The production and escape of Lyman-Continuum radiation from star-forming galaxies at z ∼ 2 and their redshift evolution - Matthee, Jorryt J; Sobral, David; Best, Philip; Khostovan, Ali Ahmad; Oteo, Iván; Bouwens, Rychard; Röttgering, Huub (Monthly Notices of the Royal Astronomical Society)
We study the production rate of ionizing photons of a sample of 588 Hα emitters (HAEs) and 160 Lyman-α emitters (LAEs) at z = 2.2 in the COSMOS field in order to assess the implied emissivity from galaxies, based on their ultraviolet (UV) luminosity. By exploring the rest-frame Lyman Continuum (LyC) with GALEX/NUV data, we find fesc < 2.8 (6.4) per cent through median (mean) stacking. By combining the Hα luminosity density with intergalactic medium emissivity measurements from absorption studies, we find a globally averaged 〈fesc〉 of 5.9+14.5−4.2 per cent at z = 2.2 if we assume HAEs are the only source of ionizing photons. We find similarly low values of the global 〈fesc〉 at z ≈ 3–5, also ruling out a high 〈fesc〉 at z < 5. These low escape fractions allow us to measure ξion, the number of produced ionizing photons per unit UV luminosity, and investigate how this depends on galaxy properties. We find a typical ξion ≈ 1024.77 ± 0.04 Hz erg−1 for HAEs and ξion ≈ 1025.14 ± 0.09 Hz erg−1 for LAEs. LAEs and low-mass HAEs at z = 2.2 show similar values of ξion as typically assumed in the reionization era, while the typical HAE is three times less ionizing. Due to an increasing ξion with increasing EW(Hα), ξion likely increases with redshift. This evolution alone is fully in line with the observed evolution of ξion between z ≈ 2 and 5, indicating a typical value of ξion ≈ 1025.4 Hz erg−1 in the reionization era.
Keywords: Space and Planetary Science; Astronomy and Astrophysics; galaxies: evolution; galaxies: high-redshift; cosmology: observations; dark ages; reionization; first stars

The origin of scatter in the stellar mass–halo mass relation of central galaxies in the EAGLE simulation - Matthee, Jorryt J; Schaye, Joop; Crain, Robert A.; Schaller, Matthieu; Bower, Richard; Theuns, Tom (Monthly Notices of the Royal Astronomical Society)
We use the hydrodynamical EAGLE simulation to study the magnitude and origin of the scatter in the stellar mass–halo mass relation for central galaxies. We separate cause and effect by correlating stellar masses in the baryonic simulation with halo properties in a matched dark matter only (DMO) simulation. The scatter in stellar mass increases with redshift and decreases with halo mass. At z = 0.1, it declines from 0.25 dex at M200, DMO ≈ 1011 M⊙ to 0.12 dex at M200, DMO ≈ 1013 M⊙, but the trend is weak above 1012 M⊙. For M200, DMO < 1012.5 M⊙ up to 0.04 dex of the scatter is due to scatter in the halo concentration. At fixed halo mass, a larger stellar mass corresponds to a more concentrated halo. This is likely because higher concentrations imply earlier formation times and hence more time for accretion and star formation, and/or because feedback is less efficient in haloes with higher binding energies. The maximum circular velocity, Vmax, DMO, and binding energy are therefore more fundamental properties than halo mass, meaning that they are more accurate predictors of stellar mass, and we provide fitting formulae for their relations with stellar mass. However, concentration alone cannot explain the total scatter in the Mstar−M200,DMO relation, and it does not explain the scatter in Mstar–Vmax, DMO. Halo spin, sphericity, triaxiality, substructure and environment are also not responsible for the remaining scatter, which thus could be due to more complex halo properties or non-linear/stochastic baryonic effects.
Keywords: Space and Planetary Science; Astronomy and Astrophysics; galaxies: evolution; galaxies: formation; galaxies: haloes; cosmology: theory

