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We study the elliptic zastava spaces, their versions (twisted, Coulomb, Mirkovic local spaces, reduced) and relations with monowalls moduli spaces and Feigin-Odesskii moduli spaces of $G$-bundles with parabolic structure on an elliptic curve., Comment: v2: final published version

A process of atomic layer deposition combined with self assembled monolayers was used to investigate the possible modification of polyurethane paint surfaces. First, we used an ALD process to produce thin and uniform Al2O3 coatings of these surfaces at temperatures as low as 40 degrees. We then successfully achieved the addition of 16phosphonohexadecanoic acid SAMs to the Al2O3 coated paint samples. Al2O3 coatings reduced the contact angle of the PUR surfaces from 110 to 10 degrees, accompanied by an initial hydrophobicity which however was not stable. over time. Addition of SAMs on the Al2O3 induced a sustained reduction in their contact angles to 60 to 70 degrees, and aging of the samples revealed a further decrease to 25 to40 degrees. Testing of the Al2O3 16 PHA coating in a Weather OMeter revealed its durability even under harsh outdoor conditions. These experimental results show that by combining ALD with SAMs it is possible to produce durable coatings with modified hydrophilic or hydrophobic properties that are stable over time. The use of SAMs with different end groups may allow fine tuning of the coating wetting properties

These notes aim at providing a complete and systematic account of some foundational aspects of algebraic supergeometry, namely, the extension to the geometry of superschemes of many classical notions, techniques and results that make up the general backbone of algebraic geometry, most of them originating from Grothendieck's work. In particular, we extend to algebraic supergeometry such notions as projective and proper morphisms, finiteness of the cohomology, vector and projective bundles, cohomology base change, semicontinuity theorems, relative duality, Castelnuovo-Mumford regularity, flattening, Hilbert and Quot schemes, faithfully flat descent, quotient \'etale relations (notably, Picard schemes), among others. Some results may be found elsewhere, and, in particular, there is some overlap with a recent preprint by Moosavian and Zhou. However, many techniques and constructions are presented here for the first time, notably, a first development of Grothendieck relative duality for proper morphisms of superschemes, the construction of the Hilbert superscheme in a more general situation than the one already known (which in particular allows one to treat the case of sub-superschemes of supergrassmannians), and a rigorous construction of the Picard superscheme for a locally superprojective morphism of noetherian superschemes with geometrically integral fibres. Moreover, some of the proofs given here are new as well, even when restricted to ordinary schemes. In a final section we construct a period map from an open substack of the moduli of proper and smooth supercurves to the moduli stack of principally polarized abelian superchemes., Comment: 86 pages. v2: 88 pages. Added a comparison of the superperiod map with the D'Hoker-Phong superperiod matrix. Minor corrections. v3: final version accepted for publication in Advances in Mathematics. Minor corrections, changes and additions as suggested by the referee

In this paper, generalizing the construction of \cite{HP1}, we equip the relative moduli stack of complexes over a Calabi-Yau fibration (possibly with singular fibers) with a shifted Poisson structure. Applying this construction to the anticanonical linear systems on surfaces, we get examples of compatible Poisson brackets on projective spaces extending Feigin-Odesskii Poisson brackets. Computing explicitly the corresponding compatible brackets coming from Hirzebruch surfaces, we recover the brackets defined by Odesskii-Wolf in \cite{OW}., Comment: This is an updated version to appear on Journal of Topology

Motivated by indoor localization by tripwire lasers, we study the problem of cutting a polygon into small-size pieces, using the chords of the polygon. Several versions are considered, depending on the definition of the "size" of a piece. In particular, we consider the area, the diameter, and the radius of the largest inscribed circle as a measure of the size of a piece. We also consider different objectives, either minimizing the maximum size of a piece for a given number of chords, or minimizing the number of chords that achieve a given size threshold for the pieces. We give hardness results for polygons with holes and approximation algorithms for multiple variants of the problem., Comment: This paper will appear in ESA2020, Track A proceedings

We prove that the moduli of stable supercurves with punctures is a smooth proper DM stack and study an analog of the Mumford's isomorphism for its canonical line bundle., Comment: v1: 63 pages; v2: 74 pages, some details added, exposition improved

