In search of Robbins stability

We speculate on whether a certain p-adic stability phenomenon, observed by David Robbins empirically for Dodgson condensation, appears in other nonlinear recurrence relations that "unexpectedly" produce integer or nearly-integer sequences. We exhibit an example (number friezes) where this phenomenon provably occurs.Comment: 10 pages; to appear in the David Robbins memorial issue of Advances in Applied Mathematic

Classification using distance nearest neighbours

This paper proposes a new probabilistic classification algorithm using a Markov random field approach. The joint distribution of class labels is explicitly modelled using the distances between feature vectors. Intuitively, a class label should depend more on class labels which are closer in the feature space, than those which are further away. Our approach builds on previous work by Holmes and Adams (2002, 2003) and Cucala et al. (2008). Our work shares many of the advantages of these approaches in providing a probabilistic basis for the statistical inference. In comparison to previous work, we present a more efficient computational algorithm to overcome the intractability of the Markov random field model. The results of our algorithm are encouraging in comparison to the k-nearest neighbour algorithm.Comment: 12 pages, 2 figures. To appear in Statistics and Computin

Interlaced particle systems and tilings of the Aztec diamond

Motivated by the problem of domino tilings of the Aztec diamond, a weighted particle system is defined on $N$ lines, with line $j$ containing $j$ particles. The particles are restricted to lattice points from 0 to $N$, and particles on successive lines are subject to an interlacing constraint. It is shown that marginal distributions for this particle system can be computed exactly. This in turn is used to give unified derivations of a number of fundamental properties of the tiling problem, for example the evaluation of the number of distinct configurations and the relation to the GUE minor process. An interlaced particle system associated with the domino tiling of a certain half Aztec diamond is similarly defined and analyzed.Comment: 17 pages, 4 figure

Reference performance test Methodology for degradation assessment of lithium-sulfur batteries

Lithium-Sulfur (Li-S) is an emerging battery technology receiving a growing amount of attention due to its potentially high gravimetric energy density, safety, and low production cost. However, there are still some obstacles preventing its swift commercialization. Li-S batteries are driven by different electrochemical processes than commonly used Lithium-ion batteries, which often results in very different behavior. Therefore, the testing and modeling of these systems have to be adjusted to reflect their unique behavior and to prevent possible bias. A methodology for a Reference Performance Test (RPT) for the Li-S batteries is proposed in this study to point out Li-S battery features and provide guidance to users how to deal with them and possible results into standardization. The proposed test methodology is demonstrated for 3.4 Ah Li-S cells aged under different conditions

Непосредственные и отдаленные результаты оригинальных способов продольной панкреатоеюностомии с расширением площади анастомозирования панкреатоеюнального соустья

