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Ferromagnetic/antiferromagnetic bilayers are interfaced with normal metal/ferromagnetic bilayers to form F*/AF/N/F valves. The N-spacer thickness is chosen such that it mediates strong indirect exchange (RKKY) between the outer magnetic layers, which varies in strength/direction depending on the N thickness and in direction on switching F. The system exhibits a strong modulation of the F*/AF exchange bias, oscillating in strength syncronously with the oscillation in the interlayer RKKY exchange across the normal metal spacer. The effect is explained as due to a superposition taking place within the antiferromagnetic layer of the direct-exchange proximity effect from the F*/AF interface and the indirect RKKY exchange from F penetrating AF via N. The modulation, expressed via the strength of the F*/AF bias field, reaches 400% at the first RKKY peak., Comment: 5 pages, 4 figures

We study magnetic multilayers, incorporating dilute ferromagnetic spacers between strongly-ferromagnetic layers exhibiting a proximity-enhanced magnetocaloric effect. Using magnetometry and direct measurements of the adiabatic temperature change based on a nanomembrane-calorimetry, we find that the magnetocaloric effect in the studied multilayer is indeed enhanced compared to that in the bulk spacer material. We develop a phenomenological numerical model of the studied trilayer and find that a long-range exchange interaction through the weakly-ferromagnetic spacer is required to adequately describe the magnetic and magnetocaloric properties of the system.

Superhydrophobcity is a well-known wetting phenomenon found in numerous plants and insects. It is achieved by the combination of the surfaces chemical properties and its surface roughness. Inspired by nature, numerous synthetic superhydrophobic surfaces have been developed for various applications. Designated surface coating is one of the fabrication routes to achieve the superhydrophobicity. Yet, many of these coatings, such as fluorine-based formulations, may pose severe health and environmental risks, limiting the applicability. Herein, we present a new family of superhydrophobic coatings comprised of natural saturated fatty acids, which are not only a part of our daily diet, but can be produced from renewable feedstock, providing a safe and sustainable alternative to existing state-of-the-art. These crystalline coatings are readily fabricated via single-step deposition routes, thermal deposition or spray-coating. The fatty acids self-assemble into highly hierarchical crystalline structures exhibiting a water contact angle of about 165 degrees and contact angle hysteresis lower than 6 degrees, while their properties and morphology depend on the specific fatty acid used as well as on the deposition technique. Moreover, the fatty acid coatings demonstrate excellent thermal stability. Importantly these new family of coatings displays excellent anti-biofouling and antimicrobial properties against Escherichia coli and Listeria innocua, used as relevant model Gram-negative and Gram-positive bacteria, respectively. We believe that these coatings have a great application potential in the fields, where other alternatives are prohibited due to safety limitations, while at the same time their usage in other regulation-free applications is not limited.

Since the first case of COVID-19 disease in Wuhan in December 2019, there is a worldwide struggle to reduce the transmission of acute respiratory syndrome coronavirus SARS-CoV-2. Many countries worldwide decided to impose local lockdowns in order to reduce person-to-person interactions, masks became obligatory especially in closed spaces, and there was a general requirement for social distance. However, the most efficient method to reduce continuing spreading of infection among the population, and in the meantime maintain a regular daily life, is early detection of infected contagious people. Up to now, the most reliable method for SARS-CoV-2 detection is reverse-transcriptase PCR test (RT-PCR). It is possible to detect the virus even if there is only one RNA strand in the sample, and run hundreds of samples simultaneously. This method has a few disadvantages, such as high cost, is time consuming, the need for medical laboratories and skilled staff to perform the test, and the major flaw: the lack of appropriate number of available tests. The latterly prominent Omicron variant (B.1.1.529) and its derivatives have caused a tremendous increase in the number of infected people due to its enhanced transmissibility. This all emphasizes the high demand for easy-to-use, cheap and available detection tests.

