@article{7736,
  abstract     = {We develop a novel approach to identify regions of the genome underlying population genetic differentiation in any genetic data where the underlying population structure is unknown, or where the interest is assessing divergence along a gradient. By combining the statistical framework for genome-wide association studies (GWASs) with eigenvector decomposition (EigenGWAS), which is commonly used in population genetics to characterize the structure of genetic data, loci under selection can be identified without a requirement for discrete populations. We show through theory and simulation that our approach can identify regions under selection along gradients of ancestry, and in real data we confirm this by demonstrating LCT to be under selection between HapMap CEU–TSI cohorts, and we then validate this selection signal across European countries in the POPRES samples. HERC2 was also found to be differentiated between both the CEU–TSI cohort and within the POPRES sample, reflecting the likely anthropological differences in skin and hair colour between northern and southern European populations. Controlling for population stratification is of great importance in any quantitative genetic study and our approach also provides a simple, fast and accurate way of predicting principal components in independent samples. With ever increasing sample sizes across many fields, this approach is likely to be greatly utilized to gain individual-level eigenvectors avoiding the computational challenges associated with conducting singular value decomposition in large data sets. We have developed freely available software, Genetic Analysis Repository (GEAR), to facilitate the application of the methods.},
  author       = {Chen, G-B and Lee, S H and Zhu, Z-X and Benyamin, B and Robinson, Matthew Richard},
  issn         = {0018-067X},
  journal      = {Heredity},
  pages        = {51--61},
  publisher    = {Springer Nature},
  title        = {{EigenGWAS: Finding loci under selection through genome-wide association studies of eigenvectors in structured populations}},
  doi          = {10.1038/hdy.2016.25},
  volume       = {117},
  year         = {2016},
}

@article{7737,
  abstract     = {Genome-wide association studies (GWAS) have identified thousands of genetic variants associated with human complex traits. However, the genes or functional DNA elements through which these variants exert their effects on the traits are often unknown. We propose a method (called SMR) that integrates summary-level data from GWAS with data from expression quantitative trait locus (eQTL) studies to identify genes whose expression levels are associated with a complex trait because of pleiotropy. We apply the method to five human complex traits using GWAS data on up to 339,224 individuals and eQTL data on 5,311 individuals, and we prioritize 126 genes (for example, TRAF1 and ANKRD55 for rheumatoid arthritis and SNX19 and NMRAL1 for schizophrenia), of which 25 genes are new candidates; 77 genes are not the nearest annotated gene to the top associated GWAS SNP. These genes provide important leads to design future functional studies to understand the mechanism whereby DNA variation leads to complex trait variation.},
  author       = {Zhu, Zhihong and Zhang, Futao and Hu, Han and Bakshi, Andrew and Robinson, Matthew Richard and Powell, Joseph E and Montgomery, Grant W and Goddard, Michael E and Wray, Naomi R and Visscher, Peter M and Yang, Jian},
  issn         = {1061-4036},
  journal      = {Nature Genetics},
  number       = {5},
  pages        = {481--487},
  publisher    = {Springer Nature},
  title        = {{Integration of summary data from GWAS and eQTL studies predicts complex trait gene targets}},
  doi          = {10.1038/ng.3538},
  volume       = {48},
  year         = {2016},
}

@article{7760,
  abstract     = {We propose a Widom-like scaling ansatz for the critical jamming transition. Our ansatz for the elastic energy shows that the scaling of the energy, compressive strain, shear strain, system size, pressure, shear stress, bulk modulus, and shear modulus are all related to each other via scaling relations, with only three independent scaling exponents. We extract the values of these exponents from already known numerical or theoretical results, and we numerically verify the resulting predictions of the scaling theory for the energy and residual shear stress. We also derive a scaling relation between pressure and residual shear stress that yields insight into why the shear and bulk moduli scale differently. Our theory shows that the jamming transition exhibits an emergent scale invariance, setting the stage for the potential development of a renormalization group theory for jamming.},
  author       = {Goodrich, Carl Peter and Liu, Andrea J. and Sethna, James P.},
  issn         = {0027-8424},
  journal      = {Proceedings of the National Academy of Sciences},
  number       = {35},
  pages        = {9745--9750},
  publisher    = {Proceedings of the National Academy of Sciences},
  title        = {{Scaling ansatz for the jamming transition}},
  doi          = {10.1073/pnas.1601858113},
  volume       = {113},
  year         = {2016},
}

