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Fisheries management is essential to guarantee sustainable capture of target species and avoid undesirable declines of incidentally captured species. A key challenge is halting and reversing declines of shark and ray species, and specifically assessing the degree to which management is sufficient to avoid declines in relatively data-poor fisheries. While ecological risk analyses focus on intrinsic ‘productivity’ and extrinsic ‘susceptibility’, one would ideally consider the influence of ‘fisheries management’. Currently, there is no single management evaluation that can be applied to a combination of fishery types at the scale of individual country or Regional Fisheries Management Organisations (RFMOs). Here, we outline a management risk (M-Risk) framework for sharks, rays, and chimaeras used to evaluate species’ risk to overfishing resulting from ineffective management. We illustrate our approach with application to one country (Ecuador) and RFMO (Inter-American Tropical Tuna Commission) and illustrate the variation in scores among species. We found that while both management units assessed had similar overall scores, the scores for individual attributes varied. Ecuador scored higher in reporting-related attributes, while the IATTC scored higher in attributes related to data collection and use. We evaluated whether management of individual species was sufficient for their relative sensitivity by combining the management risk score for each species with their intrinsic sensitivity to determine a final M-Risk score. This framework can be applied to determine which species face the greatest risk of overfishing and be used by fisheries managers to identify effective management policies by replicating regulations from countries with lower risk scores.

Early in the SARS-CoV-2 pandemic, the M Health Fairview Hospital System established dedicated hospitals for establishing cohorts and caring for patients with COVID-19, yet the association between treatment at COVID-19-dedicated hospitals and mortality and complications is not known.To analyze the mortality rate and complications associated with treatment at the COVID-19-dedicated hospitals.This retrospective cohort study evaluated data prospectively collected from March 1, 2020, through June 30, 2021, from 11 hospitals in Minnesota, including 2 hospitals created solely to care for patients with COVID-19. Data obtained included demographic characteristics, treatments, and outcomes of interest for all patients with a confirmed COVID-19 infection admitted to this hospital system during the study period.Patients were grouped based on whether they received treatment from 1 of the 2 COVID-19-dedicated hospitals compared with the remainder of the hospitals within the hospital system.Multivariate analyses, including risk-adjusted logistic regression and propensity score matching, were performed to evaluate the primary outcome of in-hospital mortality and secondary outcomes, including complications and use of COVID-specific therapeutics.There were 5504 patients with COVID-19 admitted during the study period (median age, 62.5 [IQR, 45.0-75.6] years; 2854 women [51.9%]). Of these, 2077 patients (37.7%) (median age, 63.4 [IQR, 50.7-76.1] years; 1080 men [52.0%]) were treated at 1 of the 2 COVID-19-dedicated hospitals compared with 3427 (62.3%; median age, 62.0 [40.0-75.1] years; 1857 women (54.2%) treated at other hospitals. The mortality rate was 11.6% (n = 241) at the dedicated hospitals compared with 8.0% (n = 274) at the other hospitals (P .001). However, risk-adjusted in-hospital mortality was significantly lower for patients in the COVID-19-dedicated hospitals in both the unmatched group (n = 2077; odds ratio [OR], 0.75; 95% CI, 0.59-0.95) and the propensity score-matched group (n = 1317; OR, 0.78; 95% CI, 0.58-0.99). The rate of overall complications in the propensity score-matched group was significantly lower (OR, 0.81; 95% CI, 0.66-0.99) and the use of COVID-19-specific therapeutics including deep vein thrombosis prophylaxis (83.9% vs 56.9%; P .001), high-dose corticosteroids (56.1% vs 22.2%; P .001), remdesivir (61.5% vs 44.5%; P .001), and tocilizumab (7.9% vs 2.0; P .001) was significantly higher.In this cohort study, COVID-19-dedicated hospitals had multiple benefits, including providing high-volume repetitive treatment and isolating patients with the infection. This experience suggests improved in-hospital mortality for patients treated at dedicated hospitals owing to improved processes of care and supports the use of establishing cohorts for future pandemics.

