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ObjectiveTo perform a systematic and meta-analysis on the prevalence rates of mental health symptoms including anxiety and depression during the COVID-19 pandemic in the general population in Eastern Europe, as well as three select sub-populations: students, general healthcare workers, and frontline healthcare workers.Data sourcesStudies in PubMed, Embase, Web of Science, Psycinfo, and medRxiv up to February 6, 2021.Eligibility criteria and data analysisPrevalence rates of mental health symptoms in the general population and key sub-populations during the COVID-19 pandemic in Eastern Europe. Data were pooled using a random-effects meta-analysis to estimate the prevalence rates of anxiety and depression.ResultsThe meta-analysis identifies and includes 21 studies and 26 independent samples in Eastern Europe. Poland (n=4), Serbia (n=4), Russia (n=3), and Croatia (n=3) had the greatest number of studies. To our knowledge, no studies have been conducted in eleven Eastern European countries including Hungary, Slovakia, and Slovenia. The pooled prevalence of anxiety in 18 studies with 22 samples was 30% (95% CI: 24% – 37%) and pooled prevalence of depression in 18 studies with 23 samples was 27% (95% CI: 21% – 34%).ImplicationsThe cumulative evidence from the meta-analysis reveals high prevalence rates of clinically significant symptoms during the COVID-19 pandemic in Eastern Europe. The findings suggest evidence of a potential mental health crisis in Eastern Europe during the ongoing COVID-19 pandemic. Our synthesis also reveals a relative lack of studies in certain Eastern European countries as well as high heterogeneities among the existing studies, calling for more effort to achieve evidence-based mental healthcare in Eastern Europe.HighlightsThe pooled prevalence of anxiety and depression were 30% and 27% in Eastern Europe, respectively.Trial registrationCRD42020224458

Objective This paper provides a systematic review and meta-analysis on the prevalence rate of mental health issues of the major population, including general population, general healthcare workers (HCWs), and frontline healthcare workers (HCWs), in China over one year of the COVID-19 crisis. Design A systematic review and meta-analysis. Data sources articles in PubMed, Embase, Web of Science, and medRxiv up to November 16, 2020, one year after the first publicly known confirmed COVID-19 case. Eligibility criteria and data analysis any COVID-19 and mental disorders relevant English studies with frontline/general healthcare workers, general adult population sample, using validated scales. We pooled data using random-effects meta-analyses to estimate the prevalence rates of anxiety, depression, distress, general psychological symptoms (GPS), insomnia, and PTSD and ran meta-regression to tease out the heterogeneity. Results The meta-analysis includes 131 studies and 171 independent samples. The overall prevalence of anxiety, depression, distress, GPS, insomnia, and PTSD are 11%, 13%, 20%, 13%, 19%, and 20%, respectively. The meta-regression results uncovered several predictors of the prevalence rates, including severity (e.g., above severe vs. above moderate, p Limitations First, we only focus on China population, which may limit the generalizability of the results. Second, 96.2% studies included in this meta-analysis were cross-sectional. Last, since we only included studies published in English, we expect to have a language bias. Conclusion Our pooled prevalence rates are significantly different from, yet largely between, the findings of previous meta-analyses, suggesting the results of our larger study are consistent with, yet fine-tune, the findings of the smaller, previous meta-analyses. Hence, this meta-analysis not only provides a significant update on the mental health prevalence rates in COVID-19 but also suggests the need to update meta-analyses continuously to provide more accurate estimates of the prevalence of mental illness during this ongoing health crisis. While prior meta-analyses focused on the prevalence rates of mental health disorders based on one level of severity (i.e., above mild), our findings also suggest a need to examine the prevalence rates at varying levels of severity. The one-year cumulative evidence on sampling locations (Wuhan vs. non-Wuhan) corroborates the typhoon eye effect theory. Our finding that the prevalence rates of distress and insomnia and those of frontline healthcare workers are higher suggest future research and interventions should pay more attention to those mental outcomes and populations. Trial registration CRD42020220592

Many advancements have been made in the field of topological mechanics. The majority of the work, however, concerns the topological invariant in a linear theory. In this Letter, we present a generic prescription to define topological indices that accommodates nonlinear effects in mechanical systems without taking any approximation. Invoking the tools of differential geometry, a $\mathbb{Z}$-valued quantity in terms of a topological index in differential geometry known as the Poincar\'e-Hopf index, which features the topological invariant of nonlinear zero modes (ZMs), is predicted. We further identify one type of topologically protected solitons that are robust to disorders. Our prescription constitutes a new direction of searching for novel topologically protected nonlinear ZMs in the future.