@article{7761,
  abstract     = {We study the effect of dilute pinning on the jamming transition. Pinning reduces the average contact number needed to jam unpinned particles and shifts the jamming threshold to lower densities, leading to a pinning susceptibility, χp. Our main results are that this susceptibility obeys scaling form and diverges in the thermodynamic limit as χp∝|ϕ−ϕ∞c|−γp where ϕ∞c is the jamming threshold in the absence of pins. Finite-size scaling arguments yield these values with associated statistical (systematic) errors γp=1.018±0.026(0.291) in d=2 and γp=1.534±0.120(0.822) in d=3. Logarithmic corrections raise the exponent in d=2 to close to the d=3 value, although the systematic errors are very large.},
  author       = {Graves, Amy L. and Nashed, Samer and Padgett, Elliot and Goodrich, Carl Peter and Liu, Andrea J. and Sethna, James P.},
  issn         = {0031-9007},
  journal      = {Physical Review Letters},
  number       = {23},
  publisher    = {American Physical Society},
  title        = {{Pinning susceptibility: The effect of dilute, quenched disorder on jamming}},
  doi          = {10.1103/physrevlett.116.235501},
  volume       = {116},
  year         = {2016},
}

@article{7762,
  abstract     = {Characterizing structural inhomogeneity is an essential step in understanding the mechanical response of amorphous materials. We introduce a threshold-free measure based on the field of vectors pointing from the center of each particle to the centroid of the Voronoi cell in which the particle resides. These vectors tend to point in toward regions of high free volume and away from regions of low free volume, reminiscent of sinks and sources in a vector field. We compute the local divergence of these vectors, where positive values correspond to overpacked regions and negative values identify underpacked regions within the material. Distributions of this divergence are nearly Gaussian with zero mean, allowing for structural characterization using only the moments of the distribution. We explore how the standard deviation and skewness vary with the packing fraction for simulations of bidisperse systems and find a kink in these moments that coincides with the jamming transition.},
  author       = {Rieser, Jennifer M. and Goodrich, Carl Peter and Liu, Andrea J. and Durian, Douglas J.},
  issn         = {0031-9007},
  journal      = {Physical Review Letters},
  number       = {8},
  publisher    = {American Physical Society},
  title        = {{Divergence of Voronoi cell anisotropy vector: A threshold-free characterization of local structure in amorphous materials}},
  doi          = {10.1103/physrevlett.116.088001},
  volume       = {116},
  year         = {2016},
}

@article{7763,
  abstract     = {An orthogonal wavelet basis is characterized by its approximation order, which relates to the ability of the basis to represent general smooth functions on a given scale. It is known, though perhaps not widely known, that there are ways of exceeding the approximation order, i.e., achieving higher-order error in the discretized wavelet transform and its inverse. The focus here is on the development of a practical formulation to accomplish this first for 1D smooth functions, then for 1D functions with discontinuities and then for multidimensional (here 2D) functions with discontinuities. It is shown how to transcend both the wavelet approximation order and the 2D Gibbs phenomenon in representing electromagnetic fields at discontinuous dielectric interfaces that do not simply follow the wavelet-basis grid.},
  author       = {Lombardini, Richard and Acevedo, Ramiro and Kuczala, Alexander and Keys, Kerry P. and Goodrich, Carl Peter and Johnson, Bruce R.},
  issn         = {0021-9991},
  journal      = {Journal of Computational Physics},
  pages        = {244--262},
  publisher    = {Elsevier},
  title        = {{Higher-order wavelet reconstruction/differentiation filters and Gibbs phenomena}},
  doi          = {10.1016/j.jcp.2015.10.035},
  volume       = {305},
  year         = {2016},
}

@article{7764,
  abstract     = {States of self stress, organizations of internal forces in many-body systems that are in equilibrium with an absence of external forces, can be thought of as the constitutive building blocks of the elastic response of a material. In overconstrained disordered packings they have a natural mathematical correspondence with the zero-energy vibrational modes in underconstrained systems. While substantial attention in the literature has been paid to diverging length scales associated with zero- and finite-energy vibrational modes in jammed systems, less is known about the spatial structure of the states of self stress. In this work we define a natural way in which a unique state of self stress can be associated with each bond in a disordered spring network derived from a jammed packing, and then investigate the spatial structure of these bond-localized states of self stress. This allows for an understanding of how the elastic properties of a system would change upon changing the strength or even existence of any bond in the system.},
  author       = {Sussman, Daniel M. and Goodrich, Carl Peter and Liu, Andrea J.},
  issn         = {1744-683X},
  journal      = {Soft Matter},
  number       = {17},
  pages        = {3982--3990},
  publisher    = {Royal Society of Chemistry},
  title        = {{Spatial structure of states of self stress in jammed systems}},
  doi          = {10.1039/c6sm00094k},
  volume       = {12},
  year         = {2016},
}

