Efficient tilings of de Bruijn and Kautz graphs

Kautz and de Bruijn graphs have a high degree of connectivity which makes them ideal candidates for massively parallel computer network topologies. In order to realize a practical computer architecture based on these graphs, it is useful to have a means of constructing a large-scale system from smaller, simpler modules. In this paper we consider the mathematical problem of uniformly tiling a de Bruijn or Kautz graph. This can be viewed as a generalization of the graph bisection problem. We focus on the problem of graph tilings by a set of identical subgraphs. Tiles should contain a maximal number of internal edges so as to minimize the number of edges connecting distinct tiles. We find necessary and sufficient conditions for the construction of tilings. We derive a simple lower bound on the number of edges which must leave each tile, and construct a class of tilings whose number of edges leaving each tile agrees asymptotically in form with the lower bound to within a constant factor. These tilings make possible the construction of large-scale computing systems based on de Bruijn and Kautz graph topologies.Comment: 29 pages, 11 figure

Full-field structured-illumination super-resolution X-ray transmission microscopy

Modern transmission X-ray microscopy techniques provide very high resolution at low and medium X-ray energies, but suffer from a limited field-of-view. If sub-micrometre resolution is desired, their field-of-view is typically limited to less than one millimetre. Although the field-of-view increases through combining multiple images from adjacent regions of the specimen, so does the required data acquisition time. Here, we present a method for fast full-field super-resolution transmission microscopy by structured illumination of the specimen. This technique is well-suited even for hard X-ray energies above 30 keV, where efficient optics are hard to obtain. Accordingly, investigation of optically thick specimen becomes possible with our method combining a wide field-of-view spanning multiple millimetres, or even centimetres, with sub-micron resolution and hard X-ray energies

X-ray dark-field tomography reveals tooth cracks

Abstract Cracked tooth syndrome (CTS) is a common clinical finding for teeth, it affects about 5% of all adults each year. The finding of CTS is favored by several risk factors such as restorations, bruxism, occlusion habits, and age. Treatment options range, depending on the severity, from no treatment at all to tooth extraction. Early diagnosis of CTS is crucial for optimal treatment and symptom reduction. There is no standard procedure for an evidence-based diagnosis up to date. The diagnosis is a challenge by the fact that the symptoms, including pain and sensitivity to temperature stimuli, cannot be clearly linked to the disease. Commonly used visual inspection does not provide in-depth information and is limited by the resolution of human eyes. This can be overcome by magnifying optics or contrast enhancers, but the diagnosis will still strongly rely on the practicians experience. Other methods are symptom reproduction with percussions, thermal pulp tests or bite tests. Dental X-ray radiography, as well as computed tomography, rarely detect cracks as they are limited in resolution. Here, we investigate X-ray dark-field tomography (XDT) for the detection of tooth microcracks. XDT simultaneously detects X-ray small-angle scattering (SAXS) in addition to the attenuation, whereas it is most sensitive to the micrometer regime. Since SAXS originates from gradients in electron density, the signal is sensitive to the sample morphology. Microcracks create manifold interfaces which lead to a strong signal. Therefore, it is possible to detect structural changes originating from subpixel-sized structures without directly resolving them. Together with complementary attenuation information, which visualizes comparatively large cracks, cracks are detected on all length-scales for a whole tooth in a non-destructive way. Hence, this proof-of principle study on three ex-vivo teeth shows the potential of X-ray scattering for evidence-based detection of cracked teeth

Intensity-based Choroidal Registration Using Regularized Block Matching

Detecting and monitoring changes in the human choroid play a crucial role in treating ocular diseases such as myopia. However, reliable segmentation of optical coherence tomography (OCT) images at the choroid-sclera interface (CSI) is notoriously difficult due to poor contrast, signal loss and OCT artefacts. In this paper we present blockwise registration of successive scans to improve stability also during complete loss of the CSI-signal. First, we formulated the problem as minimization of a regularized energy functional. Then, we tested our automated method for piecewise Intensity-based Choroidal rigid Registration using regularized block matching (ICR) on 20 OCT 3D-volume scan-rescan data set pairs. Finally, we used these data set pairs to determine the precision of our method, while the accuracy was determined by comparing our results with those using manually annotated scans