We prove that several Feigin-Odesskii Poisson brackets associated with normal elliptic curves in ${\mathbb P}^n$ are compatible if and only if they are contained in a scroll or in a Veronese surface in ${\mathbb P}^5$ (with an exception of one case when $n=3$). In the case $n=3$ we determine the quartic corresponding to the Schouten bracket of two (non-compatible) Poisson brackets associated with normal elliptic curves $E_1$ and $E_2$., Comment: 15 pages, v2: strengthened Corollary C for even n

We prove that for any cubic polynomial of slice rank $r$, the intersection of all linear subspaces of minimal codimension contained in the corresponding hypersurface has codimension $\le r^2+\frac{(r+1)^2}{4}+r$ in the affine space. This is deduced from the following result of independent interest. Consider the intersection $I$ of linear ideals $(P_i)$ in $k[x_1,\ldots,x_n]$, with $\dim P_i\le r$. Then the number of quadratic generators of $I$ is $\le r^2$., Comment: 8 pages

We identify Feigin-Odesskii brackets $q_{n,1}(C)$, associated with a normal elliptic curve of degree $n$, $C\subset {\mathbb P}^{n-1}$, with the skew-symmetric $n\times n$ matrix of quadratic forms introduced by Fisher in arXiv:1510.04327 in connection with some minimal free resolutions related to the secant varieties of $C$. On the other hand, we show that for odd $n$, the generators of the ideal of the secant variety of $C$ of codimension $3$ give a Cremona transformation of ${\mathbb P}^{n-1}$, generalizing the quadro-cubic Cremona transformation of ${\mathbb P}^4$. We identify this transformation with the one considered in arXiv:alg-geom/9712022 and find explict formulas for the inverse transformation. We also find polynomial formulas for Cremona transformations from arXiv:alg-geom/9712022 associated with higher rank bundles on $C$., Comment: 10 pages; v2: 12 pages, added Theorem D on Cremona transformations associated with higher rank bundles

Incorporation of organic molecules into the lattice of inorganic crystalline hosts is a common phenomenon in biomineralization, and has been shown to alter various properties of the crystalline host. Taking this phenomenon as our source of inspiration, we show herein that incorporation of specific single amino acids into the lattice of manganese (II) carbonate strongly alters its inherent magnetic properties. At room temperature, the magnetic susceptibility of the amino-acid-incorporating paramagnetic MnCO3 decreases, following a simple rule of mixtures. When cooled below the N\'eel temperature, however, the opposite trend is observed, namely an increase in magnetic susceptibility measured in a high magnetic field. Such an increase, accompanied by a drastic change in the N'eel phase transformation temperature, results from a decrease in MnCO3 orbital overlapping and the weakening of superexchange interactions.

The classical and extensively-studied Fr\'echet distance between two curves is defined as an inf max, where the infimum is over all traversals of the curves, and the maximum is over all concurrent positions of the two agents. In this article we investigate a "flipped" Fr\'echet measure defined by a sup min -- the supremum is over all traversals of the curves, and the minimum is over all concurrent positions of the two agents. This measure produces a notion of "social distance" between two curves (or general domains), where agents traverse curves while trying to stay as far apart as possible. We first study the flipped Fr\'echet measure between two polygonal curves in one and two dimensions, providing conditional lower bounds and matching algorithms. We then consider this measure on polygons, where it denotes the minimum distance that two agents can maintain while restricted to travel in or on the boundary of the same polygon. We investigate several variants of the problem in this setting, for some of which we provide linear time algorithms. Finally, we consider this measure on graphs. We draw connections between our proposed flipped Fr\'echet measure and existing related work in computational geometry, hoping that our new measure may spawn investigations akin to those performed for the Fr\'echet distance, and into further interesting problems that arise.