@inproceedings{785,
  abstract     = {High memory contention is generally agreed to be a worst-case scenario for concurrent data structures. There has been a significant amount of research effort spent investigating designs which minimize contention, and several programming techniques have been proposed to mitigate its effects. However, there are currently few architectural mechanisms to allow scaling contended data structures at high thread counts. In this paper, we investigate hardware support for scalable contended data structures. We propose Lease/Release, a simple addition to standard directory-based MSI cache coherence protocols, allowing participants to lease memory, at the granularity of cache lines, by delaying coherence messages for a short, bounded period of time. Our analysis shows that Lease/Release can significantly reduce the overheads of contention for both non-blocking (lock-free) and lock-based data structure implementations, while ensuring that no deadlocks are introduced. We validate Lease/Release empirically on the Graphite multiprocessor simulator, on a range of data structures, including queue, stack, and priority queue implementations, as well as on transactional applications. Results show that Lease/Release consistently improves both throughput and energy usage, by up to 5x, both for lock-free and lock-based data structure designs.},
  author       = {Haider, Syed and Hasenplaugh, William and Alistarh, Dan-Adrian},
  publisher    = {ACM},
  title        = {{Lease/Release: Architectural support for scaling contended data structures}},
  doi          = {10.1145/2851141.2851155},
  volume       = {12-16-March-2016},
  year         = {2016},
}

@article{786,
  abstract     = {Lock-free concurrent algorithms guarantee that some concurrent operation will always make progress in a finite number of steps. Yet programmers prefer to treat concurrent code as if it were wait-free, guaranteeing that all operations always make progress. Unfortunately, designing wait-free algorithms is generally a very complex task, and the resulting algorithms are not always efficient. Although obtaining efficient wait-free algorithms has been a long-time goal for the theory community, most nonblocking commercial code is only lock-free. This article suggests a simple solution to this problem.We show that for a large class of lock-free algorithms, under scheduling conditions that approximate those found in commercial hardware architectures, lock-free algorithms behave as if they are wait-free. In other words, programmers can continue to design simple lock-free algorithms instead of complex wait-free ones, and in practice, they will get wait-free progress. Our main contribution is a new way of analyzing a general class of lock-free algorithms under a stochastic scheduler. Our analysis relates the individual performance of processes to the global performance of the system using Markov chain lifting between a complex per-process chain and a simpler system progress chain. We show that lock-free algorithms are not only wait-free with probability 1 but that in fact a general subset of lock-free algorithms can be closely bounded in terms of the average number of steps required until an operation completes. To the best of our knowledge, this is the first attempt to analyze progress conditions, typically stated in relation to a worst-case adversary, in a stochastic model capturing their expected asymptotic behavior.},
  author       = {Alistarh, Dan-Adrian and Censor Hillel, Keren and Shavit, Nir},
  journal      = {Journal of the ACM},
  number       = {4},
  publisher    = {ACM},
  title        = {{Are lock free concurrent algorithms practically wait free }},
  doi          = {10.1145/2903136},
  volume       = {63},
  year         = {2016},
}

@article{8020,
  abstract     = {Balance of cortical excitation and inhibition (EI) is thought to be disrupted in several neuropsychiatric conditions, yet it is not clear how it is maintained in the healthy human brain. When EI balance is disturbed during learning and memory in animal models, it can be restabilized via formation of inhibitory replicas of newly formed excitatory connections. Here we assess evidence for such selective inhibitory rebalancing in humans. Using fMRI repetition suppression we measure newly formed cortical associations in the human brain. We show that expression of these associations reduces over time despite persistence in behavior, consistent with inhibitory rebalancing. To test this, we modulated excitation/inhibition balance with transcranial direct current stimulation (tDCS). Using ultra-high-field (7T) MRI and spectroscopy, we show that reducing GABA allows cortical associations to be re-expressed. This suggests that in humans associative memories are stored in balanced excitatory-inhibitory ensembles that lie dormant unless latent inhibitory connections are unmasked.},
  author       = {Barron, H.C. and Vogels, Tim P and Emir, U.E. and Makin, T.R. and O’Shea, J. and Clare, S. and Jbabdi, S. and Dolan, R.J. and Behrens, T.E.J.},
  issn         = {0896-6273},
  journal      = {Neuron},
  number       = {1},
  pages        = {191--203},
  publisher    = {Elsevier},
  title        = {{Unmasking latent inhibitory connections in human cortex to reveal dormant cortical memories}},
  doi          = {10.1016/j.neuron.2016.02.031},
  volume       = {90},
  year         = {2016},
}

