Vertex Fault Tolerant Additive Spanners

A {\em fault-tolerant} structure for a network is required to continue functioning following the failure of some of the network's edges or vertices. In this paper, we address the problem of designing a {\em fault-tolerant} additive spanner, namely, a subgraph $H$ of the network $G$ such that subsequent to the failure of a single vertex, the surviving part of $H$ still contains an \emph{additive} spanner for (the surviving part of) $G$, satisfying $dist(s,t,H\setminus \{v\}) \leq dist(s,t,G\setminus \{v\})+\beta$ for every $s,t,v \in V$. Recently, the problem of constructing fault-tolerant additive spanners resilient to the failure of up to $f$ \emph{edges} has been considered by Braunschvig et. al. The problem of handling \emph{vertex} failures was left open therein. In this paper we develop new techniques for constructing additive FT-spanners overcoming the failure of a single vertex in the graph. Our first result is an FT-spanner with additive stretch $2$ and $\widetilde{O}(n^{5/3})$ edges. Our second result is an FT-spanner with additive stretch $6$ and $\widetilde{O}(n^{3/2})$ edges. The construction algorithm consists of two main components: (a) constructing an FT-clustering graph and (b) applying a modified path-buying procedure suitably adopted to failure prone settings. Finally, we also describe two constructions for {\em fault-tolerant multi-source additive spanners}, aiming to guarantee a bounded additive stretch following a vertex failure, for every pair of vertices in $S \times V$ for a given subset of sources $S\subseteq V$. The additive stretch bounds of our constructions are 4 and 8 (using a different number of edges)

The Konkoly Blazhko Survey: Is light-curve modulation a common property of RRab stars?

A systematic survey to establish the true incidence rate of the Blazhko modulation among short-period, fundamental-mode, Galactic field RR Lyrae stars has been accomplished. The Konkoly Blazhko Survey (KBS) was initiated in 2004. Since then more than 750 nights of observation have been devoted to this project. A sample of 30 RRab stars was extensively observed, and light-curve modulation was detected in 14 cases. The 47% occurrence rate of the modulation is much larger than any previous estimate. The significant increase of the detected incidence rate is mostly due to the discovery of small-amplitude modulation. Half of the Blazhko variables in our sample show modulation with so small amplitude that definitely have been missed in the previous surveys. We have found that the modulation can be very unstable in some cases, e.g. RY Com showed regular modulation only during one part of the observations while during two seasons it had stable light curve with abrupt, small changes in the pulsation amplitude. This type of light-curve variability is also hard to detect in other Survey's data. The larger frequency of the light-curve modulation of RRab stars makes it even more important to find the still lacking explanation of the Blazhko phenomenon. The validity of the [Fe/H](P,phi_{31}) relation using the mean light curves of Blazhko variables is checked in our sample. We have found that the formula gives accurate result for small-modulation-amplitude Blazhko stars, and this is also the case for large-modulation-amplitude stars if the light curve has complete phase coverage. However, if the data of large-modulation-amplitude Blazhko stars are not extended enough (e.g. < 500 data points from < 15 nights), the formula may give false result due to the distorted shape of the mean light curve used.Comment: Accepted for publication in MNRAS, 14 pages, 7 Figure

The dynamics of proving uncolourability of large random graphs I. Symmetric Colouring Heuristic

We study the dynamics of a backtracking procedure capable of proving uncolourability of graphs, and calculate its average running time T for sparse random graphs, as a function of the average degree c and the number of vertices N. The analysis is carried out by mapping the history of the search process onto an out-of-equilibrium (multi-dimensional) surface growth problem. The growth exponent of the average running time is quantitatively predicted, in agreement with simulations.Comment: 5 figure

Low autocorrelated multi-phase sequences

The interplay between the ground state energy of the generalized Bernasconi model to multi-phase, and the minimal value of the maximal autocorrelation function, $C_{max}=\max_K{|C_K|}$, $K=1,..N-1$, is examined analytically and the main results are: (a) The minimal value of $\min_N{C_{max}}$ is $0.435\sqrt{N}$ significantly smaller than the typical value for random sequences $O(\sqrt{\log{N}}\sqrt{N})$. (b) $\min_N{C_{max}}$ over all sequences of length N is obtained in an energy which is about 30% above the ground-state energy of the generalized Bernasconi model, independent of the number of phases m. (c) The maximal merit factor $F_{max}$ grows linearly with m. (d) For a given N, $\min_N{C_{max}}\sim\sqrt{N/m}$ indicating that for m=N, $\min_N{C_{max}}=1$, i.e. a Barker code exits. The analytical results are confirmed by simulations.Comment: 4 pages, 4 figure

