822 research outputs found
The web of Calabi-Yau hypersurfaces in toric varieties
Recent results on duality between string theories and connectedness of their
moduli spaces seem to go a long way toward establishing the uniqueness of an
underlying theory. For the large class of Calabi-Yau 3-folds that can be
embedded as hypersurfaces in toric varieties the proof of mathematical
connectedness via singular limits is greatly simplified by using polytopes that
are maximal with respect to certain single or multiple weight systems. We
identify the multiple weight systems occurring in this approach. We show that
all of the corresponding Calabi-Yau manifolds are connected among themselves
and to the web of CICY's. This almost completes the proof of connectedness for
toric Calabi-Yau hypersurfaces.Comment: TeX, epsf.tex; 24 page
Recommended from our members
Dissociable Recruitment of Rostral Anterior Cingulate and Inferior Frontal Cortex in Emotional Response Inhibition
The integrity of decision-making under emotionally evocative circumstances is critical to navigating complex environments, and dysfunctions in these processes may play an important role in the emergence and maintenance of various psychopathologies. The goal of the present study was to examine the spatial and temporal dynamics of neural responses to emotional stimuli and emotion-modulated response inhibition. High-density event-related brain potentials (ERPs) were measured as participants (N=25) performed an emotional Go/NoGo task that required button presses to words of a "target" emotional valence (i.e., positive, negative, neutral) and response inhibition to words of a different "distractor" valence. Using scalp ERP analyses in conjunction with source-localization techniques, we identified distinct neural responses associated with affective salience and affect- modulated response inhibition, respectively. Both earlier (similar to 300 ms) and later (similar to 700 ms) ERP components were enhanced with successful response inhibition to emotional distractors. Only ERPs to target stimuli differentiated affective from neutral cues. Moreover, Source localization analyses revealed right ventral lateral prefrontal cortex (VLPFC) activation in affective response inhibition regardless of emotional valence, whereas rostral anterior cingulate activation (rACC) was potentiated by emotional valence but was not modulated by response inhibition. This dissociation was supported by a significant Region x Trial Type x Emotion interaction, confirming that distinct regional dynamics characterize neural responses to affective valence and affective response-inhibition. The results are discussed in the context of an emerging affective neuroscience literature and implications for understanding psychiatric pathologies characterized by a detrimental susceptibility to emotional cues, with an emphasis on major depressive disorder.Psycholog
String Dualities and Toric Geometry: An Introduction
This note is supposed to be an introduction to those concepts of toric
geometry that are necessary to understand applications in the context of string
and F-theory dualities. The presentation is based on the definition of a toric
variety in terms of homogeneous coordinates, stressing the analogy with
weighted projective spaces. We try to give both intuitive pictures and precise
rules that should enable the reader to work with the concepts presented here.Comment: 17 pages, Latex, 7 figures, invited paper to appear in the special
issue of the Journal of Chaos, Solitons and Fractals on "Superstrings, M, F,
S, ... Theory" (M.S. El Naschie and C. Castro, editors
The tax identity for Markov additive risk processes
Taxed risk processes, i.e. processes which change their drift when reaching new maxima, represent a certain type of generalizations of Lévy and of Markov additive processes (MAP), since the times at which their Markovian mechanism changes are allowed to depend on the current position. In this paper we study generalizations of the tax identity of Albrecher and Hipp (2007) from the classical risk model to more general risk processes driven by spectrally-negative MAPs. We use the Sparre Andersen risk processes with phase-type interarrivals to illustrate the ideas in their simplest form
Searching for K3 Fibrations
We present two methods for studying fibrations of Calabi-Yau manifolds
embedded in toric varieties described by single weight systems. We analyse
184,026 such spaces and identify among them 124,701 which are K3 fibrations. As
some of the weights give rise to two or three distinct types of fibrations, the
total number we find is 167,406. With our methods one can also study elliptic
fibrations of 3-folds and K3 surfaces. We also calculate the Hodge numbers of
the 3-folds obtaining more than three times as many as were previously known.Comment: 21 pages, LaTeX2e, 4 eps figures, uses packages
amssymb,latexsym,cite,epi
Recommended from our members
Real-world heart rate norms in the Health eHeart study.
Emerging technology allows patients to measure and record their heart rate (HR) remotely by photoplethysmography (PPG) using smart devices like smartphones. However, the validity and expected distribution of such measurements are unclear, making it difficult for physicians to help patients interpret real-world, remote and on-demand HR measurements. Our goal was to validate HR-PPG, measured using a smartphone app, against HR-electrocardiogram (ECG) measurements and describe out-of-clinic, real-world, HR-PPG values according to age, demographics, body mass index, physical activity level, and disease. To validate the measurements, we obtained simultaneous HR-PPG and HR-ECG in 50 consecutive patients at our cardiology clinic. We then used data from participants enrolled in the Health eHeart cohort between 1 April 2014 and 30 April 2018 to derive real-world norms of HR-PPG according to demographics and medical conditions. HR-PPG and HR-ECG were highly correlated (Intraclass correlation = 0.90). A total of 66,788 Health eHeart Study participants contributed 3,144,332 HR-PPG measurements. The mean real-world HR was 79.1 bpm ± 14.5. The 95th percentile of real-world HR was ≤110 in individuals aged 18-45, ≤100 in those aged 45-60 and ≤95 bpm in individuals older than 60 years old. In multivariable linear regression, the number of medical conditions, female gender, increasing body mass index, and being Hispanic was associated with an increased HR, whereas increasing age was associated with a reduced HR. Our study provides the largest real-world norms for remotely obtained, real-world HR according to various strata and they may help physicians interpret and engage with patients presenting such data
Reduction and reconstruction of stochastic differential equations via symmetries
An algorithmic method to exploit a general class of infinitesimal symmetries
for reducing stochastic differential equations is presented and a natural
definition of reconstruction, inspired by the classical reconstruction by
quadratures, is proposed. As a side result the well-known solution formula for
linear one-dimensional stochastic differential equations is obtained within
this symmetry approach. The complete procedure is applied to several examples
with both theoretical and applied relevance
An Abundance of K3 Fibrations from Polyhedra with Interchangeable Parts
Even a cursory inspection of the Hodge plot associated with Calabi-Yau
threefolds that are hypersurfaces in toric varieties reveals striking
structures. These patterns correspond to webs of elliptic-K3 fibrations whose
mirror images are also elliptic-K3 fibrations. Such manifolds arise from
reflexive polytopes that can be cut into two parts along slices corresponding
to the K3 fibers. Any two half-polytopes over a given slice can be combined
into a reflexive polytope. This fact, together with a remarkable relation on
the additivity of Hodge numbers, explains much of the structure of the observed
patterns.Comment: 30 pages, 15 colour figure
- …