Several studies have shown that COVID-19 patients with prior comorbidities have a higher risk for adverse outcomes, resulting in a disproportionate impact on older adults and minorities that fit that profile. However, although there is considerable heterogeneity in the comorbidity profiles of these populations, not much is known about how prior comorbidities co-occur to form COVID-19 patient subgroups, and their implications for targeted care. Here we used bipartite networks to quantitatively and visually analyze heterogeneity in the comorbidity profiles of COVID-19 inpatients, based on electronic health records from 12 hospitals and 60 clinics in the greater Minneapolis region. This approach enabled the analysis and interpretation of heterogeneity at three levels of granularity (cohort, subgroup, and patient), each of which enabled clinicians to rapidly translate the results into the design of clinical interventions. We discuss future extensions of the multigranular heterogeneity framework, and conclude by exploring how the framework could be used to analyze other biomedical phenomena including symptom clusters and molecular phenotypes, with the goal of accelerating translation to targeted clinical care.

BACKGROUND Studies evaluating strategies for the rapid development, implementation, and evaluation of clinical decision support (CDS) systems supporting guidelines for diseases with a poor knowledge base, such as COVID-19, are limited. OBJECTIVE We developed an anticoagulation clinical practice guideline (CPG) for COVID-19, which was delivered and scaled via CDS across a 12-hospital Midwest health care system. This study represents a preplanned 6-month postimplementation evaluation guided by the RE-AIM (Reach, Effectiveness, Adoption, Implementation, and Maintenance) framework. METHODS The implementation outcomes evaluated were reach, adoption, implementation, and maintenance. To evaluate effectiveness, the association of CPG adherence on hospital admission with clinical outcomes was assessed via multivariable logistic regression and nearest neighbor propensity score matching. A time-to-event analysis was conducted. Sensitivity analyses were also conducted to evaluate the competing risk of death prior to intensive care unit (ICU) admission. The models were risk adjusted to account for age, gender, race/ethnicity, non-English speaking status, area deprivation index, month of admission, remdesivir treatment, tocilizumab treatment, steroid treatment, BMI, Elixhauser comorbidity index, oxygen saturation/fraction of inspired oxygen ratio, systolic blood pressure, respiratory rate, treating hospital, and source of admission. A preplanned subgroup analysis was also conducted in patients who had laboratory values (D-dimer, C-reactive protein, creatinine, and absolute neutrophil to absolute lymphocyte ratio) present. The primary effectiveness endpoint was the need for ICU admission within 48 hours of hospital admission. RESULTS A total of 2503 patients were included in this study. CDS reach approached 95% during implementation. Adherence achieved a peak of 72% during implementation. Variation was noted in adoption across sites and nursing units. Adoption was the highest at hospitals that were specifically transformed to only provide care to patients with COVID-19 (COVID-19 cohorted hospitals; 74%-82%) and the lowest in academic settings (47%-55%). CPG delivery via the CDS system was associated with improved adherence (odds ratio [OR] 1.43, 95% CI 1.2-1.7; PPP CONCLUSIONS Our institutional experience demonstrated that adherence with the institutional CPG delivered via the CDS system resulted in improved clinical outcomes for patients with COVID-19. CDS systems are an effective means to rapidly scale a CPG across a heterogeneous health care system. Further research is needed to investigate factors associated with adherence at low and high adopting sites and nursing units.