@inproceedings{8094,
  abstract     = {With the accelerated development of robot technologies, optimal control becomes one of the central themes of research. In traditional approaches, the controller, by its internal functionality, finds appropriate actions on the basis of the history of sensor values, guided by the goals, intentions, objectives, learning schemes, and so forth. The idea is that the controller controls the world---the body plus its environment---as reliably as possible. This paper focuses on new lines of self-organization for developmental robotics. We apply the recently developed differential extrinsic synaptic plasticity to a muscle-tendon driven arm-shoulder system from the Myorobotics toolkit. In the experiments, we observe a vast variety of self-organized behavior patterns: when left alone, the arm realizes pseudo-random sequences of different poses. By applying physical forces, the system can be entrained into definite motion patterns like wiping a table. Most interestingly, after attaching an object, the controller gets in a functional resonance with the object's internal dynamics, starting to shake spontaneously bottles half-filled with water or sensitively driving an attached pendulum into a circular mode. When attached to the crank of a wheel the neural system independently discovers how to rotate it. In this way, the robot discovers affordances of objects its body is interacting with.},
  author       = {Martius, Georg S and Hostettler, Rafael and Knoll, Alois and Der, Ralf},
  booktitle    = {Proceedings of the Artificial Life Conference 2016},
  isbn         = {9780262339360},
  location     = {Cancun, Mexico},
  pages        = {142--143},
  publisher    = {MIT Press},
  title        = {{Self-organized control of an tendon driven arm by differential extrinsic plasticity}},
  doi          = {10.7551/978-0-262-33936-0-ch029},
  volume       = {28},
  year         = {2016},
}

@unpublished{8128,
  abstract     = {The stimulus selectivity of synaptic currents in cortical neurons often shows a co-tuning of excitation and inhibition, but the mechanisms that underlie the emergence and plasticity of this co-tuning are not fully understood. Using a computational model, we show that an interaction of excitatory and inhibitory synaptic plasticity reproduces both the developmental and – when combined with a disinhibitory gate – the adult plasticity of excitatory and inhibitory receptive fields in auditory cortex. The co-tuning arises from inhibitory plasticity that balances excitation and inhibition, while excitatory stimulus selectivity can result from two different mechanisms. Inhibitory inputs with a broad stimulus tuning introduce a sliding threshold as in Bienenstock-Cooper-Munro rules, introducing an excitatory stimulus selectivity at the cost of a broader inhibitory receptive field. Alternatively, input asymmetries can be amplified by synaptic competition. The latter leaves any receptive field plasticity transient, a prediction we verify in recordings in auditory cortex.},
  author       = {Clopath, Claudia and Vogels, Tim P and Froemke, Robert C. and Sprekeler, Henning},
  booktitle    = {bioRxiv},
  pages        = {43},
  publisher    = {Cold Spring Harbor Laboratory},
  title        = {{Receptive field formation by interacting excitatory and inhibitory synaptic plasticity}},
  year         = {2016},
}