BackgroundThe recent outbreak of COVID-19 impacts the mental health of people worldwide. The mental conditions and the associated predictors of adults in Pakistan, the fifth most populous country in the world, during the COVID-19 remains understudied. We aim to investigate distress, anxiety and overall mental health and their associated predictors among Pakistani adults in this pandemic. We specifically examine the mental health issues based on the distance to the epicenter, a predictor that has revealed opposing evidence in other countries based on the theories of typhoon eye effect and ripple effect. The samples consist of 601 adults who were surveyed online about 2.5 months into the outbreak across Pakistan with varying distance to the epicenter of COVID-19 of Karachi in Pakistan.ResultsThe results showed that 9.2% and 19.0% of the participants surpassed the cut-off of distress and anxiety disorders, respectively. Overall, the distance to the epicenter positively predicted the mental health of adults in Pakistan, and family size negatively moderated this effect. The distance to the epicenter negatively predicted distress and anxiety disorders for adults in large families, which are quite common in Pakistan.ConclusionThe evidence of the study interestingly finds the prediction of the mental health of people by their distance to the epicenter depends on the family. The evidence of this study can help to provide the initial indicator for mental health care providers to screen vulnerable groups in Pakistan, a populous country that continues to struggle to cope with the COVID-19 pandemic.

Funding: NSF Award No. PHY-1554887 (B.G.C.). NSF DMR-1822638 (C.S.). Georgia Institute of Technology President’s Fellowship and the STAMI Graduate Student Fellowship ( J.M.). We consider the zero-energy deformations of periodic origami sheets with generic crease patterns. Using a mapping from the linear folding motions of such sheets to force-bearing modes in conjunction with the Maxwell–Calladine index theorem we derive a relation between the number of linear folding motions and the number of rigid body modes that depends only on the average coordination number of the origami’s vertices. This supports the recent result by Tachi [T. Tachi, Origami 6, 97–108 (2015)] which shows periodic origami sheets with triangular faces exhibit two-dimensional spaces of rigidly foldable cylindrical configurations. We also find, through analytical calculation and numerical simulation, branching of this configuration space from the flat state due to geometric compatibility constraints that prohibit finite Gaussian curvature. The same counting argument leads to pairing of spatially varying modes at opposite wavenumber in triangulated origami, preventing topological polarization but permitting a family of zero-energy deformations in the bulk that may be used to reconfigure the origami sheet. Postprint

This article describes a class of nonlinear topological mechanical systems whose continuum elasticity displays connections with the supersymmetric field theory introduced by Witten and Olive.

Modern fabrication tools have now provided a number of platforms for designing flat sheets that, by virtue of their nonuniform growth, can buckle and fold into target three-dimensional structures. Theoretically, there is an infinitude of growth patterns that can produce the same shape, yet almost nothing is understood about which of these many growth patterns is optimal from the point of view of experiment, and few can even be realized at all. Here, we ask the question: what is the optimal way to design isotropic growth patterns for a given target shape? We propose a computational algorithm to produce optimal growth patterns by introducing cuts into the target surfaces. Within this framework, we propose that the patterns requiring the fewest or shortest cuts produce the best approximations to the target shape at finite thickness. The results are tested by simulation on spherical surfaces, and new challenges are highlighted for surfaces with both positive and negative Gaussian curvatures.

Sidney Coleman was a physicist's physicist. He is largely unknown outside of the theoretical physics community, and known only by reputation to the younger generation. He was an unusually effective teacher, famed for his wit, his insight and his encyclopedic knowledge of the field to which he made many important contributions. There are many first-rate quantum field theory books (the venerable Bjorken and Drell, the more modern Itzykson and Zuber, the now-standard Peskin and Schroeder, and the recent Zee), but the immediacy of Prof. Coleman's approach and his ability to present an argument simply without sacrificing rigor makes his book easy to read and ideal for the student. Part of the motivation in producing this book is to pass on the work of this outstanding physicist to later generations, a record of his teaching that he was too busy to leave himself.