A 1.4 deg2 blind survey for C II], C III] and C IV at z ∼ 0.7–1.5 – I. Nature, morphologies and equivalent widths - Stroe, Andra; Sobral, David; Matthee, Jorryt J; Calhau, João; Oteo, Ivan (Monthly Notices of the Royal Astronomical Society)
While traditionally associated with active galactic nuclei (AGN), the properties of the C II] (λ = 2326 Å), C III] (λ, λ = 1907, 1909 Å) and C IV (λ, λ = 1549, 1551 Å) emission lines are still uncertain as large, unbiased samples of sources are scarce. We present the first blind, statistical study of C II], C III] and C IV emitters at z ∼ 0.68, 1.05, 1.53, respectively, uniformly selected down to a flux limit of ∼4 × 10−17 erg s−1 cm−1 through a narrow-band survey covering an area of ∼1.4 deg2 over COSMOS and UDS. We detect 16 C II], 35 C III] and 17 C IV emitters, whose nature we investigate using optical colours as well as Hubble Space Telescope (HST), X-ray, radio and far-infrared data. We find that z ∼ 0.7 C II] emitters are consistent with a mixture of blue (UV slope β = −2.0 ± 0.4) star-forming (SF) galaxies with discy HST structure and AGN with Seyfert-like morphologies. Bright C II] emitters have individual X-ray detections as well as high average black hole accretion rates (BHARs) of ∼0.1 M⊙ yr−1. C III] emitters at z ∼ 1.05 trace a general population of SF galaxies, with β = −0.8 ± 1.1, a variety of optical morphologies, including isolated and interacting galaxies and low BHAR (<0.02 M⊙ yr−1). Our C IV emitters at z ∼ 1.5 are consistent with young, blue quasars (β ∼ −1.9) with point-like optical morphologies, bright X-ray counterparts and large BHAR (0.8  M⊙ yr−1). We also find some surprising C II], C III] and C IV emitters with rest-frame equivalent widths (EWs) that could be as large as 50–100 Å. AGN or spatial offsets between the UV continuum stellar disc and the line-emitting regions may explain the large EW. These bright C II], C III] and C IV emitters are ideal candidates for spectroscopic follow-up to fully unveil their nature.
Keywords: Space and Planetary Science; Astronomy and Astrophysics; galaxies: active; galaxies: high-redshift; quasars: emission lines; galaxies: star formation; cosmology: observations

A 1.4 deg2 blind survey for C II], C III] and C IV at z ∼ 0.7–1.5 – II. Luminosity functions and cosmic average line ratios - Stroe, Andra; Sobral, David; Matthee, Jorryt J; Calhau, João; Oteo, Ivan (Monthly Notices of the Royal Astronomical Society)
Recently, the C III] and C IV emission lines have been observed in galaxies in the early Universe (z > 5), providing new ways to measure their redshift and study their stellar populations and active galactic nuclei (AGN). We explore the first blind C II], C III] and C IV survey (z ∼ 0.68, 1.05, 1.53, respectively) presented in Stroe et al. (2017). We derive luminosity functions (LF) and study properties of C II], C III] and C IV line emitters through comparisons to the LFs of H α and Ly α emitters, UV selected star-forming (SF) galaxies and quasars at similar redshifts. The C II] LF at z ∼ 0.68 is equally well described by a Schechter or a power-law LF, characteristic of a mixture of SF and AGN activity. The C III] LF (z ∼ 1.05) is consistent to a scaled down version of the Schechter H α and Ly α LF at their redshift, indicating a SF origin. In stark contrast, the C IV LF at z ∼ 1.53 is well fit by a power-law, quasar-like LF. We find that the brightest UV sources (MUV < −22) will universally have C III] and C IV emission. However, on average, C III] and C IV are not as abundant as H α or Ly α emitters at the same redshift, with cosmic average ratios of ∼0.02–0.06 to H α and ∼0.01–0.1 to intrinsic Ly α. We predict that the C III] and C IV lines can only be truly competitive in confirming high-redshift candidates when the hosts are intrinsically bright and the effective Ly α escape fraction is below 1 per cent. While C III] and C IV were proposed as good tracers of young, relatively low-metallicity galaxies typical of the early Universe, we find that, at least at z ∼ 1.5, C IV is exclusively hosted by AGN/quasars, especially at large line equivalent widths.
Keywords: Space and Planetary Science; Astronomy and Astrophysics; galaxies: active; galaxies: high redshift; galaxies: luminosity function; mass function; quasars: emission lines; star formation; cosmology: observations

