Doeblin Trees

This paper is centered on the random graph generated by a Doeblin-type coupling of discrete time processes on a countable state space whereby when two paths meet, they merge. This random graph is studied through a novel subgraph, called a bridge graph, generated by paths started in a fixed state at any time. The bridge graph is made into a unimodular network by marking it and selecting a root in a specified fashion. The unimodularity of this network is leveraged to discern global properties of the larger Doeblin graph. Bi-recurrence, i.e., recurrence both forwards and backwards in time, is introduced and shown to be a key property in uniquely distinguishing paths in the Doeblin graph, and also a decisive property for Markov chains indexed by $\mathbb{Z}$. Properties related to simulating the bridge graph are also studied.Comment: 44 pages, 4 figure

Data on the annual aggregated income taxes of the Italian municipalities over the quinquennium 2007–2011

This dataset contains the annual aggregated income taxes of all the Italian municipalities over the years 2007-2011. Data are clustered over the Italian regions and provinces. The source of the data is the Italian Ministry of Economics and Finance. The administrative variations in Italy over the quinquennium have been taken into account. Data are useful to understand the economic structure of Italy at the microscopic level of municipalities. They can serve also for making comparisons between economical aspects and other features of the Italian cities

Benford’s law predicted digit distribution of aggregated income taxes: the surprising conformity of Italian cities and regions

The yearly aggregated tax income data of all, more than 8000, Italian municipalities are analyzed for a period of five years, from 2007 to 2011, to search for conformity or not with Benford’s law, a counter-intuitive phenomenon observed in large tabulated data where the occurrence of numbers having smaller initial digits is more favored than those with larger digits. This is done in anticipation that large deviations from Benford’s law will be found in view of tax evasion supposedly being widespread across Italy. Contrary to expectations, we show that the overall tax income data for all these years is in excellent agreement with Benford’s law. Furthermore, we also analyze the data of Calabria, Campania and Sicily, the three Italian regions known for strong presence of mafia, to see if there are any marked deviations from Benford’s law. Again, we find that all yearly data sets for Calabria and Sicily agree with Benford’s law whereas only the 2007 and 2008 yearly data show departures from the law for Campania. These results are again surprising in view of underground and illegal nature of economic activities of mafia which significantly contribute totax evasion. Some hypothesis for the found conformity is presented

Confronting the opioid crisis: Practical pain management and strategies: AOA 2018 critical issues symposium

The United States is in the midst of an opioid crisis. Clinicians have been part of the problem because of overprescribing of narcotics for perioperative pain management. Clinicians need to understand the pathophysiology and science of addiction to improve perioperative management of pain for their patients. Multiple modalities for pain management exist that decrease the use of narcotics. Physical strategies, cognitive strategies, and multimodal medication can all provide improved pain relief and decrease the use of narcotics. National medical societies are developing clinical practice guidelines for pain management that incorporate multimodal strategies and multimodal medication. Changes to policy that improve provider education, access to naloxone, and treatment for addiction can decrease narcotic misuse and the risk of addiction

Satellite Image Denoising Using Discrete Cosine Transform

The process of adding and removing the noises to an image is said to be as Image denoising. The process can be used in many image applications. This paper presents a method of satellite image denoising scheme using a wavelet transform called as Discrete Cosine Transform (DCT). The noise that is added in this scheme is the salt and pepper noise. By using hard thresholding method in the noise image the co-ordinates of the image can be changed and the original image can be retrieved by removing the noise. This can be done by Inverse Discrete Cosine Transform (IDCT). The performance measures of the proposed system can be done by measuring the PRNR values of the denoised image