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The spatiotemporal features of normal in vivo cardiac motion are well established. Longitudinal velocity has become a focus of diastolic function (DF) characterization, particularly the tissue Doppler e′-wave, manifesting in early diastole when the left ventricle (LV) is a mechanical suction pump (dP/dV < 0). To characterize DF and elucidate mechanistic features, several models have been proposed and have been previously compared algebraically, numerically, and in their ability to fit physiological velocity data. We analyze two previously noncompared models of early rapid-filling lengthening velocity (Doppler e′-wave): parametrized diastolic filling (PDF) and force balance model (FBM). Our initial numerical experiments sampled FBM-generated e′( t) contours as input to determine PDF model predicted fit. The resulting exact numerical agreement [standard error of regression (SER) = 9.06 × 10−16] was not anticipated. Therefore, we analyzed all published FBM-generated e′( t) contours and observed identical agreement. We re-expressed FBM’s algebraic expressions for e′( t) and observed for the first time that model-based predictions for lengthening velocity by the FBM and the PDF model are mathematically identical: e′( t) = γe−α tsinh(β t), thereby providing exact algebraic relations between the three PDF parameters and the six FBM parameters. Previous pioneering experiments have independently established the unique determinants of e′( t) to be LV relaxation, restoring forces (stiffness), and load. In light of the exact intermodel agreement, we conclude that the three PDF parameters, relaxation, stiffness (restoring forces), and load, are unique determinants of DF and e′( t). Thus, we show that only the PDF formalism can compute the three unique, independent, physiological determinants of long-axis LV myocardial velocity from e′( t). NEW & NOTEWORTHY We show that two separate, independently derived physiological (kinematic) models predict mathematically identical expressions for LV-lengthening velocity (Doppler e′-wave), indicating that damped harmonic oscillatory motion is a physiologically accurate model of diastolic function. Although both models predict the same “overdamped” velocity contour, only one model solves the “inverse problem” and generates unique, lumped parameters of relaxation, stiffness (restoring force), and load from the e′-wave.

In this chapter, a mathematical model will be studied, which describes predator–prey relations. This model, consisting of a higher dimensional system of ordinary differential equations, has been motivated by ecological systems in which more different predator species are competing for a single-prey species. In order to have a more realistic model, an infinite distributed delay will be introduced into the prey’s density. This delay takes into account that the predator’s growth rate at present depends on past quantities of prey. We investigate under what conditions does the originally asymptotically stable interior equilibrium lose its stability and prove the occurrence of limit cycles.

In this paper, a mathematical model will be studied that describes the connections between three species: people, trees, and rats. This model, consisting of a three-dimensional system of ordinary differential equations, has been motivated by attempts to explain the ecological disaster of Easter Island. The system has four equilibria from which three ones are on the boundary of the positive octant of the phase space and—under appropriate conditions—there is a unique interior equilibrium. The existence, uniqueness, and boundedness of the solutions are established. We study the local asymptotical stability of the equilibria and show that Hopf bifurcation takes place: limit cycles occur.

Conventional echocardiographic diastolic function (DF) assessment approximates transmitral flow velocity contours (Doppler E-waves) as triangles, with peak (Epeak), acceleration time (AT), and deceleration time (DT) as indexes. These metrics have limited value because they are unable to characterize the underlying physiology. The parametrized diastolic filling (PDF) formalism provides a physiologic, kinematic mechanism based characterization of DF by extracting chamber stiffness (k), relaxation (c), and load (x o ) from E-wave contours. We derive the mathematical relationship between the PDF parameters and Epeak, AT, DT and thereby introduce the geometric method (GM) that computes the PDF parameters using Epeak, AT, and DT as input. Numerical experiments validated GM by analysis of 208 E-waves from 31 datasets spanning the full range of clinical diastolic function. GM yielded indistinguishable average parameter values per subject vs. the gold-standard PDF method (k: R2 = 0.94, c: R2 = 0.95, x o : R2 = 0.95, p

The purpose of this note is to show that in characteristic two there exists a smooth Fano variety for which the square of the anti-canonical bundle violates Kodaira vanishing. This is used in turn to construct non-Cohen-Macaulay canonical singularities in characteristic two., added references to related work done recently

We prove that any coarse moduli space of stable log-varieties of general type is projective. We also prove subadditivity of log-Kodaira dimension for fiber spaces whose general fiber is of log general type.

