation and inhibition are as tightly balanced as recently reported in experiments across several brain areas, suggesting inhibitory control of complex excitatory recurrence as a generic organizational principle in cortex.},
  author       = {Hennequin, Guillaume and Vogels, Tim P and Gerstner, Wulfram},
  issn         = {0896-6273},
  journal      = {Neuron},
  number       = {6},
  pages        = {1394--1406},
  publisher    = {Elsevier},
  title        = {{Optimal control of transient dynamics in balanced networks supports generation of complex movements}},
  doi          = {10.1016/j.neuron.2014.04.045},
  volume       = {82},
  year         = {2014},
}

@article{8023,
  abstract     = {Uniform random sparse network architectures are ubiquitous in computational neuroscience, but the implicit hypothesis that they are a good representation of real neuronal networks has been met with skepticism. Here we used two experimental data sets, a study of triplet connectivity statistics and a data set measuring neuronal responses to channelrhodopsin stimuli, to evaluate the fidelity of thousands of model networks. Network architectures comprised three neuron types (excitatory, fast spiking, and nonfast spiking inhibitory) and were created from a set of rules that govern the statistics of the resulting connection types. In a high-dimensional parameter scan, we varied the degree distributions (i.e., how many cells each neuron connects with) and the synaptic weight correlations of synapses from or onto the same neuron. These variations converted initially uniform random and homogeneously connected networks, in which every neuron sent and received equal numbers of synapses with equal synaptic strength distributions, to highly heterogeneous networks in which the number of synapses per neuron, as well as average synaptic strength of synapses from or to a neuron were variable. By evaluating the impact of each variable on the network structure and dynamics, and their similarity to the experimental data, we could falsify the uniform random sparse connectivity hypothesis for 7 of 36 connectivity parameters, but we also confirmed the hypothesis in 8 cases. Twenty-one parameters had no substantial impact on the results of the test protocols we used.},
  author       = {Tomm, Christian and Avermann, Michael and Petersen, Carl and Gerstner, Wulfram and Vogels, Tim P},
  issn         = {1522-1598},
  journal      = {Journal of Neurophysiology},
  number       = {8},
  pages        = {1801--1814},
  publisher    = {American Physiological Society},
  title        = {{Connection-type-specific biases make uniform random network models consistent with cortical recordings}},
  doi          = {10.1152/jn.00629.2013},
  volume       = {112},
  year         = {2014},
}

@inproceedings{8044,
  abstract     = {Many questions concerning models in quantum mechanics require a detailed analysis of the spectrum of the corresponding Hamiltonian, a linear operator on a suitable Hilbert space. Of particular relevance for an understanding of the low-temperature properties of a system is the structure of the excitation spectrum, which is the part of the spectrum close to the spectral bottom. We present recent progress on this question for bosonic many-body quantum systems with weak two-body interactions. Such system are currently of great interest, due to their experimental realization in ultra-cold atomic gases. We investigate the accuracy of the Bogoliubov approximations, which predicts that the low-energy spectrum is made up of sums of elementary excitations, with linear dispersion law at low momentum. The latter property is crucial for the superfluid behavior the system.},
  author       = {Seiringer, Robert},
  booktitle    = {Proceeding of the International Congress of Mathematicans},
  isbn         = {9788961058063},
  location     = {Seoul, South Korea},
  pages        = {1175--1194},
  publisher    = {International Congress of Mathematicians},
  title        = {{Structure of the excitation spectrum for many-body quantum systems}},
  volume       = {3},
  year         = {2014},
}

@article{1629,
  abstract     = {We propose a method for propagating edit operations in 2D vector graphics, based on geometric relationship functions. These functions quantify the geometric relationship of a point to a polygon, such as the distance to the boundary or the direction to the closest corner vertex. The level sets of the relationship functions describe points with the same relationship to a polygon. For a given query point, we first determine a set of relationships to local features, construct all level sets for these relationships, and accumulate them. The maxima of the resulting distribution are points with similar geometric relationships. We show extensions to handle mirror symmetries, and discuss the use of relationship functions as local coordinate systems. Our method can be applied, for example, to interactive floorplan editing, and it is especially useful for large layouts, where individual edits would be cumbersome. We demonstrate populating 2D layouts with tens to hundreds of objects by propagating relatively few edit operations.},
  author       = {Guerrero, Paul and Jeschke, Stefan and Wimmer, Michael and Wonka, Peter},
  journal      = {ACM Transactions on Graphics},
  number       = {2},
  publisher    = {ACM},
  title        = {{Edit propagation using geometric relationship functions}},
  doi          = {10.1145/2591010},
  volume       = {33},
  year         = {2014},
}

@inproceedings{1643,
  abstract     = {We extend the notion of verifiable random functions (VRF) to constrained VRFs, which generalize the concept of constrained pseudorandom functions, put forward by Boneh and Waters (Asiacrypt’13), and independently by Kiayias et al. (CCS’13) and Boyle et al. (PKC’14), who call them delegatable PRFs and functional PRFs, respectively. In a standard VRF the secret key sk allows one to evaluate a pseudorandom function at any point of its domain; in addition, it enables computation of a non-interactive proof that the function value was computed correctly. In a constrained VRF from the key sk one can derive constrained keys skS for subsets S of the domain, which allow computation of function values and proofs only at points in S. After formally defining constrained VRFs, we derive instantiations from the multilinear-maps-based constrained PRFs by Boneh and Waters, yielding a VRF with constrained keys for any set that can be decided by a polynomial-size circuit. Our VRFs have the same function values as the Boneh-Waters PRFs and are proved secure under the same hardness assumption, showing that verifiability comes at no cost. Constrained (functional) VRFs were stated as an open problem by Boyle et al.},
  author       = {Fuchsbauer, Georg},
  booktitle    = {SCN 2014},
  editor       = {Abdalla, Michel and De Prisco, Roberto},
  location     = {Amalfi, Italy},
  pages        = {95 -- 114},
  publisher    = {Springer},
  title        = {{Constrained Verifiable Random Functions }},
  doi          = {10.1007/978-3-319-10879-7_7},
  volume       = {8642},
  year         = {2014},
}

@inproceedings{1702,
  abstract     = {In this paper we present INTERHORN, a solver for recursion-free Horn clauses. The main application domain of INTERHORN lies in solving interpolation problems arising in software verification. We show how a range of interpolation problems, including path, transition, nested, state/transition and well-founded interpolation can be handled directly by INTERHORN. By detailing these interpolation problems and their Horn clause representations, we hope to encourage the emergence of a common back-end interpolation interface useful for diverse verification tools.},
  author       = {Gupta, Ashutosh and Popeea, Corneliu and Rybalchenko, Andrey},
  booktitle    = {Electronic Proceedings in Theoretical Computer Science, EPTCS},
  location     = {Vienna, Austria},
  pages        = {31 -- 38},
  publisher    = {Open Publishing},
  title        = {{Generalised interpolation by solving recursion free-horn clauses}},
  doi          = {10.4204/EPTCS.169.5},
  volume       = {169},
  year         = {2014},
}