VALIDATION OF A HYBRID EVAPOTRANSPIRATION MODEL USING SATELLITE IMAGERY AND PRECIPITATION-FLOW DATA RAONI WAINER DUARTE BOSQUILIA1; CHRISTOPHER MICHAEL USHER NEALE2; SERGIO NASCIMENTO DUARTE3; SILVIO FROSINI DE BARROS FERRAZ3; PEDRO PAULO DA SILVA BARROS4 AND FRANK EDGAR MULLER-KARGER5 1 Federal Technological University of Paraná (UTFPR), Dois Vizinhos Campus, Estrada para Boa Esperança, km 4, CEP 85660-000, Dois Vizinhos, Paraná, Brazil, e-mail: raonibosquilia@utfpr.edu.br 2 University of Nebraska-Lincoln, Water for Food Institute, 2021 Transformation Dr Suite 3220, zipcode 68588, Lincoln, NE, USA, e-mail: cneale@nebraska.edu 3 University of São Paulo (USP), Luiz de Queiroz College of Agriculture (ESALQ), Av. Pádua Dias, 235, CEP 13418-900, Piracicaba, São Paulo, Brazil, e-mail: snduarte@usp.br; silvio.ferraz@usp.br 4 Federal University of Uberlândia (UFU), Campus Monte Carmelo, Rodovia LMG 746, Km 1, CEP 38500-000, Monte Carmelo, MG, Brazil, e-mail: pedropaulo.barros@ufu.br 5 University of South Florida, Saint Petersburg, College of Marine Sciences, 830 1st St S, zipcode 33701, St. Petersburg, FL, USA, e-mail: carib@usf.edu 1 ABSTRACT To quantify the water balance in watersheds, it is necessary to know the components of the hydrologic cycle, especially evapotranspiration (ET). Many studies have been conducted using a single-source model such as SEBAL to estimate the actual ET (ETa) from satellite imagery; however, other models have been developed and continuously improved, such as the Two Source Energy Balance (TSEB). This study evaluated ETa estimation performed by a hybrid TSEB ET model programmed in the Spatial Evapotranspiration Modeling Interface (SETMI) using satellite imagery. The evaluation was conducted over two full hydrological years, developing a new methodology to convert hourly ETa data to monthly and annual data. The results of applying the TSEB/SETMI model to Landsat 8 imagery were validated to a water balance calculation from field measurements in three representative watersheds in Corumbataí, SP, Brazil. Thus, it was concluded that the adjustment applied to monthly and annual ET data produced results statistically correlated to those obtained through a simplified annual water balance, confirming that the developed methodology can be used to estimate monthly and annual ET from Landsat 8 imagery and the hybrid ET model. Keywords: Landsat 8, two source energy balance, remote sensing, water balance BOSQUILIA, R. W. D.; NEALE, C. M. U.; DUARTE, S. N.; FERRAZ, S. F. B.; BARROS, P. P. S.; MULLER-KARGER, F. E. VALIDAÇÃO DE UM MODELO HÍBRIDO DE EVAPOTRANSPIRAÇÃO UTILIZANDO IMAGENS DE SATÉLITE E DADOS DE CHUVA-VAZÃO 2 RESUMO Para quantificar o balanço hídrico em bacias hidrográficas, é necessário conhecer os componentes do ciclo hidrológico, especialmente, a evapotranspiração (ET). Muitos estudos têm sido realizados utilizando um modelo de fonte única como o SEBAL para estimar a ET real (ETa) a partir de imagens de satélite; contudo, outros modelos têm sido desenvolvidos e continuamente melhorados, tais como o Balanço Energético de Duas Fontes (TSEB). Este estudo avaliou a estimativa da ETa realizada por um modelo de ET híbrido de TSEB programado na Interface de Modelagem de Evapotranspiração Espacial (SETMI) utilizando imagens de satélite. A avaliação foi realizada ao longo de dois anos hidrológicos completos, desenvolvendo-se uma nova metodologia para converter os dados de ETa horários em dados mensais e anuais. Os resultados da aplicação do modelo TSEB/SETMI às imagens do Landsat 8 foram validados contra um de cálculo do balanço hídrico a partir de medições de campo em três bacias hidrográficas representativas de Corumbataí, SP, Brasil. Assim, concluiu-se que o ajustamento aplicado aos dados mensais e anuais da ET produziu resultados estatisticamente correlacionados aos obtidos através de um balanço hídrico anual simplificado, confirmando que a metodologia desenvolvida pode ser empregada em estimativas mensais e anuais da ET a partir de imagens do satélite Landsat 8 e do modelo de ET híbrido. Palavras-chave: Landsat 8, balanço energético de duas fontes, sensoriamento remoto, balanço hídrico