SummaryObjective The aim of this study was to compare an in-person, group-based behavioral weight loss intervention to technology-based interventions in adults with obesity. Methods Adults (N = 39; body mass index: 39.5 ± 2.8 kg m−2; age: 39.9 ± 11.5 years) participated in a 6-month program with randomization to one of three intervention groups: standard behavioral weight loss, a technology-based system combined with a monthly intervention telephone call (TECH) or an enhanced technology-based system combined with a monthly intervention telephone call (EN-TECH). All groups were prescribed an energy-restricted diet and physical activity. Assessments occurred at 0, 3 and 6 months. Separate mixed-effects models using unstructured dependence structure were fit to the outcomes. Results Weight loss (least square means ± standard error) at 6 months was −6.57 ± 1.65 kg in standard behavioral weight loss, −5.18 ± 1.72 kg in TECH and −6.25 ± 1.95 kg in EN-TECH (p-value for time effect ≤ 0.0001). A similar pattern was observed for change in body mass index, waist circumference and percent body fat. There was a decrease in total energy intake (p = 0.0005) and percent dietary fat intake (p = 0.0172), and physical activity increased (p = 0.0003). Conclusions Findings provide initial information on the use of technology-based interventions that include wearable devices combined with brief monthly telephone calls for weight loss in adults with obesity.

Some tools are briefly presented which are useful at non-linear inverse problems. It is found that some parameters can be eliminated under some conditions from the minimization. If all parameters are eliminated except one, then the transformed merit-function is one-dimensional and can easily be minimized (and can easily be used for reliability testing, too). On the other hand, since each real-life merit function has a closest, noise-free merit-function in the Least Squares sense, this so called follower can be used in the minimization, and for reliability testing. The methods are illustrated by the evaluation of a laboratory and an in situ test. Both models are linear PDE-s resulting in ‘nice’, convex shaped follower merit functions.

We introduce a lifting property for local cohomology, which leads to a unified treatment of the dualizing complex for flat morphisms with semi-log-canonical, Du Bois or F-pure fibers. As a consequence we obtain that, in all 3 cases, the cohomology sheaves of the relative dualizing complex are flat and commute with base change. We also derive several consequences for deformations of semi-log-canonical, Du Bois and F-pure singularities., Comment: This is a substantially generalized and expanded version of arXiv:1803.03325 [math.AG]. Version 3: new references added to related works

The pumping attributes of the heart remain active topics of investigation and mastery of how the heart functions as a pump is part of the fund of knowledge of physiologists and cardiologists. The advent of high-resolution, real-time imaging (computed tomography, magnetic resonance imaging cardiac catheterization, two- and three-dimensional echocardiography) has continued to advance our understanding of how the four-chambered heart (left heart, right heart) works as it fills and as it empties. The insights that have evolved emanate from a conceptual framework based on motion (kinematics) of selected phases and portions of the four-chambered heart and the contents of the pericardial sac. Concepts include pressure pumping, volume pumping, constant-volume pumping, the relationship between atrial and ventricular function and atrial and ventricular indexes, the role of the heart as a suction pump, laws that govern isovolumic relaxation, and the relationship of intraventricular fluid mechanics to diastolic function and wall motion. Accordingly, by asking such questions as ‘What is the ejection fraction of the pericardial sack, and why does it have the numerical value it has?’ or ‘Why does the left atrium fill in two phases—one in systole and one in diastole?’ or ‘How is atrial conduit volume related to diastolic wall motion?’ one can gain new insights into pumping function. This chapter presents a simple, useful, yet powerful conceptual framework that can be used descriptively or mathematically to addresses these and other clinically important themes.

To present and validate a new method for 4D flow quantification of vortex-ring mixing during early, rapid filling of the left ventricle (LV) as a potential index of diastolic dysfunction and heart failure.

Despite Leonardo da Vinci's observation (circa 1511) that “the atria or filling chambers contract together while the pumping chambers or ventricles are relaxing and vice versa,” the dynamics of four-chamber heart function, and of diastolic function (DF) in particular, are not generally appreciated. We view DF from a global perspective, while characterizing it in terms of causality and clinical relevance. Our models derive from the insight that global DF is ultimately a result of forces generated by elastic recoil, modulated by cross-bridge relaxation, and load. The interaction between recoil and relaxation results in physical wall motion that generates pressure gradients that drive fluid flow, while epicardial wall motion is constrained by the pericardial sac. Traditional DF indexes (τ, E/E′, etc.) are not derived from causal mechanisms and are interpreted as approximating either stiffness or relaxation, but not both, thereby limiting the accuracy of DF quantification. Our derived kinematic models of isovolumic relaxation and suction-initiated filling are extensively validated, quantify the balance between stiffness and relaxation, and provide novel mechanistic physiological insight. For example, causality-based modeling provides load-independent indexes of DF and reveals that both stiffness and relaxation modify traditional DF indexes. The method has revealed that the in vivo left ventricular equilibrium volume occurs at diastasis, predicted novel relationships between filling and wall motion, and quantified causal relationships between ventricular and atrial function. In summary, by using governing physiological principles as a guide, we define what global DF is, what it is not, and how to measure it.

