A survey of complex dimensions, measurability, and the lattice/nonlattice dichotomy

The theory of complex dimensions of fractal strings developed by Lapidus and van Frankenhuijsen has proven to be a powerful tool for the study of Minkowski measurability of fractal subsets of the real line. In a very general setting, the Minkowski measurability of such sets is characterized by the structure of corresponding complex dimensions. Also, this tool is particularly effective in the setting of self-similar fractal subsets of R which have been shown to be Minkowski measurable if and only if they are nonlattice. This paper features a survey on the pertinent results of Lapidus and van Frankenhuijsen and a preliminary extension of the theory of complex dimensions to subsets of Euclidean space, with an emphasis on self-similar sets that satisfy various separation conditions. This extension is developed in the context of box-counting measurability, an analog of Minkowski measurability, which is shown to be characterized by complex dimensions under certain mild conditions.National Science Foundation (U.S.) (Grant DMS–1247679

Diverging volumetric trajectories following pediatric traumatic brain injury.

Traumatic brain injury (TBI) is a significant public health concern, and can be especially disruptive in children, derailing on-going neuronal maturation in periods critical for cognitive development. There is considerable heterogeneity in post-injury outcomes, only partially explained by injury severity. Understanding the time course of recovery, and what factors may delay or promote recovery, will aid clinicians in decision-making and provide avenues for future mechanism-based therapeutics. We examined regional changes in brain volume in a pediatric/adolescent moderate-severe TBI (msTBI) cohort, assessed at two time points. Children were first assessed 2-5 months post-injury, and again 12 months later. We used tensor-based morphometry (TBM) to localize longitudinal volume expansion and reduction. We studied 21 msTBI patients (5 F, 8-18 years old) and 26 well-matched healthy control children, also assessed twice over the same interval. In a prior paper, we identified a subgroup of msTBI patients, based on interhemispheric transfer time (IHTT), with significant structural disruption of the white matter (WM) at 2-5 months post injury. We investigated how this subgroup (TBI-slow, N = 11) differed in longitudinal regional volume changes from msTBI patients (TBI-normal, N = 10) with normal WM structure and function. The TBI-slow group had longitudinal decreases in brain volume in several WM clusters, including the corpus callosum and hypothalamus, while the TBI-normal group showed increased volume in WM areas. Our results show prolonged atrophy of the WM over the first 18 months post-injury in the TBI-slow group. The TBI-normal group shows a different pattern that could indicate a return to a healthy trajectory

Functional Brain Hyperactivations Are Linked to an Electrophysiological Measure of Slow Interhemispheric Transfer Time after Pediatric Moderate/Severe Traumatic Brain Injury.

Increased task-related blood oxygen level dependent (BOLD) activation is commonly observed in functional magnetic resonance imaging (fMRI) studies of moderate/severe traumatic brain injury (msTBI), but the functional relevance of these hyperactivations and how they are linked to more direct measures of neuronal function remain largely unknown. Here, we investigated how working memory load (WML)-dependent BOLD activation was related to an electrophysiological measure of interhemispheric transfer time (IHTT) in a sample of 18 msTBI patients and 26 demographically matched controls from the UCLA RAPBI (Recovery after Pediatric Brain Injury) study. In the context of highly similar fMRI task performance, a subgroup of TBI patients with slow IHTT had greater BOLD activation with higher WML than both healthy control children and a subgroup of msTBI patients with normal IHTT. Slower IHTT treated as a continuous variable was also associated with BOLD hyperactivation in the full TBI sample and in controls. Higher WML-dependent BOLD activation was related to better performance on a clinical cognitive performance index, an association that was more pronounced within the patient group with slow IHTT. Our previous work has shown that a subgroup of children with slow IHTT after pediatric msTBI has increased risk for poor white matter organization, long-term neurodegeneration, and poor cognitive outcome. BOLD hyperactivations after msTBI may reflect neuronal compensatory processes supporting higher-order capacity demanding cognitive functions in the context of inefficient neuronal transfer of information. The link between BOLD hyperactivations and slow IHTT adds to the multi-modal validation of this electrophysiological measure as a promising biomarker

The Association Between Persistent White-Matter Abnormalities and Repeat Injury After Sport-Related Concussion

Objective: A recent systematic review determined that the physiological effects of concussion may persist beyond clinical recovery. Preclinical models suggest that ongoing physiological effects are accompanied by increased cerebral vulnerability that is associated with risk for subsequent, more severe injury. This study examined the association between signal alterations on diffusion tensor imaging following clinical recovery of sport-related concussion in athletes with and without a subsequent second concussion. Methods: Average mean diffusivity (MD) was calculated in a region of interest (ROI) in which concussed athletes (n = 82) showed significantly elevated MD acutely after injury (<48 h), at an asymptomatic time point, 7 days post-return to play (RTP), and 6 months relative to controls (n = 69). The relationship between MD in the identified ROI and likelihood of sustaining a subsequent concussion over a 1-year period was examined with a binary logistic regression (re-injured, yes/no). Results: Eleven of 82 concussed athletes (13.4%) sustained a second concussion within 12 months of initial injury. Mean MD at 7 days post-RTP was significantly higher in those athletes who went on to sustain a repeat concussion within 1 year of initial injury than those who did not (p = 0.048; d = 0.75). In this underpowered sample, the relationship between MD at 7 days post-RTP and likelihood of sustaining a secondary injury approached significance [χ2 (1) = 4.17, p = 0.057; B = 0.03, SE = 0.017; OR = 1.03, CI = 0.99, 1.07]. Conclusions: These preliminary findings raise the hypothesis that persistent signal abnormalities in diffusion imaging metrics at RTP following concussion may be predictive of a repeat concussion. This may reflect a window of cerebral vulnerability or increased susceptibility following concussion, though understanding the clinical significance of these findings requires further study

