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Systolic category information


The systole (or systolic category) is a numerical invariant of a closed manifold M, introduced by Mikhail Katz and Yuli Rudyak in 2006, by analogy with the Lusternik–Schnirelmann category. The invariant is defined in terms of the systoles of M and its covers, as the largest number of systoles in a product yielding a curvature-free lower bound for the total volume of M. The invariant is intimately related to the Lusternik-Schnirelmann category. Thus, in dimensions 2 and 3, the two invariants coincide. In dimension 4, the systolic category is known to be a lower bound for the Lusternik–Schnirelmann category.

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Systolic category

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The systole (or systolic category) is a numerical invariant of a closed manifold M, introduced by Mikhail Katz and Yuli Rudyak in 2006, by analogy with...

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Systolic geometry

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In mathematics, systolic geometry is the study of systolic invariants of manifolds and polyhedra, as initially conceived by Charles Loewner and developed...

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Systolic array

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because a strong argument can be made to distinguish systolic arrays from any of Flynn's four categories: SISD, SIMD, MISD, MIMD, as discussed later in this...

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Blood pressure

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commonly measured. Blood pressure is usually expressed in terms of the systolic pressure (maximum pressure during one heartbeat) over diastolic pressure...

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List of differential geometry topics

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Bolza surface First Hurwitz triplet Hermite constant Systoles of surfaces Systolic freedom Systolic category Envelope (mathematics) Bäcklund transform...

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Mean arterial pressure

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is to take one-third of the pulse pressure (the difference between the systolic and diastolic pressures), and add that amount to the diastolic pressure...

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Heart murmur

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the heartbeat. Continuous murmurs are not placed into the categories of diastolic or systolic murmurs. Mitral Valve Prolapse murmur at mitral area Heart...

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Heart failure

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the systolic ("top number") and diastolic ("bottom number") blood pressures, is often low/narrow (i.e. 25% or less of the level of the systolic) in people...

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Introduction to systolic geometry

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Systolic geometry is a branch of differential geometry, a field within mathematics, studying problems such as the relationship between the area inside...

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Hypertension

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birth control pills. Blood pressure is classified by two measurements, the systolic (first number) and diastolic (second number) pressures. For most adults...

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Sphygmomanometer

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to obtain a basic reading through palpation alone, this yields only the systolic pressure. Mercury sphygmomanometers are considered the gold standard. They...

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Ejection fraction

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blood left in a ventricle at the end of systole (contraction) is the end-systolic volume (ESV). The difference between EDV and ESV is the stroke volume (SV)...

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Echocardiography

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TAPSE – tricuspid annular plane systolic excursion VC – vena contracta EDD – end diastolic diameter ESD – end systolic diameter IVSd – interventricular...

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Revised Trauma Score

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of injury. The Revised Trauma Score is made up of three categories: Glasgow Coma Scale, systolic blood pressure, and respiratory rate. The score range is...

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Mitral regurgitation

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mitral valve prolapse and mitral regurgitation. Auscultating her heart, a systolic murmur and click are heard. Recorded with the stethoscope over the mitral...

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Common carotid artery

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blood flow velocities in the common carotid artery are measured as peak systolic velocity (PSV) and end diastolic velocity (EDV). In a study of normative...

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Array

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Reconfigurable datapath array, a flexible data processing architecture Systolic array, a hardware architecture Transistor array, an integrated circuit...

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Empagliflozin

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compared to placebo or other diabetic medications. Empagliflozin reduces systolic and diastolic blood pressure and can increase the risk of low blood pressure...

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Peripheral artery disease

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ankle-brachial index (ABI) less than 0.90, which is the systolic blood pressure at the ankle divided by the systolic blood pressure of the arm. Duplex ultrasonography...

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Isosorbide dinitrate

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heart. It has been found to be particularly useful in heart failure due to systolic dysfunction together with hydralazine. It is taken by mouth or under the...

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Hypertensive heart disease

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context of the International Classification of Diseases (ICD) coding categories. The definition includes heart failure and other cardiac complications...

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Pulse

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the pulse. The pulse is an expedient tactile method of determination of systolic blood pressure to a trained observer. Diastolic blood pressure is non-palpable...

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Rauvolfia serpentina

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and serpentine, among others. A 2016 review found that reserpine reduced systolic blood pressure (SBP) by about 8 mmHg compared to placebo, and may be as...

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Maps of manifolds

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the fundamental group, chains in homology theory, geodesic curves, and systolic geometry. Embedded paths and loops lead to knot theory, and related structures...

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Permissive hypotension

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pressure for these patients is a mean arterial pressure of 40-50 mmHg or systolic blood pressure of less than or equal to 80. This goes along with certain...

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