Background Heart failure (HF) epidemic has increased need for accurate diastolic dysfunction (DD) quantitation. Cardiac MRI can elucidate left atrial (LA) phasic function, and accurately quantify its conduit contribution to left ventricular (LV) filling, but has limited availability. We hypothesized that the percentage of LV stroke volume due to atrial conduit volume (LACV), as assessed using 3D-echocardiography, can differentiate among progressive degrees of DD in HF patients. Methods and results Sixty-three subjects (66 ± 12 years) with DD and ejection fraction (EF) ranging 14–62 % underwent full-volume 3D-echocardiography. Simultaneous LA and LV volume curves as function of time (t) were calculated, with LACV as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{LACV}}\left( t \right) \, = \, \left[ {{\text{LV}}\left( t \right){-}{\text{LV minimum}}} \right] \, - \, \left[ {{\text{LA maximum }} - {\text{ LA}}\left( t \right)} \right]$$\end{document}LACVt=LVt-LV minimum-LA maximum-LAt, expressed as % of stroke volume. Patients were assigned to four (0–3, from none to severe) DD grades, according to classical Doppler parameters. In this population DD is linked to LACV, with progressively higher percentages of conduit contribution to stroke volume associated with higher degrees of DD (p = 0.0007). Patients were then dichotomized into no-mild (n = 26) or severe (n = 37) DD groups. Apart from atrial volume, larger (p

During mapping between Aggtelek, J6svafO and Egerszog (Aggtelek Hills, Silica Nappe) a new basinal limestone sequence was recognised in between the Steinalm and Wetterstein platform limestones. It comprises Schreyeralm Fm. (base) and Raming Fm. (top) . The latter one is new for Hungary. We describe two section s (Nagy Jenei Hill and Baradla Cave). In both the Schreyeralm Fm. is characterised by reddish coquina rich micritic limestone. The Raming Fm. consists of allodapic calcarenites and reef detritus sand­ wiched between filament mud- to wackestones. In the upper part, the resedimented reef detritus becomes more and more frequent. In the Baradla Cave section radiolarite beds with a tuffite intercalation terminate the basinal succession. The base of the Schreyeralm Fm. is heterochronous (late Pelsonian to PelsonianlIlIyrian). The base of the Raming Fm. contains conodonts referring to an age interval of Trinodosus up to most part of Reitzi Zone (early-middle Illyrian). The top is also heterochronous.lts age is middle Illyrian (Trinodosus - most part of Reitzi Zone) in the NW and Fassanian (Curionii Zone) in the SE part. The sedimentation was controlled by a halfgraben morphology of the basement. The closest similarity to this formation can be found in the Slovak part of the Silica Nappe and in well oxi­ genated zones of Reifling basin in the Hronic Unit. In the Juvavic Domain of the Northern Calcareous Alps the "Southern" slope facies (s ensu Mandl 1999 , 2000) of the Wetterstein platform , where Raming-type allo­ dapic limestones interfinger with open marine variegated pelagic carbonates , is closely related to the newly recognised Raming Fm . in the Aggtelek Hills.

We discuss the minimal model program for b-log varieties, which is a pair of a variety and a b-divisor, as a natural generalization of the minimal model program for ordinary log varieties. We show that the main theorems of the log MMP work in the setting of the b-log MMP. If we assume that the log MMP terminates, then so does the b- log MMP. Furthermore, the b-log MMP includes both the log MMP and the equivariant MMP as special cases. There are various interesting b-log varieties arising from different objects, including the Brauer pairs, or "non-commutative algebraic varieties which are finite over their centres". The case of toric Brauer pairs is discussed in further detail., Fixed spelling mistake in one author's name