We describe a geometric construction of all nondegenerate trigonometric solutions of the associative and classical Yang-Baxter equations. In the associative case the solutions come from symmetric spherical orders over the irreducible nodal curve of arithmetic genus $1$, while in the Lie case they come from spherical sheaves of Lie algebras over the same curve., Comment: v2:37 pages, exposition improved

This paper introduces Pythia, the first fuzzer that augments grammar-based fuzzing with coverage-guided feedback and a learning-based mutation strategy for stateful REST API fuzzing. Pythia uses a statistical model to learn common usage patterns of a target REST API from structurally valid seed inputs. It then generates learning-based mutations by injecting a small amount of noise deviating from common usage patterns while still maintaining syntactic validity. Pythia's mutation strategy helps generate grammatically valid test cases and coverage-guided feedback helps prioritize the test cases that are more likely to find bugs. We present experimental evaluation on three production-scale, open-source cloud services showing that Pythia outperforms prior approaches both in code coverage and new bugs found. Using Pythia, we found 29 new bugs which we are in the process of reporting to the respective service owners.

We demonstrate a 20-fold enhancement in the strength of the RKKY interlayer exchange in dilute-ferromagnet/normal-metal multilayers by incorporating ultrathin Fe layers at the interfaces. Additionally, the resulting increase in the interface magnetic polarization profoundly affects the finite-size effects, sharpening the Curie transition of the multilayer, while allowing to separately tune its Curie temperature via intralayer magnetic dilution. These results should be useful for designing functional materials for applications in magneto-caloric micro-refrigeration and thermally-assisted spin-electronics., Comment: 5 pages, 4 figures

The effect of substitution atoms on the energy spectrum and the electrical conductivity of graphene was investigated in a Lifshitz one-electron tight-binding model. It is established that the ordering of impurity atoms results in a gap in the energy spectrum of electrons whose width depends on the order parameter and on the magnitude of the scattering potential. It is shown that if the order parameter is close to its maximum value, there are peaks associated with localized impurity states on the energy curve of the electron states density at the edges of the energy gap. At the electron concentration at which the Fermi level enters the gap region, the electrical conductivity is zero, and the metal-dielectric transition occurs. If the Fermi level falls in the region of the energy band, the electron relaxation time and electrical conductivity tend to infinity when the order parameter reaches its maximum value. The analytical calculations of the electron density and of the electrical conductivity of graphene, made in the limiting case of weak scattering, are compared with the results of the numerical calculations for different scattering potentials., Comment: 14 pages, 3 figures

We investigate the spin transport and ferromagnetic resonance properties of giant magnetoresistive (GMR) Co/Cu-Ni multilayers with variable levels of Ni doping in the Cu spacer. We present an experimental evidence for a magnetic-to-diamagnetic transition in the atomic magnetic moment of Ni in the Cu matrix for concentrations below 15 at. % Ni. As its concentration is increased, Ni atoms turn into spin scattering centers, which is manifested experimentally as a step-like change in the GMR of the multilayers. This behavior is observed in multilayers with gradient-doped Cu spacers, where only the inner region was doped with Ni. In the uniformly doped spacers the GMR decreases monotonously with increasing Ni content, indicating that Ni atoms are magnetic and act as spin relaxation centers in the entire dopant-concentration range studied. We explain the difference in the observed GMR behavior as due to a strong magnetic proximity effect in the uniform spacers, which is efficiently suppressed in the gradient spacers. The observed magnetic phase transition is fully supported by our detailed ab-initio calculations, taking into consideration structural relaxation in the system as well as potential Ni clustering. Controlling the loss or gain of the atomic magnetism for a specific dopant can be a tool in probing and controlling spin relaxation in materials and devices for spin-valve and spin-torque based applications., Comment: 11 pages, 5 figures