@article{813,
  abstract     = {The Gag polyprotein of retroviruses drives immature virus assembly by forming hexameric protein lattices. The assembly is primarily mediated by protein-protein interactions between capsid (CA) domains and by interactions between nucleocapsid (NC) domains and RNA. Specific interactions between NC and the viral RNA are required for genome packaging. Previously reported cryoelectron microscopy analysis of immature Mason-Pfizer monkey virus (M-PMV) particles suggested that a basic region (residues RKK) in CA may serve as an additional binding site for nucleic acids. Here, we have introduced mutations into the RKK region in both bacterial and proviral M-PMV vectors and have assessed their impact on M-PMV assembly, structure, RNA binding, budding/release, nuclear trafficking, and infectivity using in vitro and in vivo systems. Our data indicate that the RKK region binds and structures nucleic acid that serves to promote virus particle assembly in the cytoplasm. Moreover, the RKK region appears to be important for recruitment of viral genomic RNA into Gag particles, and this function could be linked to changes in nuclear trafficking. Together these observations suggest that in M-PMV, direct interactions between CA and nucleic acid play important functions in the late stages of the viral life cycle.},
  author       = {Füzik, Tibor and  Píchalová, Růžena and Florian Schur and Strohalmová, Karolína and Křížová, Ivana and Hadravová, Romana and Rumlová, Michaela and Briggs, John A and Ulbrich, Pavel and Ruml, Tomáš},
  journal      = {Journal of Virology},
  number       = {9},
  pages        = {4593 -- 4603},
  publisher    = {ASM},
  title        = {{Nucleic acid binding by Mason-Pfizer monkey virus CA promotes virus assembly and genome packaging}},
  doi          = {10.1128/JVI.03197-15},
  volume       = {90},
  year         = {2016},
}

@article{816,
  abstract     = {Immature HIV-1 assembles at and buds from the plasma membrane before proteolytic cleavage of the viral Gag polyprotein induces structural maturation. Maturation can be blocked by maturation inhibitors (MIs), thereby abolishing infectivity. The CA (capsid) and SP1 (spacer peptide 1) region of Gag is the key regulator of assembly and maturation and is the target of MIs.We applied optimized cryo-electron tomography and subtomogram averaging to resolve this region within assembled immature HIV-1 particles at 3.9 angstrom resolution and built an atomic model. The structure reveals a network of intra- And intermolecular interactions mediating immature HIV-1 assembly. The proteolytic cleavage site between CA and SP1 is inaccessible to protease.We suggest that MIs prevent CA-SP1 cleavage by stabilizing the structure, and MI resistance develops by destabilizing CA-SP1.},
  author       = {Florian Schur and Martin Obr and Hagen, Wim J and Wan, William and Jakobi, Arjen J and Kirkpatrick, Joanna M and Sachse, Carsten and Kraüsslich, Hans Georg and Briggs, John A},
  journal      = {Science},
  number       = {6298},
  pages        = {506 -- 508},
  publisher    = {American Association for the Advancement of Science},
  title        = {{An atomic model of HIV-1 capsid-SP1 reveals structures regulating assembly and maturation}},
  doi          = {10.1126/science.aaf9620},
  volume       = {353},
  year         = {2016},
}

@article{1479,
  abstract     = {Most entropy notions H(.) like Shannon or min-entropy satisfy a chain rule stating that for random variables X,Z, and A we have H(X|Z,A)≥H(X|Z)−|A|. That is, by conditioning on A the entropy of X can decrease by at most the bitlength |A| of A. Such chain rules are known to hold for some computational entropy notions like Yao’s and unpredictability-entropy. For HILL entropy, the computational analogue of min-entropy, the chain rule is of special interest and has found many applications, including leakage-resilient cryptography, deterministic encryption, and memory delegation. These applications rely on restricted special cases of the chain rule. Whether the chain rule for conditional HILL entropy holds in general was an open problem for which we give a strong negative answer: we construct joint distributions (X,Z,A), where A is a distribution over a single bit, such that the HILL entropy H HILL (X|Z) is large but H HILL (X|Z,A) is basically zero.

Our counterexample just makes the minimal assumption that NP⊈P/poly. Under the stronger assumption that injective one-way function exist, we can make all the distributions efficiently samplable.

Finally, we show that some more sophisticated cryptographic objects like lossy functions can be used to sample a distribution constituting a counterexample to the chain rule making only a single invocation to the underlying object.},
  author       = {Krenn, Stephan and Pietrzak, Krzysztof Z and Wadia, Akshay and Wichs, Daniel},
  journal      = {Computational Complexity},
  number       = {3},
  pages        = {567 -- 605},
  publisher    = {Springer},
  title        = {{A counterexample to the chain rule for conditional HILL entropy}},
  doi          = {10.1007/s00037-015-0120-9},
  volume       = {25},
  year         = {2016},
}