The SARS CoV-2 virus emerged at the end of 2019 and rapidly developed several mutated variants, specifically the Delta and Omicron, which demonstrate higher infectivity and escalating infection cases worldwide. The dominant transmission pathway of this virus is via human-to-human contact and aerosols, but another possible route is through contact with surfaces contaminated with SARS-CoV-2, often exhibiting long-period survival. Here we compare the adsorption capacities of the S1 and S2 subunits of the spike (S) protein from the original variant to that of the S1 subunit from the Delta and Omicron variants. The results clearly show a significant difference in adsorption capacity between the different variants, as well as between the S1 and S2 subunits. Overall, our study demonstrates that while the Omicron variant is able to adsorb much more successfully than the Delta, both variants show enhanced adsorption capacity than the original strain. We also examined the influence of pH conditions on the adsorption ability of the S1 subunit and found that adsorption was strongest at pH 7.4, which is the physiological pH. The main conclusion of this study is that there is a strong correlation between the adsorption capacity and the infectivity of the various SARS CoV-2 variants.

During the process of biomineralization, organisms utilize various biostrategies to enhance the mechanical durability of their skeletons. In this work, we establish that the presence of high-Mg nanoparticles embedded within lower Mg calcite matrices is a widespread strategy utilized by various organisms from different kingdoms and phyla to improve the mechanical properties of their high Mg calcite skeletons. We show that such phase separation and the formation of high-Mg nanoparticles are achieved through spinodal decomposition of an amorphous Mg calcite precursor. Such decomposition is independent of the biological characteristics of the studied organisms belonging to different phyla and even kingdoms, but rather originates from their similar chemical composition and a specific Mg content within their skeletons, which generally ranges from 14 to 48 mol percent of Mg. We show evidence of high Mg calcite nanoparticles in the cases of 6 biologically different organisms all demonstrating more than 14 mol percent Mg calcite, and consider it likely that this phenomenon is immeasurably more prevalent in nature. We also establish the absence of these high Mg nanoparticles in organisms whose Mg content is lower than 14 mol percent, providing further evidence that whether or not spinodal decomposition of an amorphous Mg calcite precursor takes place is determined by the amount of Mg it contains. The valuable knowledge gained from this biostrategy significantly impacts the understanding of how biominerals, though comprised of intrinsically brittle materials, can effectively resist fracture.

Method of U-statistics is used to analyze the efficiency of functioning of the motor transport system of a large city as a complex network system with partially ordered traffic flows. Based on the results of continuous monitoring of movement of the ordered part of flows equipped with GPS-trackers, namely, public transport means, methods of interactive, forecasting and aggregated analysis of the state and operation process of motor transport system components of various hierarchy levels have been developed. The proposed technique can be easily automated and used for operational analysis and forecasting of the development of traffic situations on city highways and creation of effective tools to optimize the process of motor transport system functioning., Comment: 11 pages, 3 figures, in Ukrainian

The paper introduces a number of structural and functional features of classification of multilayer networks (MLN), by means of which distinguish monoflow partially overlapped MLN, that are quite common in the study of intersystem interactions of different nature. The concept of MLN's aggregate-network is defined, which in many cases significantly simplifies the study of intersystem interactions, and the properties of its k-cores are investigated. The notion of p-cores is introduced, with help of which the components of MLN that are directly involved in the implementation of intersystem interactions are distinguished. Methods of reducing the complexity of multilayer network models are investigated, which allow us to significantly decrease their dimensionality and better understand the processes that take place in complex network systems and intersystem interactions of different types. Using the introduced local and global structural characteristics of elements, effective scenarios of targeted attacks on monoflow partially overlapped multilayer networks have been developed, the main attention of which is focused on the transition points of MLN through which intersystem interactions are actually realized. It is shown that these scenarios can also be used to solve the inverse problem, namely, which elements of MLN should be blocked in the first place to prevent the acceleration of spread of epidemics of dangerous infectious diseases, etc., Comment: 18 pages, 7 figures

We observe a strong thermally-controlled magnon-mediated interlayer coupling of two ferromagnetic layers via an antiferromagnetic spacer in spin-valve type trilayers. The effect manifests itself as a field-induced coherent switching of the two ferromagnets, which can be controlled by varying temperature and the spacer thickness. We explain the observed behavior as due to a strong hybridization of the ferro- and antiferro-magnetic magnon modes in the trilayer at temperatures just below the N\'eel temperature of the antiferromagnetic spacer., Comment: 4 pages, 4 figures

