(Quantum) Space-Time as a Statistical Geometry of Fuzzy Lumps and the Connection with Random Metric Spaces

We develop a kind of pregeometry consisting of a web of overlapping fuzzy lumps which interact with each other. The individual lumps are understood as certain closely entangled subgraphs (cliques) in a dynamically evolving network which, in a certain approximation, can be visualized as a time-dependent random graph. This strand of ideas is merged with another one, deriving from ideas, developed some time ago by Menger et al, that is, the concept of probabilistic- or random metric spaces, representing a natural extension of the metrical continuum into a more microscopic regime. It is our general goal to find a better adapted geometric environment for the description of microphysics. In this sense one may it also view as a dynamical randomisation of the causal-set framework developed by e.g. Sorkin et al. In doing this we incorporate, as a perhaps new aspect, various concepts from fuzzy set theory.Comment: 25 pages, Latex, no figures, some references added, some minor changes added relating to previous wor

(Quantum) Space-Time as a Statistical Geometry of Lumps in Random Networks

In the following we undertake to describe how macroscopic space-time (or rather, a microscopic protoform of it) is supposed to emerge as a superstructure of a web of lumps in a stochastic discrete network structure. As in preceding work (mentioned below), our analysis is based on the working philosophy that both physics and the corresponding mathematics have to be genuinely discrete on the primordial (Planck scale) level. This strategy is concretely implemented in the form of \tit{cellular networks} and \tit{random graphs}. One of our main themes is the development of the concept of \tit{physical (proto)points} or \tit{lumps} as densely entangled subcomplexes of the network and their respective web, establishing something like \tit{(proto)causality}. It may perhaps be said that certain parts of our programme are realisations of some early ideas of Menger and more recent ones sketched by Smolin a couple of years ago. We briefly indicate how this \tit{two-story-concept} of \tit{quantum} space-time can be used to encode the (at least in our view) existing non-local aspects of quantum theory without violating macroscopic space-time causality.Comment: 35 pages, Latex, under consideration by CQ

Abundance analysis for long period variables. Velocity effects studied with O-rich dynamic model atmospheres

(abbreviated) Measuring the surface abundances of AGB stars is an important tool for studying the effects of nucleosynthesis and mixing in the interior of low- to intermediate mass stars during their final evolutionary phases. The atmospheres of AGB stars can be strongly affected by stellar pulsation and the development of a stellar wind, though, and the abundance determination of these objects should therefore be based on dynamic model atmospheres. We investigate the effects of stellar pulsation and mass loss on the appearance of selected spectral features (line profiles, line intensities) and on the derived elemental abundances by performing a systematic comparison of hydrostatic and dynamic model atmospheres. High-resolution synthetic spectra in the near infrared range were calculated based on two dynamic model atmospheres (at various phases during the pulsation cycle) as well as a grid of hydrostatic COMARCS models. Equivalent widths of a selection of atomic and molecular lines were derived in both cases and compared with each other. In the case of the dynamic models, the equivalent widths of all investigated features vary over the pulsation cycle. A consistent reproduction of the derived variations with a set of hydrostatic models is not possible, but several individual phases and spectral features can be reproduced well with the help of specific hydrostatic atmospheric models. In addition, we show that the variations in equivalent width that we found on the basis of the adopted dynamic model atmospheres agree qualitatively with observational results for the Mira R Cas over its light cycle. The findings of our modelling form a starting point to deal with the problem of abundance determination in strongly dynamic AGB stars (i.e., long-period variables).Comment: 13 pages, 22 figures, accepted for publication in A&

Dimension Theory of Graphs and Networks

Starting from the working hypothesis that both physics and the corresponding mathematics have to be described by means of discrete concepts on the Planck-scale, one of the many problems one has to face in this enterprise is to find the discrete protoforms of the building blocks of continuum physics and mathematics. A core concept is the notion of dimension. In the following we develop such a notion for irregular structures like (large) graphs and networks and derive a number of its properties. Among other things we show its stability under a wide class of perturbations which is important if one has 'dimensional phase transitions' in mind. Furthermore we systematically construct graphs with almost arbitrary 'fractal dimension' which may be of some use in the context of 'dimensional renormalization' or statistical mechanics on irregular sets.Comment: 20 pages, 7 figures, LaTex2e, uses amsmath, amsfonts, amssymb, latexsym, epsfi