We study the dynamical response of a diatomic periodic chain of rotors coupled by springs, whose unit cell breaks spatial inversion symmetry. In the continuum description, we derive a nonlinear field theory which admits topological kinks and antikinks as nonlinear excitations but where a topological boundary term breaks the symmetry between the two and energetically favors the kink configuration. Using a cobweb plot, we develop a fixed-point analysis for the kink motion and demonstrate that kinks propagate without the Peierls-Nabarro potential energy barrier typically associated with lattice models. Using continuum elasticity theory, we trace the absence of the Peierls-Nabarro barrier for the kink motion to the topological boundary term which ensures that only the kink configuration, and not the antikink, costs zero potential energy. Further, we study the eigenmodes around the kink and antikink configurations using a tangent stiffness matrix approach appropriate for pre-stressed structures to explicitly show how the usual energy degeneracy between the two no longer holds. We show how the kink-antikink asymmetry also manifests in the way these nonlinear excitations interact with impurities introduced in the chain as disorder in the spring stiffness. Finally, we discuss the effect of impurities in the (bond) spring length and build prototypes based on simple linkages that verify our predictions., 20 pages, 21 figures

We investigate how material rigidity acts as a key control parameter for the failure of solids under stress. In both experiments and simulations, we demonstrate that material failure can be continuously tuned by varying the underlying rigidity of the material while holding the amount of disorder constant. As the rigidity transition is approached, failure due to the application of uniaxial stress evolves from brittle cracking to system-spanning diffuse breaking. This evolution in failure behavior can be parameterized by the width of the crack. As a system becomes more and more floppy, this crack width increases until it saturates at the system size. Thus, the spatial extent of the failure zone can be used as a direct probe for material rigidity.

The homotopy theory of topological defects in ordered media fails to completely characterize systems with broken translational symmetry. We argue that the problem can be understood in terms of the lack of rotational Goldstone modes in such systems and provide an alternate approach that correctly accounts for the interaction between translations and rotations. Dislocations are associated, as usual, with branch points in a phase field, whereas disclinations arise as critical points and singularities in the phase field. We introduce a three-dimensional model for two-dimensional smectics that clarifies the topology of disclinations and geometrically captures known results without the need to add compatibility conditions. Our work suggests natural generalizations of the two-dimensional smectic theory to higher dimensions and to crystals.

We compared the abilities of media from agar plates surrounding swarming and nonswarming cells of Salmonella enterica serovar Typhimurium to wet a nonpolar surface by measuring the contact angles of small drops. The swarming cells were wild type for chemotaxis, and the nonswarming cells were nonchemotactic mutants with motor biases that were counterclockwise ( cheY ) or clockwise ( cheZ ). The latter strains have been shown to be defective for swarming because the agar remains dry (Q. Wang, A. Suzuki, S. Mariconda, S. Porwollik, and R. M. Harshey, EMBO J. 24:2034-2042, 2005). We found no differences in the abilities of the media surrounding these cells, either wild type or mutant, to wet a low-energy surface (freshly prepared polydimethylsiloxane); although, their contact angles were smaller than that of the medium harvested from the underlying agar. So the agent that promotes wetness produced by wild-type cells is not a surfactant; it is an osmotic agent.

Topological mechanical structures exhibit robust properties protected by topological invariants. In this letter, we study a family of deformed square lattices that display topologically protected zero-energy bulk modes analogous to the massless fermion modes of Weyl semimetals. Our findings apply to sufficiently complex lattices satisfying the Maxwell criterion of equal numbers of constraints and degrees of freedom. We demonstrate that such systems exhibit pairs of oppositely charged Weyl points, corresponding to zero-frequency bulk modes, that can appear at the origin of the Brillouin zone and move away to the zone edge (or return to the origin) where they annihilate. We prove that the existence of these Weyl points leads to a wavenumber-dependent count of topological mechanical states at free surfaces and domain walls.