@article{1480,
  abstract     = {Exponential varieties arise from exponential families in statistics. These real algebraic varieties have strong positivity and convexity properties, familiar from toric varieties and their moment maps. Among them are varieties of inverses of symmetric matrices satisfying linear constraints. This class includes Gaussian graphical models. We develop a general theory of exponential varieties. These are derived from hyperbolic polynomials and their integral representations. We compare the multidegrees and ML degrees of the gradient map for hyperbolic polynomials. },
  author       = {Michałek, Mateusz and Sturmfels, Bernd and Uhler, Caroline and Zwiernik, Piotr},
  journal      = {Proceedings of the London Mathematical Society},
  number       = {1},
  pages        = {27 -- 56},
  publisher    = {Oxford University Press},
  title        = {{Exponential varieties}},
  doi          = {10.1112/plms/pdv066},
  volume       = {112},
  year         = {2016},
}

@article{1482,
  abstract     = {Plants have the ability to continously generate new organs by maintaining populations of stem cells throught their lives. The shoot apical meristem (SAM) provides a stable environment for the maintenance of stem cells. All cells inside the SAM divide, yet boundaries and patterns are maintained. Experimental evidence indicates that patterning is independent of cell lineage, thus a dynamic self-regulatory mechanism is required. A pivotal role in the organization of the SAM is played by the WUSCHEL gene (WUS). An important question in this regard is that how WUS expression is positioned in the SAM via a cell-lineage independent signaling mechanism. In this study we demonstrate via mathematical modeling that a combination of an inhibitor of the Cytokinin (CK) receptor, Arabidopsis histidine kinase 4 (AHK4) and two morphogens originating from the top cell layer, can plausibly account for the cell lineage-independent centering of WUS expression within SAM. Furthermore, our laser ablation and microsurgical experiments support the hypothesis that patterning in SAM occurs at the level of CK reception and signaling. The model suggests that the interplay between CK signaling, WUS/CLV feedback loop and boundary signals can account for positioning of the WUS expression, and provides directions for further experimental investigation.},
  author       = {Adibi, Milad and Yoshida, Saiko and Weijers, Dolf and Fleck, Christian},
  journal      = {PLoS One},
  number       = {2},
  publisher    = {Public Library of Science},
  title        = {{Centering the organizing center in the Arabidopsis thaliana shoot apical meristem by a combination of cytokinin signaling and self-organization}},
  doi          = {10.1371/journal.pone.0147830},
  volume       = {11},
  year         = {2016},
}

@article{1484,
  author       = {Chen, Xu and Wu, Shuang and Liu, Zengyu and Friml, Jiřĺ},
  journal      = {Trends in Cell Biology},
  number       = {6},
  pages        = {409 -- 419},
  publisher    = {Cell Press},
  title        = {{Environmental and endogenous control of cortical microtubule orientation}},
  doi          = {10.1016/j.tcb.2016.02.003},
  volume       = {26},
  year         = {2016},
}

@article{1485,
  abstract     = {In this article the notion of metabolic turnover is revisited in the light of recent results of out-of-equilibrium thermodynamics. By means of Monte Carlo methods we perform an exact sampling of the enzymatic fluxes in a genome scale metabolic network of E. Coli in stationary growth conditions from which we infer the metabolites turnover times. However the latter are inferred from net fluxes, and we argue that this approximation is not valid for enzymes working nearby thermodynamic equilibrium. We recalculate turnover times from total fluxes by performing an energy balance analysis of the network and recurring to the fluctuation theorem. We find in many cases values one of order of magnitude lower, implying a faster picture of intermediate metabolism.},
  author       = {De Martino, Daniele},
  journal      = {Physical Biology},
  number       = {1},
  publisher    = {IOP Publishing Ltd.},
  title        = {{Genome-scale estimate of the metabolic turnover of E. Coli from the energy balance analysis}},
  doi          = {10.1088/1478-3975/13/1/016003},
  volume       = {13},
  year         = {2016},
}

@article{1486,
  abstract     = {We review recent results concerning the mathematical properties of the Bardeen-Cooper-Schrieffer (BCS) functional of superconductivity, which were obtained in a series of papers, partly in collaboration with R. Frank, E. Hamza, S. Naboko, and J. P. Solovej. Our discussion includes, in particular, an investigation of the critical temperature for a general class of interaction potentials, as well as a study of its dependence on external fields. We shall explain how the Ginzburg-Landau model can be derived from the BCS theory in a suitable parameter regime.},
  author       = {Hainzl, Christian and Seiringer, Robert},
  journal      = {Journal of Mathematical Physics},
  number       = {2},
  publisher    = {American Institute of Physics},
  title        = {{The Bardeen–Cooper–Schrieffer functional of superconductivity and its mathematical properties}},
  doi          = {10.1063/1.4941723},
  volume       = {57},
  year         = {2016},
}