BACKGROUND The increasing incidence of COVID-19 infection has challenged health care systems to increase capacity while conserving personal protective equipment (PPE) supplies and minimizing nosocomial spread. Telemedicine shows promise to address these challenges but lacks comprehensive evaluation in the inpatient environment. OBJECTIVE The aim of this study is to evaluate an intrahospital telemedicine program (virtual care), along with its impact on exposure risk and communication. METHODS We conducted a natural experiment of virtual care on patients admitted for COVID-19. The primary exposure variable was documented use of virtual care. Patient characteristics, PPE use rates, and their association with virtual care use were assessed. In parallel, we conducted surveys with patients and clinicians to capture satisfaction with virtual care along the domains of communication, medical treatment, and exposure risk. RESULTS Of 137 total patients in our primary analysis, 43 patients used virtual care. In total, there were 82 inpatient days of use and 401 inpatient days without use. Hospital utilization and illness severity were similar in patients who opted in versus opted out. Virtual care was associated with a significant reduction in PPE use and physical exam rate. Surveys of 41 patients and clinicians showed high rates of recommendation for further use, and subjective improvements in communication. However, providers and patients expressed limitations in usability, medical assessment, and empathetic communication. CONCLUSIONS In this pilot natural experiment, only a subset of patients used inpatient virtual care. When used, virtual care was associated with reductions in PPE use, reductions in exposure risk, and patient and provider satisfaction.

We show that if the image of a Legendrian submanifold under a contact homeomorphism (i.e. a homeomorphism that is a $C^0$-limit of contactomorphisms) is smooth then it is Legendrian, assuming only positive local lower bounds on the conformal factors of the approximating contactomorphisms. More generally the analogous result holds for coisotropic submanifolds in the sense of arXiv:1306.6367. This is a contact version of the Humili\`ere-Leclercq-Seyfaddini coisotropic rigidity theorem in $C^0$ symplectic geometry, and the proof adapts the author's recent re-proof of that result in arXiv:1912.13043 based on a notion of local rigidity of points on locally closed subsets. We also provide two different flavors of examples showing that a contact homeomorphism can map a submanifold that is transverse to the contact structure to one that is smooth and tangent to the contact structure at a point., Comment: 38 pages. v2: minor edits

We show that many toric domains $X$ in $R^4$ admit symplectic embeddings $\phi$ into dilates of themselves which are knotted in the strong sense that there is no symplectomorphism of the target that takes $\phi(X)$ to $X$. For instance $X$ can be taken equal to a polydisk $P(1,1)$, or to any convex toric domain that both is contained in $P(1,1)$ and properly contains a ball $B^4(1)$; by contrast a result of McDuff shows that $B^4(1)$ (or indeed any four-dimensional ellipsoid) cannot have this property. The embeddings are constructed based on recent advances on symplectic embeddings of ellipsoids, though in some cases a more elementary construction is possible. The fact that the embeddings are knotted is proven using filtered positive $S^1$-equivariant symplectic homology., Comment: 52 pages, 4 figures

We study the symplectic embedding capacity function $C_{\beta}$ for ellipsoids $E(1,\alpha)\subset R^4$ into dilates of polydisks $P(1,\beta)$ as both $\alpha$ and $\beta$ vary through $[1,\infty)$. For $\beta=1$ Frenkel and Mueller showed that $C_{\beta}$ has an infinite staircase accumulating at $\alpha=3+2\sqrt{2}$, while for integer $\beta\geq 2$ Cristofaro-Gardiner, Frenkel, and Schlenk found that no infinite staircase arises. We show that, for arbitrary $\beta\in (1,\infty)$, the restriction of $C_{\beta}$ to $[1,3+2\sqrt{2}]$ is determined entirely by the obstructions from Frenkel and Mueller's work, leading $C_{\beta}$ on this interval to have a finite staircase with the number of steps tending to $\infty$ as $\beta\to 1$. On the other hand, in contrast to the case of integer $\beta$, for a certain doubly-indexed sequence of irrational numbers $L_{n,k}$ we find that $C_{L_{n,k}}$ has an infinite staircase; these $L_{n,k}$ include both numbers that are arbitrarily large and numbers that are arbitrarily close to $1$, with the corresponding accumulation points respectively arbitrarily large and arbitrarily close to $3+2\sqrt{2}$., Comment: 72 pages, 9 figures