Origami and kirigami have emerged as potential tools for the design of mechanical metamaterials whose properties such as curvature, Poisson ratio, and existence of metastable states can be tuned using purely geometric criteria. A major obstacle to exploiting this property is the scarcity of tools to identify and program the flexibility of fold patterns. We exploit a recent connection between spring networks and quantum topological states to design origami with localized folding motions at boundaries and study them both experimentally and theoretically. These folding motions exist due to an underlying topological invariant rather than a local imbalance between constraints and degrees of freedom. We give a simple example of a quasi-1D folding pattern that realizes such topological states. We also demonstrate how to generalize these topological design principles to two dimensions. A striking consequence is that a domain wall between two topologically distinct, mechanically rigid structures is deformable even when constraints locally match the degrees of freedom., 5 pages, 3 figures + ~5 pages SI

We explore the surprisingly rich energy landscape of origami-like folding planar structures. We show that the configuration space of rigid-paneled degree-4 vertices, the simplest building blocks of such systems, consists of at least two distinct branches meeting at the flat state. This suggests that generic vertices are at least bistable, but we find that the nonlinear nature of these branches allows for vertices with as many as five distinct stable states. In vertices with collinear folds and/or symmetry, more branches emerge leading to up to six stable states. Finally, we introduce a procedure to tile arbitrary 4-vertices while preserving their stable states, thus allowing the design and creation of multistable origami metasheets., For supplemental movies please visit http://www.lorentz.leidenuniv.nl/~chen/multisheets

We study rigidity percolation transitions in two-dimensional central-force isostatic lattices, including the square and the kagome lattices, as next-nearest-neighbor bonds ("braces") are randomly added to the system. In particular, we focus on the differences between regular lattices, which are perfectly periodic, and generic lattices with the same topology of bonds but whose sites are at random positions in space. We find that the regular square and kagome lattices exhibit a rigidity percolation transition when the number of braces is $\sim L\ln L$, where $L$ is the linear size of the lattice. This transition exhibits features of both first order and second order transitions: the whole lattice becomes rigid at the transition, whereas there exists a diverging length scale. In contrast, we find that the rigidity percolation transition in the generic lattices occur when the number of braces is very close to the number obtained from the Maxwell's law for floppy modes, which is $\sim L$. The transition in generic lattices is a very sharp first-order-like transition, at which the addition of one brace connects all small rigid regions in the bulk of the lattice, leaving only floppy modes on the edge. We characterize these transitions using numerical simulations and develop analytic theories capturing each transition. Our results relate to other interesting problems including jamming and bootstrap percolation.

Networks of rigid bars connected by joints, termed linkages, provide a minimal framework to design robotic arms and mechanical metamaterials built out of folding components. Here, we investigate a chain-like linkage that, according to linear elasticity, behaves like a topological mechanical insulator whose zero-energy modes are localized at the edge. Simple experiments we performed using prototypes of the chain vividly illustrate how the soft motion, initially localized at the edge, can in fact propagate unobstructed all the way to the opposite end. We demonstrate using real prototypes, simulations and analytical models that the chain is a mechanical conductor, whose carriers are nonlinear solitary waves, not captured within linear elasticity. Indeed, the linkage prototype can be regarded as the simplest example of a topological metamaterial whose protected mechanical excitations are solitons, moving domain walls between distinct topological mechanical phases. More practically, we have built a topologically protected mechanism that can perform basic tasks such as transporting a mechanical state from one location to another. Our work paves the way towards adopting the principle of topological robustness in the design of robots assembled from activated linkages as well as in the fabrication of complex molecular nanostructures., Comment: 9 pages, 9 figures, see http://lorentz.leidenuniv.nl/~chen/kinks for Supporting movies. v2: New section in appendix, new figures

Mechanical metamaterials are artificial structures with unusual properties, such as negative Poisson ratio, bistability or tunable vibrational properties, that originate in the geometry of their unit cell. At the heart of such unusual behaviour is often a soft mode: a motion that does not significantly stretch or compress the links between constituent elements. When activated by motors or external fields, soft modes become the building blocks of robots and smart materials. Here, we demonstrate the existence of topological soft modes that can be positioned at desired locations in a metamaterial while being robust against a wide range of structural deformations or changes in material parameters. These protected modes, localized at dislocations, are the mechanical analogue of topological states bound to defects in electronic systems. We create physical realizations of the topological modes in prototypes of kagome lattices built out of rigid triangular plates. We show mathematically that they originate from the interplay between two Berry phases: the Burgers vector of the dislocation and the topological polarization of the lattice. Our work paves the way towards engineering topologically protected nano-mechanical structures for molecular robotics or information storage and read-out., Comment: 13 pages, 6 figures; changes to text and figures and added analysis on mode localization; see http://www.lorentz.leidenuniv.nl/~paulose/dislocation-modes/ for accompanying videos