Myocardial active relaxation and restoring forces are known determinants of left ventricular (LV) diastolic function. We hypothesize the existence of an additional mechanism involved in LV filling, namely, a hydraulic force contributing to the longitudinal motion of the atrioventricular (AV) plane. A prerequisite for the presence of a net hydraulic force during diastole is that the atrial short-axis area (ASA) is smaller than the ventricular short-axis area (VSA). We aimed (a) to illustrate this mechanism in an analogous physical model, (b) to measure the ASA and VSA throughout the cardiac cycle in healthy volunteers using cardiovascular magnetic resonance imaging, and (c) to calculate the magnitude of the hydraulic force. The physical model illustrated that the anatomical difference between ASA and VSA provides the basis for generating a hydraulic force during diastole. In volunteers, VSA was greater than ASA during 75–100% of diastole. The hydraulic force was estimated to be 10–60% of the peak driving force of LV filling (1–3 N vs 5–10 N). Hydraulic forces are a consequence of left heart anatomy and aid LV diastolic filling. These findings suggest that the relationship between ASA and VSA, and the associated hydraulic force, should be considered when characterizing diastolic function and dysfunction.

The Doppler echocardiographic E-wave is generated when the left ventricle's suction pump attribute initiates transmitral flow. In some subjects E-waves are accompanied by L-waves, the occurrence of which has been correlated with diastolic dysfunction. The mechanisms for L-wave generation have not been fully elucidated. We propose that the recirculating diastolic intraventricular vortex ring generates L-waves and based on this mechanism, we predict the presence of L-waves in the right ventricle (RV). We imaged intraventricular flow using Doppler echocardiography and phase-contrast magnetic resonance imaging (PC-MRI) in 10 healthy volunteers. L-waves were recorded in all subjects, with highest velocities measured typically 2 cm below the annulus. Fifty-five percent of cardiac cycles (189 of 345) had L-waves. Color M-mode images eliminated mid-diastolic transmitral flow as the cause of the observed L-waves. Three-dimensional intraventricular flow patterns were imaged via PC-MRI and independently validated our hypothesis. Additionally as predicted, L-waves were observed in the RV, by both echocardiography and PC-MRI. The re-entry of the E-wave-generated vortex ring flow through a suitably located echo sample volume can be imaged as the L-wave. These waves are a general feature and a direct consequence of LV and RV diastolic fluid mechanics.

The mechanical suction-pump feature of the left ventricle aspirates atrial blood and generates a rapid rise and fall in transmitral flow (Doppler E-wave). Initially, E-wave deceleration time (DT), a routine index of clinical diastolic function, was thought to be determined only by chamber stiffness. Kinematic modeling of filling, in analogy to damped oscillatory motion [Parametrized Diastolic Filling (PDF) formalism], has been extensively validated and accurately predicts clinically observed E-wave contours while, revealing that DT is actually an algebraic function of both stiffness (PDF parameter k) and relaxation (PDF parameter c). We hypothesize that kinematic modeling based E-wave analysis accurately predicts the stiffness (DTs) and relaxation (DTr) components of DT such that DT = DTs + DTr. For validation, pressure–volume (P–V) and E-wave data from 12 control (DT 220 ms) subjects, 738 beats total, were analyzed. For each E-wave, DTs and DTr was compared to simultaneous, gold-standard, high fidelity (Millar catheter) determined, chamber stiffness (K = ΔP/ΔV) and chamber relaxation (time-constant of isovolumic relaxation—τ), respectively. For the group linear regression yielded DTs = αK + β (R = 0.82) with α = −0.38 and β = 0.20, and DTr = mτ + b (R = 0.94) with m = 2.88 and b = −0.12. We conclude that PDF-based E-wave analysis provides the DTs and DTr components of DT with simultaneous chamber stiffness (K) and relaxation (τ) respectively, as primary determinants. This kinematic modeling based method of E-wave analysis is immediately translatable clinically and can assess the effects of pathology and pharmacotherapy as causal determinants of DT.

The study by Stokke et al. [(1)][1] notes that circumferential strain contributes more than twice as much as longitudinal strain to left ventricular ejection fraction, but previous research has shown that 60% of stroke volume is generated by left ventricular longitudinal function [(2)][2]. The

we have read with great interest the recent Perspective by Arutunyan ([2][1]), titled “Atrioventricular plane displacement is the sole mechanism of atrial and ventricular refill,” in which the author revisited important, and perhaps not well-known, aspects of cardiac pumping physiology in an