Following proposals of Ostrover and Polterovich, we introduce and study "coarse" and "fine" versions of a symplectic Banach-Mazur distance on certain open subsets of $\mathbb{C}^n$ and other open Liouville domains. The coarse version declares two such domains to be close to each other if each domain admits a Liouville embedding into a slight dilate of the other; the fine version, which is similar to the distance on subsets of cotangent bundles of surfaces recently studied by Stojisavljevi\'c and Zhang, imposes an additional requirement on the images of these embeddings that is motivated by the definition of the classical Banach-Mazur distance on convex bodies. Our first main result is that the coarse and fine distances are quite different from each other, in that there are sequences that converge coarsely to an ellipsoid but diverge to infinity with respect to the fine distance. Our other main result is that, with respect to the fine distance, the space of star-shaped domains in $\mathbb{C}^n$ admits quasi-isometric embeddings of $\mathbb{R}^D$ for every finite dimension $D$. Our constructions are obtained from a general method of constructing $(2n+2)$-dimensional Liouville domains whose boundaries have Reeb dynamics determined by certain autonomous Hamiltonian flows on a given $2n$-dimensional Liouville domain. The bounds underlying our main results are proven using filtered equivariant symplectic homology via methods from prior joint work with Gutt., Comment: v2: 56 pages, several corrections and additional explanations based on referee's comments. To appear in J. Top. Anal

We consider various constructions of monotone Lagrangian submanifolds of ℂ Pn, S2 × S2, and quadric hypersurfaces of ℂ Pn. In S2 × S2 and ℂ P2 we show that several different known constructions of exotic monotone tori yield results that are Hamiltonian isotopic to each other, in particular answering a question of Wu by showing that the monotone fiber of a toric degeneration model of ℂ P2 is Hamiltonian isotopic to the Chekanov torus. Generalizing our constructions to higher dimensions leads us to consider monotone Lagrangian submanifolds (typically not tori) of quadrics and of ℂ Pn which can be understood either in terms of the geodesic flow on T∗Sn or in terms of the Biran circle bundle construction. Unlike previously known monotone Lagrangian submanifolds of closed simply connected symplectic manifolds, many of our higher-dimensional Lagrangian submanifolds are provably displaceable.

We show that if (M ,ω) is a closed symplectic manifold which admits a nontrivial Hamiltonian vector field all of whose contractible closed orbits are constant, then Hofer’s metric on the group of Hamiltonian diffeomorphisms of (M ,ω) has infinite diameter, and indeed admits infinite-dimensional quasi-isometrically embedded normed vector spaces. A similar conclusion applies to Hofer’s metric on various spaces of Lagrangian submanifolds, including those Hamiltonian-isotopic to the diagonal in M × M when M satisfies the above dynamical condition. To prove this, we use the properties of a Floer-theoretic quantity called the boundary depth, which measures the nontriviality of the boundary operator on the Floer complex in a way that encodes robust symplectic-topological information.

We exhibit many examples of closed symplectic manifolds on which there is an autonomous Hamiltonian whose associated flow has no nonconstant periodic orbits (the only previous explicit example in the literature was the torus T 2 n T^{2n} ( n ≥ 2 n\geq 2 ) with an irrational symplectic structure). The underlying smooth manifolds of our examples include, for instance: the K 3 K3 surface and also infinitely many smooth manifolds homeomorphic but not diffeomorphic to it; infinitely many minimal four-manifolds having any given finitely-presented group as their fundamental group; and simply connected minimal four-manifolds realizing all but finitely many points in the first quadrant of the geography plane below the line corresponding to signature 3 3 . The examples are constructed by performing symplectic sums along suitable tori and then perturbing the symplectic form in such a way that hypersurfaces near the “neck” in the symplectic sum have no closed characteristics. We conjecture that any closed symplectic four-manifold with b + > 1 b^+>1 admits symplectic forms with a similar property.