Let $k$ be a perfect field of characteristic $\neq 2$. We prove that the Schmidt rank (also known as strength) of a quartic polynomial $f$ over $k$ is bounded above in terms of only the Schmidt rank of $f$ over $\overline{k}$, an algebraic closure of $k$., Comment: 13 pages. arXiv admin note: text overlap with arXiv:2107.08080

We give a description of the formal neighborhoods of the components of the boundary divisor in the Deligne-Mumford moduli stack $\overline{{\mathcal M}}_g$ of stable curves in terms of the extended clutching construction that we define. This construction can be viewed as a formal version of the analytic plumbing construction. The advantage of our formal construction is that we can control the effect of changing formal parameters at the marked points that are being glued. As an application, we prove that the infinitesimal neighborhood of the boundary component $\Delta_{1,1}$ in $\overline{{\mathcal M}}_2$ is canonically isomorphic to the infinitesimal neighborhood of the zero section in the normal bundle. As another application, we show how to study the period map near the boundary components $\Delta_{g_1,g_2}$ in terms of the coordinates coming from our extended clutching construction., Comment: 23 pages; v2: corrected a mistake in Theorem 1.2; v3: corrected typos

The magnetocaloric effect in exchange-coupled synthetic-antiferromagnet multilayers is investigated experimentally and theoretically. We observe a temperature-controlled inversion of the effect, where the entropy increases on switching the individual ferromagnetic layers from anti-parallel to parallel alignment near their Curie point. Using a microscopic analytical model as well as numerical atomistic-spin simulations of the system, we explain the observed effect as due to the interplay between the intra- and inter-layer exchange interactions, which either add up or counteract to effectively modulate the Curie temperature of the dilute ferromagnetic layers. The proposed method of designing tunable, strongly magneto-caloric materials should be of interest for such applications as heat-assisted spintronics and magnetic refrigeration., Comment: 6 pages, 5 figures

Hard-to-predict bursts of COVID-19 pandemic revealed significance of statistical modeling which would resolve spatio-temporal correlations over geographical areas, for example spread of the infection over a city with census tract granularity. In this manuscript, we provide algorithmic answers to the following two inter-related public health challenges. (1) Inference Challenge: assuming that there are $N$ census blocks (nodes) in the city, and given an initial infection at any set of nodes, what is the probability for a subset of census blocks to become infected by the time the spread of the infection burst is stabilized? (2) Prevention Challenge: What is the minimal control action one can take to minimize the infected part of the stabilized state footprint? To answer the challenges, we build a Graphical Model of pandemic of the attractive Ising (pair-wise, binary) type, where each node represents a census track and each edge factor represents the strength of the pairwise interaction between a pair of nodes. We show that almost all attractive Ising Models on dense graphs result in either of the two modes for the most probable state: either all nodes which were not infected initially became infected, or all the initially uninfected nodes remain uninfected. This bi-modal solution of the Inference Challenge allows us to re-state the Prevention Challenge as the following tractable convex programming: for the bare Ising Model with pair-wise and bias factors representing the system without prevention measures, such that the MAP state is fully infected for at least one of the initial infection patterns, find the closest, in $l_1$ norm, set of factors resulting in all the MAP states of the Ising model, with the optimal prevention measures applied, to become safe.

We investigate spin dynamics in nanodisc arrays of synthetic-antiferromagnets (SAF) made of Py/NiCu/Py trilayers, where the NiCu spacer undergoes a Curie transition at about 200 K. The observed ferromagnetic resonance spectra have three distinct resonance modes at room temperature, which are fully recreated in our micromagnetic simulations showing also how the intra-SAF asymmetry can be used to create and control the higher-order resonances in the structure. Below the Curie temperature of the spacer, the system effectively transitions into a single-layer nanodisc array with only two resonance modes. Our results show how multi-layering of nano-arrays can add tunable GHz functionality relevant for such rapidly developing fields as magnetic meta-materials, magnonic crystals, arrays of spin-torque oscillators and neuromorphic junctions., Comment: 5 pages, 3 figures