Below the Middle to lower Upper Jurassic ophiolitic melange and their overlying ophiolite nappes of the Dinaridic Ophiolite Belt in the Zlatibor Mountain area occur olistoliths and slideblocks. These consist of Triassic carbonates and radiolarites of variable age and palaeogeographic provenance. The matrixes of these blocks are late Middle Jurassic radiolarites and clays. The different carbonate rocks were commonly interpreted to derive from the near-by Drina-Ivanjica Unit. In contrast, the radiolarites should represent the original sedimentary cover of the ophiolitic rocks of the Dinaridic Ophiolite Belt, i.e. the obducted oceanic crust of the Neotethys Ocean, originally located far to the east. The carbonate blocks in the Zlatibor (Sirogojno) melange reach several tens to hundreds of metres in size, occasionally even kilometres. Several olistoliths and blocks contain well-preserved parts of the Middle Triassic sedimentary succession. Their stratigraphy and facies evolution allowed the reconstruction of a sedimentary succession originating from the same palaeogeographic provenance of a relatively proximal passive continental margin setting, located originally east of the Drina-Ivanjica Unit. Different red nodular limestones of the Bulog Formation were deposited on top of a drowned Middle Anisian (Pelsonian) shallow-water carbonate ramp; beside condensed sections of red nodular limestones equal-aged thick successions with megabreccias occur, indicating the creation of steep fault escarpments and rapid subsidence. In contrast to this continuous sedimentary succession, Triassic sections of the relatively autochthonous Drina-Ivanjica Unit indicate Late Pelsonian uplift of the Middle Anisian carbonate ramp. After a hiatus (Late Pelsonian to Early Illyrian), deposition of grey cherty limestones with shallow-water debris (newly described as Rid Formation) started in the Middle to Late Illyrian. The focus of this paper is on the age, the depositional environment and the facies characteristics of the Late Anisian hemipelagic successions. Based on this study it is concluded that in the Inner Dinarides domain the Middle Anisian Neotethyan break-up resulted in the generation of a horst-and-graben topography. Blocks were uplifted in a rift shoulder manner and asymmetric basins were formed. Mass flows and slide blocks were mobilized along normal faults of the evolving western passive continental margin of the Neotethys Ocean.

Physiologic hypertrophy of the athlete heart, compared to the heart of nonathletic controls, is characterized by an increase in the left ventricular (LV) chamber dimension, mass, and wall thickness. Comparisons of the diastolic function (DF) between athletes and controls have employed conventional echocardiographic transmitral flow (Doppler E-wave)-derived indexes such as the peak flow velocity and deceleration time (which are load-dependent) and obscure the mechanistic determinants (e.g., stiffness, relaxation, load) of E-wave. With a focus on stiffness and relaxation chamber properties, conventional kinematic model-derived and load-independent indexes of the DF were compared between athletes and controls in this study. Echocardiographic and magnetic resonance imaging (MRI) data from 22 master athletes (whose sport was canoeing) and 21 sedentary controls were analyzed (1290 Doppler E-waves; 702 from athletes and 588 from the controls; on average, there were 30 pieces of data per subject). The LV mass and chamber size were determined from the MRI data. Quantitative DF assessment utilized an established kinematic model of filling that used the digitized Doppler E-wave contour as the input and characterized the DF on the basis of the chamber stiffness (k), relaxation/viscoelasticity (c), load (xo). We observed significant chamber stiffness (k), load (xo), and E-wave duration differences between the two groups. Concordant with the findings of previous studies, we also noted significant group differences in LV mass and dimension. These results indicated that physiological LV remodeling of the athlete heart at rest generates numerically quantifiable alterations in specific chamber properties. Assessment of the DF by using these methods during exercise will further elucidate the dynamic interplay between relaxation and stiffness as DF determinants.

The laws of fluid dynamics govern vortex ring formation and precede cardiac development by billions of years, suggesting that diastolic vortex ring formation is instrumental in defining the shape of the heart. Using novel and validated magnetic resonance imaging measurements, we show that the healthy left ventricle moves in tandem with the expanding vortex ring, indicating that cardiac form and function is epigenetically optimized to accommodate vortex ring formation for volume pumping. Healthy hearts demonstrate a strong coupling between vortex and cardiac volumes (R2 = 0.83), but this optimized phenotype is lost in heart failure, suggesting restoration of normal vortex ring dynamics as a new and possibly important consideration for individualized heart failure treatment. Vortex ring volume was unrelated to early rapid filling (E-wave) velocity in patients and controls. Characteristics of vortex-wall interaction provide unique physiologic and mechanistic information about cardiac diastolic function that may be applied to guide the design and implantation of prosthetic valves and have potential clinical utility as therapeutic targets for tailored medicine or measures of cardiac health.