Conceptual design of the MHD Engineering Test Facility

The reference conceptual design of the MHD engineering test facility, a prototype 200 MWe coal-fired electric generating plant designed to demonstrate the commerical feasibility of open cycle MHD is summarized. Main elements of the design are identified and explained, and the rationale behind them is reviewed. Major systems and plant facilities are listed and discussed. Construction cost and schedule estimates are included and the engineering issues that should be reexamined are identified

The application of in utero magnetic resonance imaging in the study of the metabolic and cardiovascular consequences of the developmental origins of health and disease

Observing fetal development in utero is vital to further the understanding of later-life diseases. Magnetic resonance imaging (MRI) offers a tool for obtaining a wealth of information about fetal growth, development, and programming not previously available using other methods. This review provides an overview of MRI techniques used to investigate the metabolic and cardiovascular consequences of the developmental origins of health and disease (DOHaD) hypothesis. These methods add to the understanding of the developing fetus by examining fetal growth and organ development, adipose tissue and body composition, fetal oximetry, placental microstructure, diffusion, perfusion, flow, and metabolism. MRI assessment of fetal growth, organ development, metabolism, and the amount of fetal adipose tissue could give early indicators of abnormal fetal development. Noninvasive fetal oximetry can accurately measure placental and fetal oxygenation, which improves current knowledge on placental function. Additionally, measuring deficiencies in the placenta\u27s transport of nutrients and oxygen is critical for optimizing treatment. Overall, the detailed structural and functional information provided by MRI is valuable in guiding future investigations of DOHaD

Photoacoustic dose monitoring in clinical high-energy photon beams

This work describes all stages of development (setup, optimization, performance, and first experimental measurements) of an acoustic sensor that can be used for range monitoring and dosimetry of clinical radiotherapy beams. The detection device consists of an ultrasonic transducer, a combination of preamplifiers and differential amplifiers with filtered outputs and a digital oscilloscope. Simulations of the experimental setup were carried out to study the optimal measurement geometry and choice of transducer. The dose distributions were calculated with the Monte Carlo code FLUKA, while the acoustic simulations were performed with the analytical wave transport code k-Wave. The temporal profiles of the dose pulses, in the order of mu s, were measured with a scintillating crystal coupled to a photomultiplier and used as input for the acoustic simulation. Measurements were performed in a Cyberknife (TM) radiosurgery beam and a TrueBeam unit. A lead block was submerged in water and placed partially or totally in the irradiation field in order to increase the acoustic signal. Photoacoustic signals were detected with both beams with the expected shape and time-delay, after the frequency response of the detection system was taken into account. The proposed setup can detect photoacoustic signals originating from the penumbra of the treatment fields after being processed with the appropriate image analysis tools

Overcoming the mobility penalty introduced by dipole disorder in small-molecule HTM films

The importance of the hole-transport material (HTM) in perovskite solar cells (PSCs) is now very well-established, with state-of-the-art materials such as Spiro-OMeTAD attracting significant attention in the last decade. The high cost of such materials still limits the commercialisation of these HTMs. To tackle this, the amide linker has recently been introduced into HTM systems via EDOT-Amide-TPA, utilising condensation chemistry as a cheap and effective route to HTMs. EDOT-Amide-TPA is capable of a variety of intermolecular interactions such as dipole-dipole interactions and hydrogen bonding, both of which are beneficial for enhancing the film morphology and improving charge transport. However, the interplay between these different interactions is not trivial, and understanding how they affect each other is paramount to inform new HTM designs whilst minimising material waste. To date, studies investigating the combined effects of different intermolecular interactions within the HTL on the charge transport properties of these materials are lacking. Furthermore, dipole disorder within the film introduces a mobility ‘penalty’: mobility decreases with stronger overall dipole due to energetic disorder within the film, which hinders charge hopping. In this work, we investigate three amide-based HTM analogs with differing intermolecular interaction capabilities, and show that this penalty can be compensated by a preferentially increased dipole ordering, likely achieved through intermolecular hydrogen bonding. This effectively cancels out the dipole disorder while retaining the beneficial effects on the molecular packing. Our aim is that this work provides a good foundation for navigating the complex interplay between hydrogen bonding, dipole moments, conductivity, and film formation in small-molecule HTM

The balancing act between high electronic and low ionic transport influenced by perovskite grain boundaries

\ua9 2024 The Royal Society of Chemistry.A better understanding of the materials\u27 fundamental physical processes is necessary to push hybrid perovskite photovoltaic devices towards their theoretical limits. The role of the perovskite grain boundaries is essential to optimise the system thoroughly. The influence of the perovskite grain size and crystal orientation on physical properties and their resulting photovoltaic performance is examined. We develop a novel, straightforward synthesis approach that yields crystals of a similar size but allows the tuning of their orientation to either the (200) or (002) facet alignment parallel to the substrate by manipulating dimethyl sulfoxide (DMSO) and tetrahydrothiophene-1-oxide (THTO) ratios. This decouples crystal orientation from grain size, allowing the study of charge carrier mobility, found to be improved with larger grain sizes, highlighting the importance of minimising crystal disorder to achieve efficient devices. However, devices incorporating crystals with the (200) facet exhibit an s-shape in the current density-voltage curve when standard scan rates are used, which typically signals an energetic interfacial barrier. Using the drift-diffusion simulations, we attribute this to slower-moving ions (mobility of 0.37 7 10-10 cm2 V-1 s-1) in combination with a lower density of mobile ions. This counterintuitive result highlights that reducing ion migration does not necessarily minimise hysteresis