Indirect exchange coupling in magnetic multilayers, also known as the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, is known to be highly effective in controlling the interlayer alignment of the magnetization. This coupling is typically fixed at the stage of the multilayer fabrication and does not allow ex-situ control needed for device applications. It is highly desirable, in addition to the orientational control, to also control the magnitude of the intralayer magnetization, ideally switch it on/off by switching the relevant RKKY coupling. Here we demonstrate a magnetic multilayer material, incorporating thermally -- as well as field-controlled RKKY exchange, focused on to a dilute ferromagnetic alloy layer and driving it though it's Curie transition. Such on/off magnetization switching of a thin ferromagnet, performed repeatably and fully reproducibly within a low-field sweep, results in a giant magnetocaloric effect, with the estimated isothermal entropy change of -10 mJ/K cm^3 under an external field of ~10 mT, which greatly exceeds the performance of the best rare-earth based materials used in the adiabatic-demagnetization refrigeration systems., Comment: 8 pages, 4 figures, Supplemental material (2 pages, 2 figures)

The orthogonality of Hilbert spaces whose elements can be represented as simple and double layer potentials is determined. Conditions of well-posed solvability of integral equations for the sum of simple and double layer potentials equivalent to double-sided Dirichlet, Neumann, and Dirichlet-Neumann boundary value problems for the Laplacian are established in the Hilbert space, elements of which as well as their normal derivatives have the jump through boundary surface. The properties of boundary operators that relate the double-sided boundary conditions of different types for the three-dimensional Laplace equation are investigated., Comment: 7 pages. arXiv admin note: substantial text overlap with arXiv:1910.01301

For an in invertible quasihomogeneous singularity $w$ we prove an all-genus mirror theorem establishing an isomorphism between two cohomological field theories. On the $B$-side it is the Saito-Givental theory given by a certain choice of a primitive form. On the $A$-side, it is the reduced matrix factorization CohFT for the dual singularity $w^T$ with the maximal diagonal symmetry group., Comment: 58 pages, 3rd version

Fungi live within diverse environments and survive well under extreme conditions that are usually beyond the tolerance of most other organisms. In different environments fungi are known to induce precipitation of a wide range of minerals. Various species of fungi have been shown to facilitate calcium carbonate mineralization. Here, inspired by examples of needle-fiber calcite formed via fungus-induced biomineralization typically observed in soils and sediments, we utilized inactivated fungus to synthetically induce precipitation of CaCO3 needles. To our knowledge, the feasibility of growing aragonitic needles within fungal mycelium in vitro has not been previously demonstrated. The needles we obtained were curved, displayed hexagonal facets, and demonstrated high-aspect ratios close to 60. The size and shape of these synthetic needles matched those of the mycelium of the natural fungus. Utilizing high-resolution characterization techniques, we studied the morphology and the micro- and nanostructures of the aragonitic needles. Our findings showed that even inactivated fungal mycelium, if present in the crystallization environment, can serve as a template for the formation of high-aspect ratio fibers and can stabilize metastable polymorphs.

Advanced composites are used in a variety of industrial applications and therefore attract much scientific interest. Here we describe the formation of novel carbon-based nanocomposites via incorporation of graphene oxide into the crystal lattice of single crystals of calcite. Incorporation of a 2D organic material into single-crystal lattices has never before been reported. To characterize the resulting nanocomposites we employed high-resolution synchrotron powder X-ray diffraction, electron microscopy, transmission electron microscopy, fluorescence microscopy, and nanoindentation tests. Detailed analysis revealed a layered distribution of graphene oxide sheets incorporated within the calcite host. Moreover, the optical and mechanical properties of the calcite host were altered when a carbon-based nanomaterial was introduced into its lattice. Compared to pure calcite, the composite GO-calcite crystals exhibited lower elastic modulus and higher hardness. The results of this study show that the incorporation of a 2D material within a 3D crystal lattice is not only feasible but also can lead to the formation of hybrid crystals exhibiting new properties.

Here we report on the formation of hybrid organic-metal composites via the incorporation of selected amino acids into the crystal lattice of single crystals of gold. We used electron microscopy, chemical analysis, and high resolution synchrotron powder XRD to examine these composites. Crystal shape, as well as atomic concentrations of occluded amino acids and their impact on the crystal structure of gold, were determined.

Calcium carbonate (CaCO3) was synthesized from diverse water-free alcohol solutions, resulting in the formation of vaterite and calcite precipitates, or stable particle supensions, with dimension and morphology depending upon the condition used. The obtained results shed light on the importance of water molecules during crystallization of CaCO3 and open a novel synthetic route for its precipitation in organic solvents.