Spectroscopic properties of luminous Ly α emitters at z ≈ 6–7 and comparison to the Lyman-break population - Matthee, Jorryt J; Sobral, David; Darvish, Behnam; Santos, Sérgio; Mobasher, Bahram; Paulino-Afonso, Ana; Röttgering, Huub; Alegre, Lara (Monthly Notices of the Royal Astronomical Society)
We present spectroscopic follow-up of candidate luminous Ly α emitters (LAEs) at z = 5.7–6.6 in the SA22 field with VLT/X-SHOOTER. We confirm two new luminous LAEs at z = 5.676 (SR6) and z = 6.532 (VR7), and also present HST follow-up of both sources. These sources have luminosities LLy α ≈ 3 × 1043 erg s−1, very high rest-frame equivalent widths of EW0 ≳ 200 Å and narrow Ly α lines (200–340 km s−1). VR7 is the most UV-luminous LAE at z > 6.5, with M1500 = −22.5, even brighter in the UV than CR7. Besides Ly α, we do not detect any other rest-frame UV lines in the spectra of SR6 and VR7, and argue that rest-frame UV lines are easier to observe in bright galaxies with low Ly α equivalent widths. We confirm that Ly α line widths increase with Ly α luminosity at z = 5.7, while there are indications that Ly α lines of faint LAEs become broader at z = 6.6, potentially due to reionization. We find a large spread of up to 3 dex in UV luminosity for >L⋆ LAEs, but find that the Ly α luminosity of the brightest LAEs is strongly related to UV luminosity at z = 6.6. Under basic assumptions, we find that several LAEs at z ≈ 6–7 have Ly α escape fractions ≳ 100  per cent, indicating bursty star formation histories, alternative Ly α production mechanisms, or dust attenuating Ly α emission differently than UV emission. Finally, we present a method to compute ξion, the production efficiency of ionizing photons, and find that LAEs at z ≈ 6–7 have high values of log10(ξion/Hz erg−1) ≈ 25.51 ± 0.09 that may alleviate the need for high Lyman-Continuum escape fractions required for reionization.
Keywords: Space and Planetary Science; Astronomy and Astrophysics; galaxies: evolution – galaxies: high-redshift; dark ages; reionization; first stars; cosmology: observations

The KMOS Deep Survey (KDS) – I. Dynamical measurements of typical star-forming galaxies at z ≃ 3.5 - Turner, O. J.; Cirasuolo, M.; Harrison, C. M.; McLure, R. J.; Dunlop, J. S.; Swinbank, A. M.; Johnson, H. L.; Sobral, D.; Matthee, Jorryt J; Sharples, R. M. (Monthly Notices of the Royal Astronomical Society)
We present dynamical measurements from the KMOS (K-band multi-object spectrograph) Deep Survey (KDS), which comprises 77 typical star-forming galaxies at z ≃ 3.5 in the mass range 9.0 < log (M⋆/M⊙) < 10.5. These measurements constrain the internal dynamics, the intrinsic velocity dispersions (σint) and rotation velocities (VC) of galaxies in the high-redshift Universe. The mean velocity dispersion of the galaxies in our sample is σint=70.8+3.3−3.1kms−1⁠, revealing that the increasing average σint with increasing redshift, reported for z ≲ 2, continues out to z ≃ 3.5. Only 36 ± 8 per cent of our galaxies are rotation-dominated (VC/σint > 1), with the sample average VC/σint value much smaller than at lower redshift. After carefully selecting comparable star-forming samples at multiple epochs, we find that the rotation-dominated fraction evolves with redshift with a z−0.2 dependence. The rotation-dominated KDS galaxies show no clear offset from the local rotation velocity–stellar mass (i.e. VC–M⋆) relation, although a smaller fraction of the galaxies are on the relation due to the increase in the dispersion-dominated fraction. These observations are consistent with a simple equilibrium model picture, in which random motions are boosted in high-redshift galaxies by a combination of the increasing gas fractions, accretion efficiency, specific star formation rate and stellar feedback and which may provide significant pressure support against gravity on the galactic disc scale.
Keywords: Space and Planetary Science; Astronomy and Astrophysics; galaxies: evolution; galaxies: high-redshift; galaxies: kinematics and dynamics

