Defining the energy function as the negative logarithm of the density, we explore the energy landscape of a distribution via the tree of sublevel sets of its energy. This tree represents the hierarchy among the connected components of the sublevel sets. We propose ways to annotate the tree so that it provides information on both topological and statistical aspects of the distribution, such as t...

Contour, split and join trees can be defined as functors acting on the category of scalar fields, whose morphisms are value-preserving functions. The categorical definition provides a natural way to efficiently compute a variety of topological properties of all contours, sublevel or superlevel components in a scalar field. The result is a labeling of the contour, split or join tree and can be u...

Random optical-pulse polarization switching along an active optical medium in the Λ configuration with spatially disordered occupation numbers of its lower energy sublevel pair is described using the idealized integrable Maxwell-Bloch model. Analytical results describing the light polarization-switching statistics for the single self-induced transparency pulse are compared with statistics obtai...

Background. Selective neck dissection is commonly used to clear occult neck metastases in the N0 neck. The aim of this study was to identify the incidence of occult metastases in lymph nodes of sublevel IIb (submuscular recess; SMR) in upper aerodigestive tract squamous cell carcinoma in the setting of clinically and radiologically staged N0 necks and to perform a systematic review of the liter...

Defining the energy function as the negative logarithm of the density, we explore the energy landscape of a distribution via the tree of sublevel sets of its energy. This tree represents the hierarchy among the connected components of the sublevel sets. We propose ways to annotate the tree so that it provides information on both topological and statistical aspects of the distribution, such as t...

OBJECTIVE To evaluate the prevalence of sublevel IIB lymph node (LN) metastases for head and neck primary tumors in a large cohort of patients. DESIGN Prospective study. SETTING One referral university hospital and 2 national institutes of oncology. PATIENTS Between 2003 and 2005, 297 patients (male to female ratio, 3.5:1; mean age, 58.8 years [range, 18-89 years]) affected by head and ne...

Constructions of quaternion and octonion algebras, suggested to have new level and sublevel values, are proposed and justified. In particular, octonion algebras of level and sublevel 6 and 7 are constructed. In addition, Hoffmann’s proof of the existence of infinitely many new values for the level of a quaternion algebra is generalised and adapted.

We show the existence of the nontrivial periodic solution for a class of the system of the nonlinear suspension bridge equations with Dirichlet boundary condition and periodic condition by critical point theory and linking arguments. We investigate the geometry of the sublevel sets of the corresponding functional of the system, the topology of the sublevel sets and linking construction between ...

On the face of it, contemporary “alt-tech” platforms appear more moderate than legacy hate havens. Yet it's also clear that virulent in form misogyny, white supremacy, and xenophobia has not disappeared. Probing this tension, article conceptualizes two forms hate: Surface “Hate” (moderate content is highly visible easily accessible) Sublevel Hate (explicit marginal less discernible). These term...

A mechanism is described whereby the influence of an external magnetic field on the sublevels of a triplet exciplex, subject to heavy-atom-induced sublevel-selective deactivation, modulates the radical dissociation yield of the exciplex. A sublevel selection rule for the heavy atom effect on T, So intersystem crossing in the triplex exciplex is derived. The magnetic field influence is treated o...