We utilize total-internal reflection to isolate the two-dimensional surface foam formed at the planar boundary of a three-dimensional sample. The resulting images of surface Plateau borders are consistent with Plateau's laws for a truly two-dimensional foam. Samples are allowed to coarsen into a self-similar scaling state where statistical distributions appear independent of time, except for an overall scale factor. There we find that statistical measures of side number distributions, size-topology correlations, and bubble shapes are all very similar to those for two-dimensional foams. However, the size number distribution is slightly broader, and the shapes are slightly more elongated. A more obvious difference is that T2 processes now include the creation of surface bubbles, due to rearrangement in the bulk, and von Neumann's law is dramatically violated for individual bubbles. But nevertheless, our most striking finding is that von Neumann's law appears to holds on average, namely, the average rate of area change for surface bubbles appears to be proportional to the number of sides minus six, but with individual bubbles showing a wide distribution of deviations from this average behavior.

The Hopf fibration is an example of a texture: a topologically stable, smooth, global configuration of a field. Here we demonstrate the controlled sculpting of the Hopf fibration in nematic liquid crystals through the control of point defects. We demonstrate how these are related to torons by use of a topological visualization technique derived from the Pontryagin-Thom construction.

The homotopy theory of topological defects is a powerful tool for organizing and unifying many ideas across a broad range of physical systems. Recently, experimental progress was made in controlling and measuring colloidal inclusions in liquid crystalline phases. The topological structure of these systems is quite rich but, at the same time, subtle. Motivated by experiment and the power of topological reasoning, the classification of defects in uniaxial nematic liquid crystals was reviewed and expounded upon. Particular attention was paid to the ambiguities that arise in these systems, which have no counterpart in the much-storied $XY$ model or the Heisenberg ferromagnet.

We solve the rotational abrasion model of Roth, Marques and Durian (arXiv:1009.3492), a one-dimensional quasilinear partial differential equation resembling the inviscid Burgers equation with the unusual feature of a step function factor as a coefficient. The complexity of the solution is primarily in keeping track of the cases in the piecewise function that results from certain amputation and interpolation processes, so we also extract from it a model of an evolving planar tree graph that tracks the evolution of the coarse features of the contour., Comment: 5 pages, 4 figures

Differential growth processes play a prominent role in shaping leaves and biological tissues. Using both analytical and numerical calculations, we consider the shapes of closed, elastic strips which have been subjected to an inhomogeneous pattern of swelling. The stretching and bending energies of a closed strip are frustrated by compatibility constraints between the curvatures and metric of the strip. To analyze this frustration, we study the class of "conical" closed strips with a prescribed metric tensor on their center line. The resulting strip shapes can be classified according to their number of wrinkles and the prescribed pattern of swelling. We use this class of strips as a variational ansatz to obtain the minimal energy shapes of closed strips and find excellent agreement with the results of a numerical bead-spring model. Within this class of strips, we derive a condition under which a strip can have vanishing mean curvature along the center line., 14 pages, 13 figures. Published version. Updated references and added 2 figures

The phase behavior of helical packings of thermoresponsive microspheres inside glass capillaries is studied as a function of volume fraction. Stable packings with long-range orientational order appear to evolve abruptly to disordered states as particle volume fraction is reduced, consistent with recent hard sphere simulations. We quantify this transition using correlations and susceptibilities of the orientational order parameter psi_6. The emergence of coexisting metastable packings, as well as coexisting ordered and disordered states, is also observed. These findings support the notion of phase transition-like behavior in quasi-1D systems., 5 pages, with additional 4 pages of supplemental material, accepted to Physical Review E: Rapid Communications

Focal conic domains are typically the “smoking gun” by which smectic liquid crystalline phases are identified. The geometry of the equally spaced smectic layers is highly generic but, at the same time, difficult to work with. In this Letter we develop an approach to the study of focal sets in smectics which exploits a hidden Poincare symmetry revealed only by viewing the smectic layers as projections from one-higher dimension. We use this perspective to shed light upon several classic focal conic textures, including the concentric cyclides of Dupin, polygonal textures, and tilt-grain boundaries.

We develop a theory of axisymmetric surfaces minimizing a combination of surface tension and nematic elastic energies which may be suitable for describing simple film and bubble shapes. As a function of the elastic constant and the applied tension on the bubbles, we find the analogues of the unduloid, sphere, and nodoid in addition to other new surfaces., 15 pages, 18 figures