Amorphous calcium carbonate (ACC) has been widely found in biomineralization, both as a transient precursor and a stable phase, but how organisms accurately control its formation and crystallization pathway remains unclear. Here, we aim to illu-minate the role of biologically relevant additives on the phase behaviour of calcium carbonate solution by investigating their effects on the formation of ACC. Results show that divalent cations like magnesium (Mg2+) ions and negatively charged small organic molecules like aspartic acid (Asp) have little/no effect on ACC formation. However, the particle size of ACC is significantly re-duced by poly(Aspartic acid) (pAsp) with long chain-length, but no effect on the position of the phase boundary for ACC formation was observed. Phosphate (PO43-) ions are even more effective in reducing ACC particle size, and shift the phase boundary for ACC formation to lower concentrations. These phenomena can be explained by a cooperative ion-association process where the for-mation of ACC is only influenced by additives those are able to attract either Ca2+ ions or CO32- ions and, more importantly, intro-duce an additional long range interaction between the CaCO30 complexes and promote the phase separation process. The findings corroborate with our proposed model of ACC formation via spinodal decomposition and provide a more realistic representation of how biology can direct mineralization processes.

Elucidating the underlying principles behind band gap engineering is paramount for the successful implementation of semiconductors in photonic and optoelectronic devices. Recently it has been shown that the band gap of a wide and direct band gap semiconductor, such as ZnO, can be modified upon co-crystallization with amino acids, with the role of the biomolecules remaining unclear. Here, by probing and modeling the light emitting properties of ZnO-amino acid co-crystals, we identify the amino acids role on this band gap modulation and demonstrate their effective chirality transfer to the inter-band excitations in ZnO. Our 3D quantum model suggests that the strong band edge emission blue shift in the co-crystals can be explained by a quasi-periodic distribution of amino acid potential barriers within the ZnO crystal lattice. Overall, our findings indicate that biomolecule co-crystallization can be used as a truly bio-inspired means to induce chiral quantum confinement effects in quasi-bulk semiconductors.

Inclusion of additives into calcite crystals allows one to embed non-native proprieties into the inorganic matrix and obtain new functional materials. Up to now, few parameters have been taken into account to evaluate the efficiency of inclusion of an additive. Taking inspiration from Nature, we grew calcite crystals in the presence of fluorescent silica nanoparticles carrying different functional groups (PluS-X) to investigate the effect of surface chemistry on the inclusion of the additives. PluS-X allowed us to keep constant all the particle characteristics, including size, while changing exposed functional groups and thus Zeta-potential. The effect on crystal morphology, the loading and distribution of PluS-X within the crystals have been evaluated with different microscopy techniques. Our data indicate that hydroxyl functionalized particles are entrapped more efficiently inside calcite single crystals without distortion of the crystal structure and inhibition of the growth.

The effects of calcein, a marker commonly used to assess mineral growth in calcifying organism, on calcite and aragonite structure have been investigated. Calcein is entrapped within calcite and aragonite and modifies the shape and morphology of both polymorphs. Moreover, in the presence of Mg2+, it inhibits aragonite formation in favor of magnesium calcite.

In nodal-line semimetals linearly dispersing states form Dirac loops in the reciprocal space, with high degree of electron-hole symmetry and almost-vanishing density of states near the Fermi level. The result is reduced electronic screening and enhanced correlations between Dirac quasiparticles. Here we investigate the electronic structure of ZrSiSe, by combining time- and angle-resolved photoelectron spectroscopy with ab initio density functional theory (DFT) complemented by an extended Hubbard model (DFT +U +V). We show that electronic correlations are reduced on an ultrashort timescale by optical excitation of high-energy electrons-hole pairs, which transiently screen the Coulomb interaction. Our findings demonstrate an all-optical method for engineering the band structure of a quantum material., Comment: 6 pages, 3 figures

The conditions of well-posed solvability of searched function and its normal derivative three dimensional jump problem for the Laplacian and equivalent to them integral equation system for the sum of the simple and double layer potentials are determined in the Hilbert space, element of which as well as their normal derivatives have the jump through boundary surface., Comment: 6 pages