We develop a family of deformations of the differential and of the pair-of-pants product on the Hamiltonian Floer complex of a symplectic manifold (M,\omega) which upon passing to homology yields ring isomorphisms with the big quantum homology of M. By studying the properties of the resulting deformed version of the Oh-Schwarz spectral invariants, we obtain a Floer-theoretic interpretation of a result of Lu which bounds the Hofer-Zehnder capacity of M when M has a nonzero Gromov-Witten invariant with two point constraints, and we produce a new algebraic criterion for (M,\omega) to admit a Calabi quasimorphism and a symplectic quasi-state. This latter criterion is found to hold whenever M has generically semisimple quantum homology in the sense considered by Dubrovin and Manin (this includes all compact toric M), and also whenever M is a point blowup of an arbitrary closed symplectic manifold., Comment: 73 pages, 1 color figure. Added new material explaining how to make some of the constructions on semipositive manifolds without using Kuranishi structures

We prove that a certain bilinear pairing (analogous to the Poincaré–Lefschetz intersection pairing) between filtered sub- and quotient complexes of a Floer-type chain complex and of its "opposite complex" is always nondegenerate on homology. This implies a duality relation for the Oh–Schwarz-type spectral invariants of these complexes which (in Hamiltonian Floer theory) was established in the special case that the period map has discrete image by Entov and Polterovich. The duality relation served as a key lemma in Entov and Polterovich's construction of a Calabi quasimorphism on certain rational symplectic manifolds, and the result that we prove here implies that their construction remains valid when the rationality hypothesis is dropped. Apart from this, we also use the nondegeneracy of the pairing to establish a new formula for what we have previously called the boundary depth of a Floer chain complex; this formula shows that the boundary depth is unchanged under passing to the opposite complex.

The objective of this work was to evaluate the reliability of eddy covariance measurements, analyzing the energy balance components, evapotranspiration and energy balance closure in dry and wet growing seasons, in a banana orchard. The experiment was carried out at a farm located within the irrigation district of Quixeré, in the Lower Jaguaribe basin, in Ceará state, Brazil. An eddy covariance system was used to measure the turbulent flux. An automatic weather station was installed in a grass field to obtain the reference evapotranspiration (ET0) from the combined FAO-Penman-Monteith method. Wind speed and vapor pressure deficit are the most important variables on the evaporative process in both growing seasons. In the dry season, the heat fluxes have a similar order of magnitude, and during the wet season the latent heat flux is the largest. The eddy covariance system had acceptable reliability in measuring heat flux, with actual evapotranspiration results comparing well with those obtained by using the water balance method. The energy balance closure had good results for the study area, with mean values of 0.93 and 0.86 for the dry and wet growing seasons respectively.O objetivo deste trabalho foi avaliar a confiabilidade da técnica das correlações turbulentas, analisando as componentes do balanço de energia, a evapotranspiração e o fechamento do balanço de energia nas estações de crescimento seca e úmida, na cultura da banana. O experimento foi realizado em uma fazenda localizada no distrito irrigado de Quixeré, na Bacia do Baixo Jaguaribe, Ceará. Foi utilizado um sistema de correlações turbulentas na obtenção das medidas dos fluxos turbulentos. Uma estação meteorológica automática foi instalada em um gramado para a obtenção da evapotranspiração de referência (ET0) pelo método FAO-Penman-Monteith. A velocidade do vento e o deficit de pressão do vapor são as variáveis mais importantes no processo evaporativo em ambas as estações. Na estação seca, os fluxos de calor têm ordens de magnitude similares, enquanto na estação úmida o calor latente é superior. O sistema de correlações turbulentas apresentou confiança aceitável na obtenção dos fluxos de calor, com a evapotranspiração real mostrando valores similares aos obtidos pelo método do balanço hídrico. O fechamento do balanço de energia apresentou bons resultados para a área de estudo, com valores médios de 0,93 e 0,86 para as estações seca e chuvosa, respectivamente.