The purpose of this note is to give a new proof of Alexeev's boundedness result for stable surfaces which is independent of the base field and to highlight some important consequences of this result.

Let $X$ be a variety and $H$ a Cartier divisor on $X$. We prove that if $H$ has Du Bois (or DB) singularities, then $X$ has Du Bois singularities near $H$. As a consequence, if $X \to S$ is a family over a smooth curve $S$ whose special fiber has Du Bois singularities, then the nearby fibers also have Du Bois singularities. We prove this by obtaining an injectivity theorem for certain maps of canonical modules. As a consequence, we also obtain a restriction theorem for certain non-lc ideals., Typos corrected and other expository improvements

Sponges from the Middle Triassic reef limestone of the Aggtelek Karst (NE Hungary) The hypercalcified sponge fauna of the Middle Triassic (Anisian-Ladinian) reef limestone exposed between Aggtelek-Jósvafő-Égerszög (northern Hungary) is described. Almost all the identified species are chambered sponges ("sphinctozoa"). Only two fragments of a not determinable species of non-chambered species ("inozoa") were identified. Hexactinellid sponges are not found. The majority of the Middle Anisian "sphinctozoans" are absolutely different genera, not known from the Permian reefs. The sponge fauna of the Triassic pioneer reefs in the Aggtelek Karst are distinctly small-scaled occurring in "Tubiphytes"-dominated carbonates. The following taxa are described: Amblysiphonella sp., Celyphia zoldana Ott, Pisa & Farabegoli, Colospongia catenulata catenulata Ott, C. catenulata macrocatenulata Scholz, Follicatena cautica Ott, Kovacsia baloghi (Kovács), Solenolmia manon manon (Münster), S. radiata Senowbari-Daryan & Riedel, Olangocoelia otti Bechstädt & Brandner, Thaumastocoelia dolomitica Senowbari-Daryan, Zühlke, Bechstädt & Flügel, Thaumastocoelia cf., Th. cassiana Steinmann.

Comparative volcanological, mineralogical, petrological, and geochemical studies of blocks of Triassic submarine basalt occurrences hosted by the Jurassic mélange have been carried out. The studied localities are located in displaced parts of the Dinarides in NE-Hungary (Darnó Unit), in the Dinarides (Kalnik Mts., Croatia and Vareš- Smreka, Bosnia and Herzegovina), and in the Hellenides (Stragopetra, Greece). The common characteristic of the studied occurrences is the well observable result of the lava–water-saturated sediment mingling, i.e., the presence of the so- called carbonate peperitic facies. Mixing of the basaltic lava with pelagic lime mud (representing the unconsolidated stage of the red, micritic limestone), as well as fluid inclusion and chlorite thermometry data support that the carbonate peperite was formed above CCD and at the Bosnian locality, a shallower water, about 1.4 km depth is proven. The igneous rocks show mainly within-plate basalt geochemical characteristics ; MORB signatures are not common. Low temperature (

Myocardial tissue characterization represents an extension of currently available echocardiographic imaging. The systematic variation of backscattered energy during the cardiac cycle (the “cyclic variation” of backscatter) has been employed to characterize cardiac function in a wide range of investigations. However, the mechanisms responsible for observed cyclic variation remain incompletely understood. As a step toward determining the features of cardiac structure and function that are responsible for the observed cyclic variation, the present study makes use of a kinematic approach of diastolic function quantitation to identify diastolic function determinants that influence the magnitude and timing of cyclic variation. Echocardiographic measurements of 32 subjects provided data for determination of the cyclic variation of backscatter to diastolic function relation characterized in terms of E-wave determined, kinematic model-based parameters of chamber stiffness, viscosity/relaxation and load. The normalized time delay of cyclic variation appears to be related to the relative viscoelasticity of the chamber and predictive of the kinematic filling dynamics as determined using the parametrized diastolic filling formalism (with r-values ranging from .44 to .59). The magnitude of cyclic variation does not appear to be strongly related to the kinematic parameters.

We show that the number of deformation types of canonically polarized manifolds over an arbitrary variety with proper singular locus is nite, and that this number is uniformly bounded in any nite type family of base varieties. As a corollary we show that a direct generalization of the geometric version of Shafarevich’s original conjecture holds for innitesimally rigid families of canonically polarized varieties.