Inter-fractional Respiratory Motion Modelling from Abdominal Ultrasound: A Feasibility Study

Motion management strategies are crucial for radiotherapy of mobile tumours in order to ensure proper target coverage, save organs at risk and prevent interplay effects. We present a feasibility study for an inter-fractional, patient-specific motion model targeted at active beam scanning proton therapy. The model is designed to predict dense lung motion information from 2D abdominal ultrasound images. In a pretreatment phase, simultaneous ultrasound and magnetic resonance imaging are used to build a regression model. During dose delivery, abdominal ultrasound imaging serves as a surrogate for lung motion prediction. We investigated the performance of the motion model on five volunteer datasets. In two cases, the ultrasound probe was replaced after the volunteer has stood up between two imaging sessions. The overall mean prediction error is 2.9 mm and 3.4 mm after repositioning and therefore within a clinically acceptable range. These results suggest that the ultrasound-based regression model is a promising approach for inter-fractional motion management in radiotherapy

UK Housing Market: Time Series Processes with Independent and Identically Distributed Residuals

The paper examines whether a univariate data generating process can be identified which explains the data by having residuals that are independent and identically distributed, as verified by the BDS test. The stationary first differenced natural log quarterly house price index is regressed, initially with a constant variance and then with a conditional variance. The only regression function that produces independent and identically distributed standardised residuals is a mean process based on a pure random walk format with Exponential GARCH in mean for the conditional variance. There is an indication of an asymmetric volatility feedback effect but higher frequency data is required to confirm this. There could be scope for forecasting the index but this is tempered by the reduction in the power of the BDS test if there is a non-linear conditional variance process

United States Military Fatalities During Operation Inherent Resolve and Operation Freedom\u27s Sentinel.

BACKGROUND: Military operations provide a unified action and strategic approach to achieve national goals and objectives. Mortality reviews from military operations can guide injury prevention and casualty care efforts. METHODS: A retrospective study was conducted on all U.S. military fatalities from Operation Inherent Resolve (OIR) in Iraq (2014-2021) and Operation Freedom\u27s Sentinel (OFS) in Afghanistan (2015-2021). Data were obtained from autopsy reports and other existing records. Fatalities were evaluated for population characteristics; manner, cause, and location of death; and underlying atherosclerosis. Non-suicide trauma fatalities were also evaluated for injury severity, mechanism of death, injury survivability, death preventability, and opportunities for improvement. RESULTS: Of 213 U.S. military fatalities (median age, 29 years; male, 93.0%; prehospital, 89.2%), 49.8% were from OIR, and 50.2% were from OFS. More OIR fatalities were Reserve and National Guard forces (OIR 22.6%; OFS 5.6%), conventional forces (OIR 82.1%; OFS 65.4%), and support personnel (OIR 61.3%; OFS 33.6%). More OIR fatalities also resulted from disease and non-battle injury (OIR 83.0%; OFS 28.0%). The leading cause of death was injury (OIR 81.1%; OFS 98.1%). Manner of death differed as more homicides (OIR 18.9%; OFS 72.9%) were seen in OFS, and more deaths from natural causes (OIR 18.9%; OFS 1.9%) and suicides (OIR 29.2%; OFS 6.5%) were seen in OIR. The prevalence of underlying atherosclerosis was 14.2% in OIR and 18.7% in OFS. Of 146 non-suicide trauma fatalities, most multiple/blunt force injury deaths (62.2%) occurred in OIR, and most blast injury deaths (77.8%) and gunshot wound deaths (76.6%) occurred in OFS. The leading mechanism of death was catastrophic tissue destruction (80.8%). Most fatalities had non-survivable injuries (80.8%) and non-preventable deaths (97.3%). CONCLUSIONS: Comprehensive mortality reviews should routinely be conducted for all military operation deaths. Understanding death from both injury and disease can guide preemptive and responsive efforts to reduce death among military forces