We study embeddability of superschemes into $\Pi$-projective spaces and into supergrassmannians $G(1|1,n|n)$. We give some criteria based on the relation with ${\mathbb{A}}^{0|1}$-torsors and ${\mathbb{A}}^{0|1}$-fibrations. We also prove the existence of nice quotients for free actions of ${\mathbb{A}}^{0|1}$ on superschemes., Comment: v2: 15 pages, added examples with embeddable CY 2|2-varieties

We give an elementary proof of an efficient version of the Wagner's theorem on almost invariant subspaces and deduce some consequences in the context of Galois extensions., Comment: 7 pages

Let $k$ be a perfect field and let $X\subset {\mathbb P}^N$ be a hypersurface of degree $d$ defined over $k$ and containing a linear subspace $L$ defined over an algebraic closure $\overline{k}$ with $\mathrm{codim}_{{\mathbb P}^N}L=r$. We show that $X$ contains a linear subspace $L_0$ defined over $k$ with $\mathrm{codim}_{{\mathbb P}^N}L\le dr$. We conjecture that the intersection of all linear subspaces (over $\overline{k}$) of minimal codimension $r$ contained in $X$, has codimension bounded above only in terms of $r$ and $d$. We prove this when either $d\le 3$ or $r\le 2$., Comment: 15 pages, v2 substantially rewritten: added Conjecture B and a result on hypersurfaces of rank 2; the result on Schmidt rank is moved to another paper; v3: modified Conjecture B and added examples in the introduction

The problem of selection, storage, search and analysis of information about the state, functioning and interaction of elements of complex hierarchical network systems is considered. The principles of construction of information models of such systems and models of evaluation of their operation efficiency are proposed. These models are formed on the basis of results of regular planned studies of the system and continuous monitoring of the activities of its components at all levels of the hierarchy. The problem of novelty detection in the information model of system is investigated and it is shown how the application of evaluation theory methods allows to solve it. The proposed methods of complex analysis of the behavior of real complex systems and optimization of data processing makes it possible to significantly simplify and speed up the decision-making process for further action for such systems., Comment: 12 pages, 3 figures

For an appropriate choice of a $\mathbb{Z}$-grading structure, we prove that the wrapped Fukaya category of the symmetric square of a $(k+3)$-punctured sphere, i.e. the Weinstein manifold given as the complement of $(k+3)$ generic lines in $\mathbb{C}P^2$ is quasi-equivalent to the derived category of coherent sheaves on a singular surface $\mathcal{Z}_{2,k}$ constructed as the boundary of a toric Landau-Ginzburg model $(\mathcal{X}_{2,k}, \mathbf{w}_{2,k})$. We do this by first constructing a quasi-equivalence between certain categorical resolutions of both sides and then localising. We also provide a general homological mirror symmetry conjecture concerning all the higher symmetric powers of punctured spheres. The corresponding toric LG-models $(\mathcal{X}_{n,k},\mathbf{w}_{n,k})$ are constructed from the combinatorics of curves on the punctured surface and are related to small toric resolutions of the singularity $x_1\ldots x_{n+1}= v_1\ldots v_k$., Comment: 52 pages, 8 figures. Added Section 2.4

We consider Takahashi's categorical interpretation of the Berglund-Hubsch mirror symmetry conjecture for invertible polynomials in the case of chain polynomials. Our strategy is based on a stronger claim that the relevant categories satisfy a recursion of directed $A_{\infty}$-categories, which may be of independent interest. We give a full proof of this claim on the B-side. On the A-side we give a detailed sketch of an argument, which falls short of a full proof because of certain missing foundational results in Fukaya-Seidel categories, most notably a generation statement., Comment: few minor changes, to appear in Math. Annalen