Convolution of multifractals and the local magnetization in a random field Ising chain

The local magnetization in the one-dimensional random-field Ising model is essentially the sum of two effective fields with multifractal probability measure. The probability measure of the local magnetization is thus the convolution of two multifractals. In this paper we prove relations between the multifractal properties of two measures and the multifractal properties of their convolution. The pointwise dimension at the boundary of the support of the convolution is the sum of the pointwise dimensions at the boundary of the support of the convoluted measures and the generalized box dimensions of the convolution are bounded from above by the sum of the generalized box dimensions of the convoluted measures. The generalized box dimensions of the convolution of Cantor sets with weights can be calculated analytically for certain parameter ranges and illustrate effects we also encounter in the case of the measure of the local magnetization. Returning to the study of this measure we apply the general inequalities and present numerical approximations of the D_q-spectrum. For the first time we are able to obtain results on multifractal properties of a physical quantity in the one-dimensional random-field Ising model which in principle could be measured experimentally. The numerically generated probability densities for the local magnetization show impressively the gradual transition from a monomodal to a bimodal distribution for growing random field strength h.Comment: An error in figure 1 was corrected, small additions were made to the introduction and the conclusions, some typos were corrected, 24 pages, LaTeX2e, 9 figure

COVID-19 Exposes Need for Progressive Criminal Justice Reform

Modeling conducted by the Centers for Disease Control and Prevention calculates that as many as 160 to 214 million people in the United States could become infected by the 2019 novel coronavirus (SARS-CoV-2, which causes the disease COVID-19) and that as many as 200 000 to 1.7 million may die from COVID-19

COVID-19 in corrections: Quarantine of incarcerated people

Carceral settings in the United States have been the source of many single site COVID-19 outbreaks. Quarantine is a strategy used to mitigate the spread of COVID-19 in correctional settings, and specific quarantine practices differ state to state. To better understand how states are using quarantine in prisons, we reviewed each state’s definition of quarantine and compared each state’s definition to the Centers for Disease Control’s (CDC) definition and recommendations for quarantine in jails and prisons. Most prison systems, 45 of 53, define quarantine, but definitions vary widely. No state published definitions of quarantine that align with all CDC recommendations, and only 9 states provide quarantine data. In these states, the highest recorded quarantine rate occurred in Ohio in May 2020 at 843 per 1,000. It is necessary for prison systems to standardize their definitions of quarantine and to utilize quarantine practices in accordance with CDC recommendations. In addition, data transparency is needed to better understand the use of quarantine and its effectiveness at mitigating COVID-19 outbreaks in carceral settings

Institutional distrust among gay, bisexual, and other men who have sex with men as a barrier to accessing pre-exposure prophylaxis (PrEP)

Populations at highest risk for acquiring HIV are more likely to pass through criminal justice (CJ) settings, and CJ-involved individuals are often at the intersection of multiple overlapping risk factors. The present study explored interest in, knowledge of, and barriers to PrEP uptake among gay, bisexual, and other men who have sex with men involved in the criminal justice system. Using semi-structured interviews, 26 participants who identified as MSM were asked about PrEP knowledge and interest, HIV risk, and incarceration experience. One theme that emerged across interviews was how institutional distrust in CJ settings may instill lack of trust in medical care after perceived mistreatment. Participants explained how lack of privacy fostered feelings that medical care was not confidential, care received was tied to status as an incarcerated person, and feelings of dehumanization led to distrust. Findings explore how distrust may hinder PrEP uptake and other HIV prevention efforts in CJ settings as well as after release. They highlight the need for greater privacy efforts and cultural humility, and explore how medical settings may function as spaces for people who are incarcerated to disclose HIV risk status. Few studies to our knowledge have examined the role of institutional distrust on men who have sex with men (MSM) in the context of pre-exposure prophylaxis (PrEP) interventions. The present study has implications for creating best practices to structure HIV prevention interventions in CJ settings