During early rapid filling, blood aspirated by the left ventricle (LV) generates an asymmetric toroidal vortex whose development has been quantified using vortex formation time (VFT), a dimensionless index defined by the length-to-diameter ratio of the aspirated (equivalent cylindrical) fluid column. Since LV wall motion generates the atrioventricular pressure gradient resulting in the early transmitral flow (Doppler E-wave) and associated vortex formation, we hypothesized that the causal relation between VFT and diastolic function (DF), parametrized by stiffness, relaxation, and load, can be elucidated via kinematic modeling. Gharib et al. (Gharib M, Rambod E, Kheradvar A, Sahn DJ, Dabiri JO. Proc Natl Acad Sci USA 103: 6305–6308, 2006) approximated E-wave shape as a triangle and calculated VFTGharib as triangle (E-wave) area (cm) divided by peak (Doppler M-mode derived) mitral orifice diameter (cm). We used a validated kinematic model of filling for the E-wave as a function of time, parametrized by stiffness, viscoelasticity, and load. To calculate VFTkinematic, we computed the curvilinear E-wave area (using the kinematic model) and divided it by peak effective orifice diameter. The derived VFT-to-LV early rapid filling relation predicts VFT to be a function of peak E-wave-to-peak mitral annular tissue velocity (Doppler E′-wave) ratio as (E/E′)3/2. Validation utilized 262 cardiac cycles of simultaneous echocardiographic high-fidelity hemodynamic data from 12 subjects. VFTGharib and VFTkinematic were calculated for each subject and were well-correlated ( R2 = 0.66). In accordance with prediction, VFTkinematic to (E/E′)3/2 relationship was validated ( R 2 = 0.63). We conclude that VFTkinematic is a DF index computable in terms of global kinematic filling parameters of stiffness, viscoelasticity, and load. Validation of the fluid mechanics-to-chamber kinematics relation unites previously unassociated DF assessment methods and elucidates the mechanistic basis of the strong correlation between VFT and (E/E′)3/2.

The Mid-Hungarian (or Zagreb-Zemplin) Line of WSW-ENE strike divides the Pannonian basement into two mega-units, the Tisia Composite Terrane in the SE and the ALCAPA Composite Terrane in the NW. They became juxtaposed no earlier than the Middle Miocene (Karpathian). Their present adjacent zones show very different Variscan and Alpine evolution and relationships, which are briefly reviewed here and confronted in the light of detailed correlational work published during the last decade. The present contribution summarizes Variscan and Alpine evolution of units/terranes juxtaposed along the Mid-Hungarian Line, the major terrane boundary in the pre-Neogene basement of the Pannonian Basin, as can be seen on the Circum-Pannonian terrane maps.

The Mid-Hungarian Zone is a WSW-ENE trending composite structural unit in the basement of the Pannonian Basin that is made up of displaced crustal fragments (terranes) of South Alpine and Dinaridic origin. In the early stage of the Alpine evolution these fragments were located in various sectors of the NW Neotethys region, representing different paleogeographic settings from passive margin through continental slope to oceanic basement. Middle to Late Jurassic closure of the Neotethys led to the development of a suture zone made up of subduction-related complexes that can be followed all along the strike of the Dinarides. During the Cretaceous compressional stages, nappe stacks were formed from the accretionary complex and the fragments of the previously disrupted passive margin. Eastward extrusion (escape) of the ALCAPA Mega-unit during the Oligocene to Early Miocene led to large-scale displacement of fragments of this nappe stack, transporting them to their present-day position, and resulted in ...

The geologic key section at the northwestern margin of the village of Bodvalenke represents the stratotype of the Triassic Bodvalenke Limestone Formation and can be considered as the type section of the Bodva Unit of the Rudabanya Hills. The age of the exposed part of the formation in the type section ranges from the Late Anisian (Gondolella constricta cornuta partial range zone) to the early Late Carnian (Gondolella polygnathiformis interval zone). Its typical variety consists of purplish red to pinkish, strongly chertified, thinly-bedded micritic limestone, with frequent intercalations of mmthick purplish red shale layers and whitish-gray coquina beds. These beds are made up of tiny shells of Posydonia-like juvenile bivalves, often showing gradation. This deep water facies represents the transition between Hallstatt Limestone and red radiolarite. This facies type occurs from Oman via southern Turkey throughout the western ophiolite belt of the Hellenides-Dinarides until the Zagorje region in NW...