Cis-cinnamic acid is a novel natural auxin efflux inhibitor that promotes lateral root formation - Steenackers, Ward; Klíma, Petr; Quareshy, Mussa; Cesarino, Igor; Kumpf, Robert; Corneillie, Sander; Araújo, Pedro; Viaene, Tom; Goeminne, Geert; Nowack, Moritz; Ljung, Karin; Friml, Jirí; et al. (Plant Physiology)
Auxin steers numerous physiological processes in plants, making the tight control of its endogenous levels and spatiotemporal distribution a necessity. This regulation is achieved by different mechanisms, including auxin biosynthesis, metabolic conversions, degradation, and transport. Here, we introduce cis-cinnamic acid (c-CA) as a novel and unique addition to a small group of endogenous molecules affecting in planta auxin concentrations. c-CA is the photo-isomerization product of the phenylpropanoid pathway intermediate trans-CA (t-CA). When grown on c-CA-containing medium, an evolutionary diverse set of plant species were shown to exhibit phenotypes characteristic for high auxin levels, including inhibition of primary root growth, induction of root hairs, and promotion of adventitious and lateral rooting. By molecular docking and receptor binding assays, we showed that c-CA itself is neither an auxin nor an anti-auxin, and auxin profiling data revealed that c-CA does not significantly interfere with auxin biosynthesis. Single cell-based auxin accumulation assays showed that c-CA, and not t-CA, is a potent inhibitor of auxin efflux. Auxin signaling reporters detected changes in spatiotemporal distribution of the auxin response along the root of c-CA-treated plants, and long-distance auxin transport assays showed no inhibition of rootward auxin transport. Overall, these results suggest that the phenotypes of c-CA-treated plants are the consequence of a local change in auxin accumulation, induced by the inhibition of auxin efflux. This work reveals a novel mechanism how plants may regulate auxin levels and adds a novel, naturally occurring molecule to the chemical toolbox for the studies of auxin homeostasis.

Dynamics of ferrofluidic flow in the Taylor-Couette system with a small aspect ratio - Altmeyer, Sebastian; Do, Younghae; Lai, Ying (Scientific Reports)
We investigate fundamental nonlinear dynamics of ferrofluidic Taylor-Couette flow - flow confined be-tween two concentric independently rotating cylinders - consider small aspect ratio by solving the ferro-hydrodynamical equations, carrying out systematic bifurcation analysis. Without magnetic field, we find steady flow patterns, previously observed with a simple fluid, such as those containing normal one- or two vortex cells, as well as anomalous one-cell and twin-cell flow states. However, when a symmetry-breaking transverse magnetic field is present, all flow states exhibit stimulated, finite two-fold mode. Various bifurcations between steady and unsteady states can occur, corresponding to the transitions between the two-cell and one-cell states. While unsteady, axially oscillating flow states can arise, we also detect the emergence of new unsteady flow states. In particular, we uncover two new states: one contains only the azimuthally oscillating solution in the configuration of the twin-cell flow state, and an-other a rotating flow state. Topologically, these flow states are a limit cycle and a quasiperiodic solution on a two-torus, respectively. Emergence of new flow states in addition to observed ones with classical fluid, indicates that richer but potentially more controllable dynamics in ferrofluidic flows, as such flow states depend on the external magnetic field.