The flow models of complex network system are developed and main flow characteristics of its elements are defined. Those characteristics are applied for determining actual structure of the system, analyzing its development on all lifecycle stages and finding alternative flow directions that bypass isolated areas of network. Influence and betweenness parameters of components of network systems are defined. Using those parameters, the conditions were studied under which system is resistant to negative internal and external influence. The notion of flow core of complex network systems is defined, that allows to distinguish the most important components of system structure in terms of operation to solve the problem of finding communities within the network. The notions of p-core and kernel of mono flow partially overlapped multilayered network are defined that allow to determine components of system structure that play the most important role in implementation of interactions between systems. The methodology is developed for complex evaluation of quality of complex hierarchical network systems. This methodology combines the interconnected methods of local, forecasting, interactive and aggregated analysis of system components behavior on all hierarchy levels. It is demonstrated that application of proposed complex evaluation methodology is efficient for solving problem of defining practically possible criteria of network system element quality, novelty detection, determining critical and optimal system operation modes and selecting optimal system of given class of systems., Comment: 29 pages, in Ukrainian

We revisit Schmidt's theorem connecting the Schmidt rank of a tensor with the codimension of a certain variety and adapt the proof to the case of arbitrary characteristic. We also find a sharper result of this kind for homogeneous polynomials of degree d (assuming that the characteristic does not divide d(d-1)). We then use this to relate the Schmidt rank of a homogeneous polynomial (resp., a collection of homogeneous polynomials of the same degree) with the codimension of the singular locus of the corresponding hypersurface (resp., intersection of hypersurfaces). This gives an effective version of Ananyan-Hochster's Theorem A from arXiv:1610.09268., Comment: v1: 17 pages; v2: 19 pages, added Theorem 1.5 on generic derivatives; v3: improved exposition, added references; v4: 20 pages, added Amichai Lampert as a coauthor, improved bounds in the main theorems

The magnetic properties of thin-film multilayers [Fe/Py]/FeMn/Py are investigated as a function of temperature and thickness of the antiferromagnetic FeMn spacer using SQUID magnetometry. The observed behavior differs substantially for the structures with 6-nm and 15-nm FeMn spacers. While the 15-nm-FeMn structure exhibits exchange pinning of both ferromagnetic layers in the entire measurement temperature interval from 5 to 300 K, the 6-nm-FeMn structure becomes exchange de-pinned in the vicinity of room temperature. The de-pinned state is characterized by a single hysteresis loop centered around zero field and having enhanced magnetic coercivity. The observed properties are explained in terms of finite-size effects and possibly ferromagnetic interlayer coupling through the thin antiferromagnetic spacer., Comment: 9 pages, 5 figures

The problem of blocking certain areas of network systems and their boundary case, which is the granulation of network to a set of isolated zones, is investigated in the article. The losses that await the system due to blocking of its separate components are determined, and method for finding alternative ways of flow motion bypassing the isolated zone of network are proposed. The granulation process of the network system is reflected as a temporal network and the losses that await the system during the deployment of such processes are calculated., Comment: 6 pages, 2 figures

The paper investigates the problem of finding communities in complex network systems, the detection of which allows a better understanding of the laws of their functioning. To solve this problem, two approaches are proposed based on the use of flows characteristics of complex network. The first of these approaches consists in calculating the parameters of influence of separate subsystems of the network system, distinguished by the principles of ordering or subordination, and the second, in using the concept of its flow core. Based on the proposed approaches, reliable criteria for finding communities have been formulated and efficient algorithms for their detection in complex network systems have been developed. It is shown that the proposed approaches make it possible to single out communities in cases in which the existing numerical and visual methods turn out to be disabled., Comment: 5 pages, 1 figure

Properties of the ground state and the spectrum of elementary excitations are investigated for the low density ultracold spinor 3D Bose gas of particles with arbitrary nonzero spin. Gross-Pitaevskii equations are derived. Within the framework of the considering interaction Hamiltonian it is shown that the ground state spin structure and spin part of the chemical potential is determined by the renormalized interaction, being defined by the contribution of the virtual large momenta. The ferromagnetic structure of the ground state, and the equation of the phase, density, and spin dynamics are obtained from Gross-Pitaevskii equations., Comment: 18 pages