Directed percolation near a wall

Series expansion methods are used to study directed bond percolation clusters on the square lattice whose lateral growth is restricted by a wall parallel to the growth direction. The percolation threshold $p_c$ is found to be the same as that for the bulk. However the values of the critical exponents for the percolation probability and mean cluster size are quite different from those for the bulk and are estimated by $\beta_1 = 0.7338 \pm 0.0001$ and $\gamma_1 = 1.8207 \pm 0.0004$ respectively. On the other hand the exponent $\Delta_1=\beta_1 +\gamma_1$ characterising the scale of the cluster size distribution is found to be unchanged by the presence of the wall. The parallel connectedness length, which is the scale for the cluster length distribution, has an exponent which we estimate to be $\nu_{1\parallel} = 1.7337 \pm 0.0004$ and is also unchanged. The exponent $\tau_1$ of the mean cluster length is related to $\beta_1$ and $\nu_{1\parallel}$ by the scaling relation $\nu_{1\parallel} = \beta_1 + \tau_1$ and using the above estimates yields $\tau_1 = 1$ to within the accuracy of our results. We conjecture that this value of $\tau_1$ is exact and further support for the conjecture is provided by the direct series expansion estimate $\tau_1= 1.0002 \pm 0.0003$.Comment: 12pages LaTeX, ioplppt.sty, to appear in J. Phys.

Low-density series expansions for directed percolation III. Some two-dimensional lattices

We use very efficient algorithms to calculate low-density series for bond and site percolation on the directed triangular, honeycomb, kagom\'e, and $(4.8^2)$ lattices. Analysis of the series yields accurate estimates of the critical point $p_c$ and various critical exponents. The exponent estimates differ only in the $5^{th}$ digit, thus providing strong numerical evidence for the expected universality of the critical exponents for directed percolation problems. In addition we also study the non-physical singularities of the series.Comment: 20 pages, 8 figure

Comparison of Graph Generation Methods for Structural Complexity Based Assembly Time Estimation

This paper compares two different methods of graph generation for input into the complexity connectivity method to estimate the assembly time of a product. The complexity connectivity method builds predictive models for assembly time based on 29 complexity metrics applied to the product graphs. Previously, the part connection graph was manually created, but recently the assembly mate method and the interference detection method have introduced new automated tools for creating the part connectivity graphs. These graph generation methods are compared on their ability to predict the assembly time of multiple products. For this research, eleven consumers products are used to train an artificial neural network and three products are reserved for testing. The results indicate that both the assembly mate method and the interference detection method can create connectivity graphs that predict the assembly time of a product to within 45% of the target time. The interference detection method showed less variability than the assembly mate method in the time estimations. The assembly mate method is limited to only solidworks assembly files, while the interference detection method is more flexible and can operate on different file formats including IGES, STEP, and Parasolid. Overall, both of the graph generation methods provide a suitable automated tool to form the connectivity graph, but the interference detection method provides less variance in predicting the assembly time and is more flexible in terms of file types that can be used

A quantitative model for disruption mitigation in a supply chain

© 2016 Elsevier B.V. In this paper, a three-stage supply chain network, with multiple manufacturing plants, distribution centers and retailers, is considered. For this supply chain system we develop three different approaches, (i) an ideal plan for an infinite planning horizon and an updated plan if there are any changes in the data, (ii) a predictive mitigation planning approach for managing predictive demand changes, which can be predicted in advance by using an appropriate tool, and (iii) a reactive mitigation plan, on a real-time basis, for managing sudden production disruptions, which cannot be predicted in advance. In predictive mitigation planning, we develop a fuzzy inference system (FIS) tool to predict the changes in future demand over the base forecast and the supply chain plan is revised accordingly well in advance. In reactive mitigation planning, we formulate a quantitative model for revising production and distribution plans, over a finite future planning period, while minimizing the total supply chain cost. We also consider a series of sudden disruptions, where a new disruption may or may not affect the recovery plans of earlier disruptions and which consequently require plans to be revised after the occurrence of each disruption on a real-time basis. An efficient heuristic, capable of dealing with sudden production disruptions on a real-time basis, is developed. We compare the heuristic results with those obtained from the LINGO optimization software for a good number of randomly generated test problems. Also, some numerical examples are presented to explain both the usefulness and advantages of the proposed approaches

Perspectives for Monte Carlo simulations on the CNN Universal Machine

Possibilities for performing stochastic simulations on the analog and fully parallelized Cellular Neural Network Universal Machine (CNN-UM) are investigated. By using a chaotic cellular automaton perturbed with the natural noise of the CNN-UM chip, a realistic binary random number generator is built. As a specific example for Monte Carlo type simulations, we use this random number generator and a CNN template to study the classical site-percolation problem on the ACE16K chip. The study reveals that the analog and parallel architecture of the CNN-UM is very appropriate for stochastic simulations on lattice models. The natural trend for increasing the number of cells and local memories on the CNN-UM chip will definitely favor in the near future the CNN-UM architecture for such problems.Comment: 14 pages, 6 figure

The exact evaluation of the corner-to-corner resistance of an M x N resistor network: Asymptotic expansion