Cell migration: Making the waves - Müller, Jan; Sixt, Michael K (Current Biology)
Coordinated changes of cell shape are often the result of the excitable, wave-like dynamics of the actin cytoskeleton. New work shows that, in migrating cells, protrusion waves arise from mechanochemical crosstalk between adhesion sites, membrane tension and the actin protrusive machinery.

Universal properties of high temperature superconductors from real space pairing t-J-U model and its quantitative comparison with experiment - Spałek, Jozef; Zegrodnik, Michał; Kaczmarczyk, Jan (Physical Review B - Condensed Matter and Materials Physics)
Selected universal experimental properties of high-temperature superconducting (HTS) cuprates have been singled out in the last decade. One of the pivotal challenges in this field is the designation of a consistent interpretation framework within which we can describe quantitatively the universal features of those systems. Here we analyze in a detailed manner the principal experimental data and compare them quantitatively with the approach based on a single-band model of strongly correlated electrons supplemented with strong antiferromagnetic (super)exchange interaction (the so-called t−J−U model). The model rationale is provided by estimating its microscopic parameters on the basis of the three-band approach for the Cu-O plane. We use our original full Gutzwiller wave-function solution by going beyond the renormalized mean-field theory (RMFT) in a systematic manner. Our approach reproduces very well the observed hole doping (δ) dependence of the kinetic-energy gain in the superconducting phase, one of the principal non-Bardeen-Cooper-Schrieffer features of the cuprates. The calculated Fermi velocity in the nodal direction is practically δ-independent and its universal value agrees very well with that determined experimentally. Also, a weak doping dependence of the Fermi wave vector leads to an almost constant value of the effective mass in a pure superconducting phase which is both observed in experiment and reproduced within our approach. An assessment of the currently used models (t−J, Hubbard) is carried out and the results of the canonical RMFT as a zeroth-order solution are provided for comparison to illustrate the necessity of the introduced higher-order contributions.

Unconventional superconductivity in generalized Hubbard model role of electron–hole symmetry breaking terms - Wysokiński, Marcin; Kaczmarczyk, Jan (Journal of Physics: Condensed Matter)
We investigate the effect of the electron-hole (e-h) symmetry breaking on d-wave superconductivity induced by non-local effects of correlations in the generalized Hubbard model. The symmetry breaking is introduced in a two-fold manner: by the next-to-nearest neighbor hopping of electrons and by the charge-bond interaction - the off-diagonal term of the Coulomb potential. Both terms lead to a pronounced asymmetry of the superconducting order parameter. The next-to-nearest neighbor hopping enhances superconductivity for h-doping, while diminishes it for e-doping. The charge-bond interaction alone leads to the opposite effect and, additionally, to the kinetic-energy gain upon condensation in the underdoped regime. With both terms included, with similar amplitudes, the height of the superconducting dome and the critical doping remain in favor of h-doping. The influence of the charge-bond interaction on deviations from symmetry of the shape of the gap at the Fermi surface in the momentum space is briefly discussed.

FliPer: Checking the reliability of global seismic parameters from automatic pipelines - Bugnet, Lisa Annabelle; Garcia, R. A.; Davies, G. R.; Mathur, S.; Corsaro, E. (arXiv)
Our understanding of stars through asteroseismic data analysis is limited by our ability to take advantage of the huge amount of observed stars provided by space missions such as CoRoT, Kepler , K2, and soon TESS and PLATO. Global seismic pipelines provide global stellar parameters such as mass and radius using the mean seismic parameters, as well as the effective temperature. These pipelines are commonly used automatically on thousands of stars observed by K2 for 3 months (and soon TESS for at least ∼ 1 month). However, pipelines are not immune from misidentifying noise peaks and stellar oscillations. Therefore, new validation techniques are required to assess the quality of these results. We present a new metric called FliPer (Flicker in Power), which takes into account the average variability at all measured time scales. The proper calibration of FliPer enables us to obtain good estimations of global stellar parameters such as surface gravity that are robust against the influence of noise peaks and hence are an excellent way to find faults in asteroseismic pipelines.
Keywords: asteroseismology - methods; data analysis - stars; oscillations