We prove that a Cohen-Macaulay normal variety $X$ has Du Bois singularities if and only if $\pi_*\omega_{X'}(G) \simeq \omega_X$ for a log resolution $\pi: X' \to X$, where $G$ is the reduced exceptional divisor of $\pi$. Many basic theorems about Du Bois singularities become transparent using this characterization (including the fact that Cohen-Macaulay log canonical singularities are Du Bois). We also give a straightforward and self-contained proof that (generalizations of) semi-log-canonical singularities are Du Bois, in the Cohen-Macaulay case. It also follows that the Kodaira vanishing theorem holds for semi-log-canonical varieties and that Cohen-Macaulay semi-log-canonical singularities are cohomologically insignificant in the sense of Dolgachev., Comment: Minor changes, 21 pages, to appear in Advances in Mathematics

The transmitral Doppler E-wave “delayed relaxation” (DR) pattern is an established sign of diastolic dysfunction (DD). Furthermore, chambers exhibiting a DR filling pattern are also expected to have a prolonged time-constant of isovolumic relaxation (τ). The simultaneous observation of a DR pattern and normal τ in the same heart is not uncommon, however. The simultaneous hemodynamic equivalent of the DR pattern has not been proposed. To determine the feature of the left ventricular (LV) pressure contour during the E-wave that is causally related to its DR pattern we applied kinematic and fluid mechanics based arguments to derive the pressure recovery ratio (PRR). The PRR is dimensionless and is defined by the left ventricular pressure difference between diastasis and minimum pressure, normalized to the pressure difference between a fiducial diastolic filling pressure and minimum pressure [PRR=(PDiastasis-PMin)/(PFiducial-PMin)]. We analyzed 354 cardiac cycles from 40 normal sinus rhythm (NSR) subjects and 113 beats from nine atrial fibrillation (AF) subjects from our database of simultaneous transmitral flow-micromanometric LV pressure recordings. The fiducial pressure is defined by the end diastolic pressure in NSR and by the pressure at dP/dtMIN in the setting of AF. Consistent with derivation, PRR was linearly related to a DR pattern related, model-based relaxation parameter (R2 = 0.77, 0.83 in NSR and AF, respectively). Furthermore, the PRR successfully differentiated subjects with a DR pattern from subjects with partial DR or normal E-wave pattern (p < 0.05). We conclude that the PRR may differentiate between subjects having a DR pattern and subjects with normal E-waves, even when τ cannot. (E-mail: sjk@wuphys.wustl.edu)

A recurring difficulty in the Minimal Model Program is that while log terminal singularities are quite well behaved (for instance, they are rational), log canonical singularities are much more complicated; they need not even be Cohen-Macaulay. The aim of this paper is to prove that log canonical singularities are Du Bois. The concept of Du Bois singularities, introduced by Steenbrink, is a weakening of rationality. We also prove flatness of the cohomology sheaves of the relative dualizing complex of a projective family with Du Bois fibers. This implies that each connected component of the moduli space of stable log varieties parametrizes either only Cohen-Macaulay or only non-Cohen-Macaulay objects., Comment: An error discovered in the statement and proof of Theorem 1.7 is corrected. Note that this change does not effect the rest of the article. Final version to appear in the Journal of the AMS

New heart failure affects 500 000 Americans yearly. Nearly 50% of these patients have a normal left ventricular ejection fraction (LVEF) or so-called diastolic heart failure (DHF). New onset symptomatic DHF is a lethal disease with a 5-year mortality that approaches 50%.1 Echo-Doppler techniques use LV filling patterns and tissue Doppler imaging of the mitral annulus to help identify and classify the degree of LV diastolic dysfunction, but work best in symptomatic patients with advanced disease.2 Therefore, the diagnosis of early diastolic dysfunction, when asymptomatic and most treatable, remains problematic. A detailed causality-based, mechanistic understanding of what causes DHF, and how to most easily detect it, remains one of the most important unsolved problems in cardiovascular physiology and clinical cardiology.3 Article see p 10 Segmental LV deformation analysis for calculating contractile parameters such as strain and strain rate is now possible using noninvasive echo-Doppler techniques.2 It has been reported that LA systolic and diastolic function can also be assessed using these Doppler strain techniques.4–6 Although LA enlargement increases with the severity of diastolic dysfunction,7 the ability of LA volume measurements to discriminate asymptomatic LV diastolic dysfunction from early DHF heart failure has not been possible. However, the concept that an alteration in LA function or stiffness may indicate this change is appealing. To that end in this issue Kurt et al8 seek to advance our knowledge of additional clinical, anatomic and physiological correlates of DHF, with a particular focus on LA “diastolic function” and LA stiffness. They report clinical and echo-Doppler data on 64 subjects undergoing right heart catheterization with simultaneous echocardiography, and a control group of 27 control subjects. The 64 subjects included 25 with systolic heart failure (LVEF