We show that if $K: P\to\mathbb{R}$ is an autonomous Hamiltonian on a symplectic manifold $(P,\Omega)$ which attains a Morse-Bott nondegenerate minimum of 0 along a symplectic submanifold $M$ and if $c_1(TP)$↾M vanishes in real cohomology, then the Hamiltonian flow of $K$ has contractible periodic orbits with bounded period on all sufficiently small energy levels. As a special case, if the geodesic flow on T*M is twisted by a symplectic magnetic field form, then the resulting flow has contractible periodic orbits on all low energy levels. These results were proven by Ginzburg and Gurel when $\Omega$↾M is spherically rational, and our proof builds on their work; the argument involves constructing and carefully analyzing at the chain level a version of filtered Floer homology in the symplectic normal disk bundle to $M$.

The chain complexes underlying Floer homology theories typically carry a real-valued filtration, allowing one to associate to each Floer homology class a spectral number defined as the infimum of the filtration levels of chains representing that class. These spectral numbers have been studied extensively in the case of Hamiltonian Floer homology by Oh, Schwarz, and others. We prove that the spectral number associated to any nonzero Floer homology class is always finite, and that the infimum in the definition of the spectral number is always attained. In the Hamiltonian case, this implies that what is known as the ``nondegenerate spectrality'' axiom holds on all closed symplectic manifolds. Our proofs are entirely algebraic and apply to any Floer-type theory (including Novikov homology) satisfying certain standard formal properties. The key ingredient is a theorem about the existence of best approximations of arbitrary elements of finitely generated free modules over Novikov rings by elements of prescribed submodules with respect to a certain family of non-Archimedean metrics., The main algebraic lemma (the former Theorem 1.6) has been given a more general statement and a shorter proof. This allows us to generalize the main results to cover Floer theories with integral or local coefficients. Submitted version. 13 pages

We construct "barcodes" for the chain complexes over Novikov rings that arise in Novikov's Morse theory for closed one-forms and in Floer theory on not-necessarily-monotone symplectic manifolds. In the case of classical Morse theory these coincide with the barcodes familiar from persistent homology. Our barcodes completely characterize the filtered chain homotopy type of the chain complex; in particular they subsume in a natural way previous filtered Floer-theoretic invariants such as boundary depth and torsion exponents, and also reflect information about spectral invariants. We moreover prove a continuity result which is a natural analogue both of the classical bottleneck stability theorem in persistent homology and of standard continuity results for spectral invariants, and we use this to prove a C^0-robustness result for the fixed points of Hamiltonian diffeomorphisms. Our approach, which is rather different from the standard methods of persistent homology, is based on a non-Archimedean singular value decomposition for the boundary operator of the chain complex., Comment: 71 pages. v2: several typos have been fixed. v3: the start of the proof of the stability theorem has been simplified, Appendix A has been moved to the body of the paper, and some clarifying remarks have been added

We prove the elementary but surprising fact that the Hofer distance between two closed subsets of a symplectic manifold can be expressed in terms of the restrictions of Hamiltonians to one of the subsets; this helps explain certain energy-capacity inequalities that appeared recently in work of Borman-McLean and Humiliere-Leclercq-Seyfaddini. We also build on arXiv:1201.2926 to obtain new vanishing results for the Hofer distance between subsets, applicable for instance to singular analytic subvarieties of Kahler manifolds., 9 pages