Capacity releasing diffusion for speed and locality - Wang, Di; Fountoulakis, Kimon; Henzinger, Monika H; Mahoney, Michael W.; Rao , Satish (Proceedings of the 34th International Conference on Machine Learning)
Diffusions and related random walk procedures are of central importance in many areas of machine learning, data analysis, and applied mathematics. Because they spread mass agnostically at each step in an iterative manner, they can sometimes spread mass “too aggressively,” thereby failing to find the “right” clusters. We introduce a novel Capacity Releasing Diffusion (CRD) Process, which is both faster and stays more local than the classical spectral diffusion process. As an application, we use our CRD Process to develop an improved local algorithm for graph clustering. Our local graph clustering method can find local clusters in a model of clustering where one begins the CRD Process in a cluster whose vertices are connected better internally than externally by an O(log2n) factor, where n is the number of nodes in the cluster. Thus, our CRD Process is the first local graph clustering algorithm that is not subject to the well-known quadratic Cheeger barrier. Our result requires a certain smoothness condition, which we expect to be an artifact of our analysis. Our empirical evaluation demonstrates improved results, in particular for realistic social graphs where there are moderately good—but not very good—clusters.

Sublinear-time maintenance of breadth-first spanning trees in partially dynamic networks - Henzinger, Monika H; Krinninger, Sebastian; Nanongkai, Danupon (ACM Transactions on Algorithms)
We study the problem of maintaining a breadth-first spanning tree (BFS tree) in partially dynamic distributed networks modeling a sequence of either failures or additions of communication links (but not both). We present deterministic (1+ϵ)-approximation algorithms whose amortized time (over some number of link changes) is sublinear in D, the maximum diameter of the network. Our technique also leads to a deterministic (1+ϵ)-approximate incremental algorithm for single-source shortest paths in the sequential (usual RAM) model. Prior to our work, the state of the art was the classic exact algorithm of Even and Shiloach (1981), which is optimal under some assumptions (Roditty and Zwick 2011; Henzinger et al. 2015). Our result is the first to show that, in the incremental setting, this bound can be beaten in certain cases if some approximation is allowed.

Maximizing a submodular function with viability constraints - Dvořák, Wolfgang; Henzinger, Monika H; Williamson, David P. (Algorithmica)
We study the problem of maximizing a monotone submodular function with viability constraints. This problem originates from computational biology, where we are given a phylogenetic tree over a set of species and a directed graph, the so-called food web, encoding viability constraints between these species. These food webs usually have constant depth. The goal is to select a subset of k species that satisfies the viability constraints and has maximal phylogenetic diversity. As this problem is known to be NP-hard, we investigate approximation algorithms. We present the first constant factor approximation algorithm if the depth is constant. Its approximation ratio is (1−1e√). This algorithm not only applies to phylogenetic trees with viability constraints but for arbitrary monotone submodular set functions with viability constraints. Second, we show that there is no (1−1/e+ϵ)-approximation algorithm for our problem setting (even for additive functions) and that there is no approximation algorithm for a slight extension of this setting.
Keywords: Approximation algorithms; Submodular functions; Phylogenetic diversity; Viability constraints

D inf s optimality in copula models - Perrone, Elisa; Rappold, Andreas; Müller, Werner (Statistical Methods and Applications)
Optimum experimental design theory has recently been extended for parameter estimation in copula models. The use of these models allows one to gain in flexibility by considering the model parameter set split into marginal and dependence parameters. However, this separation also leads to the natural issue of estimating only a subset of all model parameters. In this work, we treat this problem with the application of the (Formula presented.)-optimality to copula models. First, we provide an extension of the corresponding equivalence theory. Then, we analyze a wide range of flexible copula models to highlight the usefulness of (Formula presented.)-optimality in many possible scenarios. Finally, we discuss how the usage of the introduced design criterion also relates to the more general issue of copula selection and optimal design for model discrimination.