We study the corner-to-corner resistance of an M x N resistor network with resistors r and s in the two spatial directions, and obtain an asymptotic expansion of its exact expression for large M and N. For M = N, r = s =1, our result is R_{NxN} = (4/pi) log N + 0.077318 + 0.266070/N^2 - 0.534779/N^4 + O(1/N^6).Comment: 12 pages, re-arranged section

Diabetic Ketoacidosis as First Presentation of Latent Autoimmune Diabetes in Adult

A 54-year-old white female with hypothyroidism presented with abdominal pain, nausea, vomiting, and diarrhea. She was found to have diabetic ketoacidosis (DKA) and admitted to our hospital for treatment. Laboratory workup revealed positive antiglutamic acid decarboxylase antibodies and subsequently she was diagnosed with latent onset autoimmune diabetes in adult (LADA). She was successfully treated with insulin with clinical and laboratory improvement. Diagnosis of LADA has been based on three criteria as given by The Immunology of Diabetes Society: (1) adult age of onset (>30 years of age); (2) presence of at least one circulating autoantibody (GADA/ICA/IAA/IA-2); and (3) initial insulin independence for the first six months. The importance of this case is the unlikely presentation of LADA. We believe that more research is needed to determine the exact proportion of LADA patients who first present with DKA, since similar cases have only been seen in case reports. Adult patients who are obese and have high blood sugar may deserve screening for LADA, especially in the presence of other autoimmune diseases. Those patients once diagnosed with LADA need extensive diabetic education including potentially serious events such as diabetic ketoacidosis

A mathematical modelling approach for managing sudden disturbances in a three-tier manufacturing supply chain

© 2019, Springer Science+Business Media, LLC, part of Springer Nature. This paper aims to develop a recovery planning approach in a three-tier manufacturing supply chain, which has a single supplier, manufacturer, and retailer under an imperfect production environment, in which we consider three types of sudden disturbances: demand fluctuation, and disruptions to production and raw material supply, which are not known in advance. Firstly, a mathematical model is developed for generating an ideal plan under imperfect production for a finite planning horizon while maximizing total profit, and then we re-formulate the model to generate the recovery plan after happening of each sudden disturbance. Considering the high commercial cost and computational intensity and complexity of this problem, we propose an efficient heuristic, to obtain a recovery plan, for each disturbance type, for a finite future period, after the occurrence of a disturbance. The heuristic solutions are compared with a standard solution technique for a considerable number of random test instances, which demonstrates the trustworthy performance of the developed heuristics. We also develop another heuristic for managing the combined effects of multiple sudden disturbances in a period. Finally, a simulation approach is proposed to investigate the effects of different types of disturbance events generated randomly. We present several numerical examples and random experiments to explicate the benefits of our developed approaches. Results reveal that in the event of sudden disturbances, the proposed mathematical and heuristic approaches are capable of generating recovery plans accurately and consistently

Antibiotic Susceptibility Pattern of Enterococcus spp. Isolated from Poultry Feces

Enterococci, especially Enterococcus faecalis and faecium, have emerged as an important nosocomial pathogen and represent a serious threat to patients with impaired host defenses. E. faecalis and faecium are part of the normal intestinal microbial flora of poultry and man under most conditions, they are considered as an opportunistic pathogen. In the current study, an investigation of Enterococcus spp. isolated from poultry feces and their antibiotic susceptibility pattern was studied, due to the worldwide attachment with poultry by human being. Samples were collected from different sites of Allahabad, India, 80 samples collected screened for the presence of E. faecalis and E. faecium and identified based on cultural and biochemical characteristics. Thirty-five isolates were identified as E. faecalis (57.37%), while 26 were E. faecium (42.62%). The pathogens isolated were tested for their susceptibility toward 10 different commonly prescribed antibiotics. Most of the isolates showed resistance toward antibiotics under study. E. faecalis strain suggested a higher percentage of possibility of infection estimated by 15% in comparison with E. faecium as it was found to be less in a screening. The high resistance rate also indicates the negative impact of the antibiotic therapy. To evaluate the extent of transmission and impact of such transmission on the effectiveness of the antibacterial use in human medicine, further study is imperative. Periodic monitoring of antibiotic resistance pattern to detect any change in it would be necessary for the effective treatment against these pathogens. Enterococci revealed an alarming rate of resistance to the standard antimicrobial agents used for therapy and raised MIC values to vancomycin. The importance and infection control were stressed

Number of spanning clusters at the high-dimensional percolation thresholds

A scaling theory is used to derive the dependence of the average number of spanning clusters at threshold on the lattice size L. This number should become independent of L for dimensions d<6, and vary as log L at d=6. The predictions for d>6 depend on the boundary conditions, and the results there may vary between L^{d-6} and L^0. While simulations in six dimensions are consistent with this prediction (after including corrections of order loglog L), in five dimensions the average number of spanning clusters still increases as log L even up to L = 201. However, the histogram P(k) of the spanning cluster multiplicity does scale as a function of kX(L), with X(L)=1+const/L, indicating that for sufficiently large L the average will approach a finite value: a fit of the 5D multiplicity data with a constant plus a simple linear correction to scaling reproduces the data very well. Numerical simulations for d>6 and for d=4 are also presented.Comment: 8 pages, 11 figures. Final version to appear on Physical Review