Suppose $F\colon \mathcal{D}(X)\to \mathcal{T}$ is an exact functor from the bounded derived category of coherent sheaves on a smooth projective variety $X$ to a triangulated category $\mathcal{T}$. If $F$ possesses left and right adjoints, then the Bondal-Orlov criterion gives a simple way of determining if $F$ is fully faithful. We prove a natural extension to the case when $X$ is a smooth and proper DM stack with projective coarse moduli space., Comment: 11 pages, several improvements per referee request

Lead-halide perovskite (LHP) semiconductors are emergent optoelectronic materials with outstanding transport properties which are not yet fully understood. We find signatures of large polaron formation in the electronic structure of the inorganic LHP CsPbBr$_3$ by means of angle-resolved photoelectron spectroscopy. The experimental valence band dispersion shows a hole effective mass $0.26\pm0.02\,\,m_e$, 50% heavier than the bare mass $m_0 =0.17 m_e$ predicted by density functional theory. Calculations of electron-phonon coupling indicate that phonon dressing of the carriers mainly occurs via distortions of the Pb-Br bond with a Fr\"ohlich coupling parameter $\alpha=1.82$. A good agreement with our experimental data is obtained within the Feynmann polaron model, validating a viable theorical method to predict the carrier effective mass of LHPs ab-initio.

We define the Atiyah class for global matrix factorizations and use it to give a formula for the categorical Chern character and the boundary-bulk map for matrix factorizations, generalizing the formula in the local case obtained in arXiv:1002.2116. Our approach is based on developing the Lie algebra analogies observed by Kapranov alg-geom/9704009 and Markarian math/0610553., Comment: v1: 16 pages; v2: 20 pages, added a section on $Z$-graded matrix factorizations; v3: 21 pages, minor improvements

This paper provides the analysis for functional approaches of complex network systems research. In order to study the behavior of these systems the flow adjacency matrices were introduced. The concepts of strength, power, domain and diameter of influence of complex network nodes are analyzed for the purpose of determining their importance in the systems structure. The notions of measure, power, domain and diameter of betweenness of network nodes and edges are introduced to identify their significance in the operation process of network systems. These indicators quantitatively express the contribution of the corresponding element for the motion of flows in the system and determine the losses that are expected in the case of blocking this node or edge or targeted attack on it. Similar notions of influence and betweenness are introduced to determine the functional importance of separate subsystems of network system and the system as a whole. Examples of practical use of the obtained results during investigation of real complex network systems are given., Comment: 20 pages, 6 figures. arXiv admin note: substantial text overlap with arXiv:1807.06044

Ferromagnetic resonance (FMR) in exchange-coupled ferromagnet-antiferromagnet (FM/AFM) bilayers commonly shows a moderate increase in the resonance frequency owing to the induced unidirectional anisotropy. Here we report a large FMR frequency enhancement toward the sub-THz range observed in Py/FeMn with ultrathin AFM FeMn. The effect is connected with a sizable induced magnetic moment in FeMn caused by the magnetic proximity effect from the Py layer. The observed FMR properties are explained as due to the competing intrinsic antiferromagnetic order and the ferromagnetic proximity effect in nanometer thin FeMn. Our results show that combining materials with strong and weak anti/ferromagnetic ordering can potentially close the notoriously difficult GHz-THz gap important for high-speed spintronic applications., Comment: 5 pages, 4 figures, Supplemental Material (3 pages, 3 figures)

We observe and analyze tunable relaxation of a pure spin current by an antiferromagnet in spin-valves. This is achieved by carefully controlling the angle between a resonantly excited ferromagnetic layer pumping the spin current and the N\'eel vector of the antiferromagnetic layer. The effect is observed as an angle-dependent spin-pumping contribution to the ferromagnetic resonance linewidth. An interplay between spin-mixing conductance and, often disregarded, longitudinal spin conductance is found to underlie our observations, which is in agreement with a recent prediction for related ferromagnetic spin valves., Comment: 6 pages, 3 figures, Supplemental Material: 4 pages, 3 figures

The supermeasure whose integral is the genus $g$ vacuum amplitude of superstring theory is potentially singular on the locus in the moduli space of supercurves where the corresponding even theta-characteristic has nontrivial sections. We show that the supermeasure is actually regular for $g\leq 11$. The result relies on the study of the superperiod map. We also show that the minimal power of the classical Schottky ideal that annihilates the image of the superperiod map is equal to $g$ if $g$ is odd and is equal to $g$ or $g-1$ if $g$ is even., Comment: 41 pages