Spatial gene frequency waves under genotype dependent dispersal - Novak, Sebastian; Kollár, Richard (Genetics)
Dispersal is a crucial factor in natural evolution, since it determines the habitat experienced by any population and defines the spatial scale of interactions between individuals. There is compelling evidence for systematic differences in dispersal characteristics within the same population, i.e., genotype-dependent dispersal. The consequences of genotype-dependent dispersal on other evolutionary phenomena, however, are poorly understood. In this article we investigate the effect of genotype-dependent dispersal on spatial gene frequency patterns, using a generalization of the classical diffusion model of selection and dispersal. Dispersal is characterized by the variance of dispersal (diffusion coefficient) and the mean displacement (directional advection term). We demonstrate that genotype-dependent dispersal may change the qualitative behavior of Fisher waves, which change from being “pulled” to being “pushed” wave fronts as the discrepancy in dispersal between genotypes increases. The speed of any wave is partitioned into components due to selection, genotype-dependent variance of dispersal, and genotype-dependent mean displacement. We apply our findings to wave fronts maintained by selection against heterozygotes. Furthermore, we identify a benefit of increased variance of dispersal, quantify its effect on the speed of the wave, and discuss the implications for the evolution of dispersal strategies.

The Voronoi functional is maximized by the Delaunay triangulation in the plane - Edelsbrunner, Herbert; Glazyrin, Alexey; Musin, Oleg; Nikitenko, Anton (Combinatorica)
We introduce the Voronoi functional of a triangulation of a finite set of points in the Euclidean plane and prove that among all geometric triangulations of the point set, the Delaunay triangulation maximizes the functional. This result neither extends to topological triangulations in the plane nor to geometric triangulations in three and higher dimensions.

Lower bounds on key derivation for square-friendly applications - Skórski, Maciej
Security of cryptographic applications is typically defined by security games. The adversary, within certain resources, cannot win with probability much better than 0 (for unpredictability applications, like one-way functions) or much better than 1/2 (indistinguishability applications for instance encryption schemes). In so called squared-friendly applications the winning probability of the adversary, for different values of the application secret randomness, is not only close to 0 or 1/2 on average, but also concentrated in the sense that its second central moment is small. The class of squared-friendly applications, which contains all unpredictability applications and many indistinguishability applications, is particularly important for key derivation. Barak et al. observed that for square-friendly applications one can beat the "RT-bound", extracting secure keys with significantly smaller entropy loss. In turn Dodis and Yu showed that in squared-friendly applications one can directly use a "weak" key, which has only high entropy, as a secure key. In this paper we give sharp lower bounds on square security assuming security for "weak" keys. We show that any application which is either (a) secure with weak keys or (b) allows for entropy savings for keys derived by universal hashing, must be square-friendly. Quantitatively, our lower bounds match the positive results of Dodis and Yu and Barak et al. (TCC\'13, CRYPTO\'11) Hence, they can be understood as a general characterization of squared-friendly applications. While the positive results on squared-friendly applications where derived by one clever application of the Cauchy-Schwarz Inequality, for tight lower bounds we need more machinery. In our approach we use convex optimization techniques and some theory of circular matrices.

Cumulative space in black-white pebbling and resolution - Alwen, Joel F; De Rezende, Susanna; Nordstrom, Jakob; Vinyals, Marc
We study space complexity and time-space trade-offs with a focus not on peak memory usage but on overall memory consumption throughout the computation. Such a cumulative space measure was introduced for the computational model of parallel black pebbling by [Alwen and Serbinenko ’15] as a tool for obtaining results in cryptography. We consider instead the non- deterministic black-white pebble game and prove optimal cumulative space lower bounds and trade-offs, where in order to minimize pebbling time the space has to remain large during a significant fraction of the pebbling. We also initiate the study of cumulative space in proof complexity, an area where other space complexity measures have been extensively studied during the last 10–15 years. Using and extending the connection between proof complexity and pebble games in [Ben-Sasson and Nordström ’08, ’11] we obtain several strong cumulative space results for (even parallel versions of) the resolution proof system, and outline some possible future directions of study of this, in our opinion, natural and interesting space measure.