For a class of Riemannian manifolds that include products of arbitrary compact manifolds with manifolds of nonpositive sectional curvature on the one hand, or with certain positive-curvature examples such as spheres of dimension at least 3 and compact semisimple Lie groups on the other, we show that the Hamiltonian diffeomorphism group of the cotangent bundle contains as subgroups infinite-dimensional normed vector spaces that are bi-Lipschitz embedded with respect to Hofer's metric; moreover these subgroups can be taken to consist of diffeomorphisms supported in an arbitrary neighborhood of the zero section. In fact, the orbit of a fiber of the cotangent bundle with respect to any of these subgroups is quasi-isometrically embedded with respect to the induced Hofer metric on the orbit of the fiber under the whole group. The diffeomorphisms in these subgroups are obtained from reparametrizations of the geodesic flow. Our proofs involve a study of the Hamiltonian-perturbed Floer complex of a pair of cotangent fibers (or, more generally, of a conormal bundle together with a cotangent fiber). Although the homology of this complex vanishes, an analysis of its boundary depth yields the lower bounds on the Lagrangian Hofer metric required for our main results., Comment: 26 pages

For a Morse function f on a compact oriented manifold M, we show that f has more critical points than the number required by the Morse inequalities if and only if there exists a certain class of link in M whose components have nontrivial linking number, such that the minimal value of f on one of the components is larger than its maximal value on the other. Indeed we characterize the precise number of critical points of f in terms of the Betti numbers of M and the behavior of f with respect to links. This can be viewed as a refinement, in the case of compact manifolds, of the Rabinowitz Saddle Point Theorem. Our approach, inspired in part by techniques of chain-level symplectic Floer theory, involves associating to collections of chains in M algebraic operations on the Morse complex of f, which yields relationships between the linking numbers of homologically trivial (pseudo)cycles in M and an algebraic linking pairing on the Morse complex., 46 pages; some of the length is due to the inclusion of details of somewhat-standard arguments in the hopes of making the paper more broadly accessible. Preliminary version, comments very welcome

Chekanov showed that the Hofer norm on the Hamiltonian diffeomorphism group of a geometrically bounded symplectic manifold induces a nondegenerate metric on the orbit of any compact Lagrangian submanifold under the group. In this paper we consider the orbits of more general submanifolds. We show that, for the Chekanov-Hofer pseudometric on the orbit of a closed submanifold to be a genuine metric, it is necessary for the submanifold to be coisotropic, and we show that this condition is sufficient under various additional geometric assumptions. At the other extreme, we show that the image of a generic closed embedding with any codimension larger than one is "weightless," in the sense that the Chekanov-Hofer pseudometric on its orbit vanishes identically. In particular this yields examples of submanifolds which have zero displacement energy but are not infinitesimally displaceable., Comment: 38 pages. v2: several typos fixed, v3: several changes in response to referee report

Modulo trivial exceptions, we show that smoothly nontrivial symplectic sums of symplectic 4-manifolds along surfaces of positive genus are never rational or ruled, and we enumerate each case in which they have Kodaira dimension zero (i.e., are blowups of symplectic 4-manifolds with torsion canonical class). In particular, a symplectic four-manifold of Kodaira dimension zero arises by such a surgery only if it is diffeomorphic to a blowup either of the K3 surface, the Enriques surface, or a member of a particular family of T^2-bundles over T^2 each having b_1=2., Comment: Minor changes based on referee's comments. To appear in Comment. Math. Helv. 23 pages

We introduce an analogue of the inflation technique of Lalonde-McDuff, allowing us to obtain new symplectic forms from symplectic surfaces of negative self-intersection in symplectic four-manifolds. We consider the implications of this construction for the symplectic cones of K\"ahler surfaces, proving along the way a result which can be used to simplify the intersections of distinct pseudoholomorphic curves via a perturbation., Comment: 17 pages. To appear in Journal of Symplectic Geometry

Adapting a construction of D Salamon involving the U(1) vortex equations, we explore the properties of a Floer theory for 3-manifolds that fiber over S^1 which exhibits several parallels with monopole Floer homology, and in all likelihood coincides with it. The theory fits into a restricted analogue of a TQFT in which the cobordisms are required to be equipped with Lefschetz fibrations, and has connections to the dynamics of surface symplectomorphisms., This is the version published by Algebraic & Geometric Topology on 21 October 2006