We describe explicitly all hyperelliptic limits of quadrics through smooth canonical curves of genus $g$ in ${\mathbb P}^{g-1}$. Also, we construct an open embedding of the blow up of a ${\rm PGL}_g$-bundle over the moduli space of curves of genus $g$ along the hyperelliptic locus into the blow up of the canonical Hilbert scheme of ${\mathbb P}^{g-1}$ along the closure of the locus of canonical ribbons, which are certain double thickenings of rational normal curves introduced and studied by Bayer and Eisenbud., Comment: 31 pages

We study continuous analogues of "vitality" for discrete network flows/paths, and consider problems related to placing segment barriers that have highest impact on a flow/path in a polygonal domain. This extends the graph-theoretic notion of "most vital arcs" for flows/paths to geometric environments. We give hardness results and efficient algorithms for various versions of the problem, (almost) completely separating hard and polynomially-solvable cases.

We investigate the photocatalytic performance of nanocomposites prepared in a one-step process by liquid-phase exfoliation of graphite in the presence of TiO$_2$ nanoparticles (NPs) at atmospheric pressure and in water, without heating or adding any surfactant, and starting from low-cost commercial reagents. The nanocomposites show enhanced photocatalytic activity, degrading up to 40$\%$ more pollutants with respect to the starting TiO$_2$-NPs. In order to understand the photo-physical mechanisms underlying this enhancement, we investigate the photo-generation of reactive species (trapped holes and electrons) by ultrafast transient absorption spectroscopy. We observe an electron transfer process from TiO$_2$ to the graphite flakes within the first picoseconds of the relaxation dynamics, which causes the decrease of the charge recombination rate, and increases the efficiency of the reactive species photo-production., Comment: 13 pages, 12 figures, 1 table

Calcite has the ability to host large amounts of intracrystalline inclusions, a phenomenon that is known to be the case in biominerals and has been demonstrated in bio-inspired synthetic systems. In this study, we focused on barium as the inclusion. Highly substituted Ba-calcite possesses disordered carbonate orientations, characteristic of R-3m symmetry. We show that calcite undergoes an ordered-disordered transition, in which the carbonate groups undergo progressive loss of their rotational order with increasing amounts of incorporated Ba, and reach complete rotational disorder for a critical amount of Ba. We characterize this transition and propose a theoretical model justifying the influence of Ba. Moreover, the disordered R-3m Ba-substituted calcite has been previously identified as a high-temperature phase or as a highly metastable room-temperature phase. We challenge those descriptions by successfully synthesizing it under slow-rate conditions and by studying its thermal behavior, and we conclude that the fully disordered Ba-calcite is stable, whereas the transitional, partially disordered Ba-calcite phase is metastable.

We show new applications of the nearest-neighbor chain algorithm, a technique that originated in agglomerative hierarchical clustering. We apply it to a diverse class of geometric problems: we construct the greedy multi-fragment tour for Euclidean TSP in $O(n\log n)$ time in any fixed dimension and for Steiner TSP in planar graphs in $O(n\sqrt{n}\log n)$ time; we compute motorcycle graphs (which are a central part in straight skeleton algorithms) in $O(n^{4/3+\varepsilon})$ time for any $\varepsilon>0$; we introduce a narcissistic variant of the $k$-attribute stable matching model, and solve it in $O(n^{2-4/(k(1+\varepsilon)+2)})$ time; we give a linear-time $2$-approximation for a 1D geometric set cover problem with applications to radio station placement., Comment: 35 pages, 10 figures; v2: minor improvements, added Figure 1, and author order as in paper. v3: added funding acknowledgement

We consider paths with low \emph{exposure} to a 2D polygonal domain, i.e., paths which are seen as little as possible; we differentiate between \emph{integral} exposure (when we care about how long the path sees every point of the domain) and \emph{0/1} exposure (just counting whether a point is seen by the path or not). For the integral exposure, we give a PTAS for finding the minimum-exposure path between two given points in the domain; for the 0/1 version, we prove that in a simple polygon the shortest path has the minimum exposure, while in domains with holes the problem becomes NP-hard. We also highlight connections of the problem to minimum satisfiability and settle hardness of variants of planar min- and max-SAT.