Bilateral nephrectomy for adult polycystic kidney disease does not affect the graft function of transplant patients and does not result in sensitisation

Background. Native nephrectomy in Adult Polycystic Kidney Disease (ADPKD) patients is a major operation with controversy related to timing and indications. We present our single centre experience in transplanted patients and future candidates for transplantation. Methods. Retrospective analysis from an anonymised database of bilateral nephrectomies for ADPKD patients. Results were reported as median, range, and percentage. Differences between groups were tested using ANOVA and t-test. Surgery was performed between January 2012 and July 2018. Results. Thirty-three patients underwent bilateral native nephrectomy for APKD. 18 had a functioning kidney transplant (transplant group, 55%) while 15 patients were on dialysis (dialysis group, 45%) at the time of surgery; 8 patients of the latter group (24% of the whole cohort) were eventually transplanted. 53% were males, with median age of 55 years (27-71). Indications to surgery were the following: space (symptoms related to the size of the native kidneys or need to create space for transplantation) (59%), recurrent cyst infection (36%), haematuria (15%), pain (24%), and weight loss associated with cystic alteration on imaging (3%). In the transplant group, postoperative kidney function was not affected; haemoglobin serum levels significantly dropped in the whole cohort: 121 (82-150) g/L, versus 108 (58-154) g/L (p<0.001), with 14 patients being transfused perioperatively. Elevation of anti-HLA antibodies was noted in one female patient on dialysis, with no change in DSA levels and no rejection after transplant for all 26 transplanted patients. Median postoperative length of hospital stay was 9 days (6-71). One patient died (3%) after six months. Median follow-up for the whole cohort was 282 days (13-1834). Histopathological examination revealed incidental renal neoplasms in five cases (15%): 1 pT1a papillary renal cell carcinoma and 4 papillary adenomas. Conclusions. Native nephrectomy for ADPKD could be safely performed in case of refractory symptoms, suspect of cancer or to create space for transplantation. It does not affect graft function or DSA status of transplanted patients or the prospect of transplantation of those on the waiting list

Use of Prostate-specific Antigen Testing in Medicare Beneficiaries: Association with Previous Evaluation

Objective: Determine uptake of prostate-specific antigen (PSA) testing in Medicare beneficiaries according to previous receipt of PSA testing. Methods: A 5% random sample of men aged 67 years or older without a previous diagnosis of prostate cancer was identified through 2009-2012 Medicare claims. We measured the annualized frequency of PSA screening among men due for PSA testing, stratified by PSA testing use in the previous 2 years, and clustered by ordering provider. Results: Throughout the study period, PSA testing use was consistently higher for men with previous screening than for men without previous screening. For men without previous screening, there was a decline in testing that was most pronounced in 2012. Compared with 2009, the corresponding odds ratios were 0.98 [95% confidence interval (CI) (0.96-1.00)] in 2010, 0.94 [95% CI (0.92-0.95)] in 2011, and 0.66 [95% CI (0.65-0.68)] in 2012. In contrast, for men with previous screening, PSA testing frequency was stable from 2009 to 2011, and declined to a lesser extent in 2012 [odds ratio 0.80, 95% CI (0.79-0.81)]. Conclusion: Receipt of PSA testing is highly dependent on whether an individual was tested in the recent past. In previously unscreened men, the largest decrease occurred in 2012, which may reflect in part the publication of US Preventive Services Task Force guidelines, but there was much less impact among men already being screened. © 2017 Family Medicine and Community Health

Compressible flow structures interaction with a two-dimensional ejector: a cold-flow study

An experimental study has been conducted to examine the interaction of compressible flow structures such as shocks and vortices with a two-dimensional ejector geometry using a shock-tube facility. Three diaphragm pressure ratios ofP4 =P1 = 4, 8, and 12 have been employed, whereP4 is the driver gas pressure andP1 is the pressure within the driven compartment of the shock tube. These lead to incident shock Mach numbers of Ms = 1:34, 1.54, and 1.66, respectively. The length of the driver section of the shock tube was 700 mm. Air was used for both the driver and driven gases. High-speed shadowgraphy was employed to visualize the induced flowfield. Pressure measurements were taken at different locations along the test section to study theflow quantitatively. The induced flow is unsteady and dependent on the degree of compressibility of the initial shock wave generated by the rupture of the diaphragm