RELEVANCE. The dependency results of draining operations on the efficcacy of drainig of ductal system of the pancreas and adequate outflow of the pancreatic juce through anastomosis are undoubtful, therefore the development of new techniques of longitudinal pancreatojejunostomy (LPJ) extending area of anastomosis is an actual challenge.AIM OF STUDY. To compare the immediate and long-term results of longitudinal pancreatojejunostomy with the expansion of the area of anastomosis in patients with chronic pancreatitis.MATERIAL AND METHODS. We analysed immediate and long-term results of LPJ in 58 patients with chronic pancreatitis with impaired patency of the major pancreatic duct (MPD) without the head enlargement.RESULTS. All patients were divided into two groups: comparison group ( n=26, operated up to 2008 ) and main group (n=32, operated stumps during the MPD diastasis and posterior pancreatic surface (n=3) into anastomosis, with resection of the anterior pancreatic surface in the form of triangular fragments (n=11), with circulation of the small intestine loop during the recovery phase (n=19). The original LPJ in the study group of patients did not lengthened the surgery (160 [135, 185]) and intraoperative blood loss (265 [175, 340]). In the main group of patients there was no postoperative complications and fatal outcomes, but the average duration postoperative hospital treatment (18 [16; 20.5]) exceeded some data of foreign and domestic authors. Pain within 5 years after surgery in patients of the main group exceeded 26.6% and the appearance of diarrheal syndrome with dependance from reception of enzyme preparations was twice lower than in patients og the comparison group. According to questionnaire EORTC QLQ-C30, 5 years after surgery statistically significant differences between groups in terms of scales CF, NV, DY (p=0.03, 0.02, 0.006 respectively), indicating the advantage of intervention performed in the mail group.CONCLUSIONS. 1. An indication for longitudinal pancreatojejunostomy in chronic pancreatitis is impaired patency of the main pancreatic duct in the absence of an increase and inflammatory mass in the pancreatic head.2. The width of the main pancreatic duct is less than 5 mm and the presence of diastasis between its proximal and distal stumps with the posterior surface of the pancreas preserved, is not a reason for refusing longitudinal pancreatic jujunostomy in favor of the resection method.3. The expansion of pancreatojejunal anastomosis when performing longitudinal pancreatojejunostomy can improve the immediate and longterm results of surgical treatment for chronic pancreatitis.АКТУАЛЬНОСТЬ. Зависимость результатов дренирующих операций от эффективности дренирования протоковой системы поджелудочной железы (ПЖ) и адекватности оттока панкреатического сока через анастомоз не вызывает сомнений, в связи с чем разработка новых способов продольной панкреатоеюностомии (ППЕС), расширяющих площадь панкреатоеюнального соустья, является актуальной задачей.ЦЕЛЬ ИССЛЕДОВАНИЯ. Сравнить непосредственные и отдаленные результаты ППЕС с расширением площади панкреатоеюнального соустья у больных хроническим панкреатитом (ХП).МАТЕРИАЛ И МЕТОДЫ. Проведен анализ непосредственных и отдаленных результатов лечения 58 больных ХП с нарушением проходимости главного панкреатического протока (ГПП) на всем протяжении без увеличения головки поджелудочной железы (ГПЖ), оперированных в объеме ППЕС. Все больные были распределены на две группы: сравнения (n=26, оперированные до 2008 г.) и основную (n=32, оперированные после 2008 г. с использованием новых способов ППЕС: с включением в единое панкреатоеюнальное соустье дистальной и проксимальной культей при диастазе ГПП и задней поверхности ПЖ (n=3), с иссечением передней поверхности ПЖ в виде фрагментов треугольной формы (n=11), с циркуляцией петли тонкой кишки на восстановитель- ном этапе операции (n=19).РЕЗУЛЬТАТЫ. Применение оригинальных способов ППЕС в основной группе больных не удлинило среднюю продолжительность операции (160 [135; 185]) и интраоперационную кровопотерю (265 [175; 340]). В основной группе больных не было послеоперационных осложнений и летальности, но средняя продолжительность послеоперационного стационарного лечения (18 суток [16; 20,5]) превысила данные некоторых зарубежных и отечественных авторов. Купирование боли через 5 лет после операции у больных основной группы превысило на 26,6%, а развитие диарейного синдрома с зависимостью от приема ферментных препаратов оказалось вдвое ниже, чем у больных группы сравнения. По данным анкетирования EORTC QLQ-C30, через 5 лет после операции установлены статистически значимые межгрупповые различия по показателям шкал CF, NV, DY (р=0,03; р=0,02; р=0,006 соответственно), что указывает на преимущество вмешательства, примененного в основной группе.ВЫВОДЫ. 1. Показанием к продольной панкреатоеюностомии при хроническом панкреатите является нарушение проходимости главного панкреатического протока при отсутствии увеличения и воспалительной массы в головке поджелудочной железы.2. Ширина главного панкреатического протока менее 5 мм и наличие диастаза между его прок- симальной и дистальной культями при сохраненной задней поверхности поджелудочной железы не являются поводом для отказа от продольной панкреатоеюностомии в пользу резекционного метода.3. Расширение площади панкреатоеюнального соустья при выполнении продольной панкреатоеюностомии позволяет улучшить непосредственные и отдаленные результаты хирургического лечения хронического панкреатита

Transport of metal sulfides in supercritical carbon dioxide

This report presents the results of studies of supercritical fluid extraction of selected organics and of transition metal sulfides using carbon dioxide with and without modifiers. For the metal sulfides, the modifiers water, aqueous EDTA, methanol, and methanolic 2,4-pentanedione (acetyl acetone) were added in amounts ranging from 1 to 10 wt% depending on the specific modifier used. Extraction efficiency was studied as a function of fluid composition and extraction temperature and pressure. The objective of the work was to investigate the scientific feasibility of using this type of extraction process for metallurgical or environmental applications. Theoretical modeling studies were performed in an attempt to develop predictive capabilities for both solubility calculations and extraction simulation. The experimental studies have established the scientific feasibility of extraction and transport of selected cations by these fluids. Depending on the metal and conditions, transport of up to 12% of the starting material has been observed; however, the observed extraction efficiencies for inorganics do not approach those typical for organics under similar conditions

Exact sampling from non-attractive distributions using summary states

Propp and Wilson's method of coupling from the past allows one to efficiently generate exact samples from attractive statistical distributions (e.g., the ferromagnetic Ising model). This method may be generalized to non-attractive distributions by the use of summary states, as first described by Huber. Using this method, we present exact samples from a frustrated antiferromagnetic triangular Ising model and the antiferromagnetic q=3 Potts model. We discuss the advantages and limitations of the method of summary states for practical sampling, paying particular attention to the slowing down of the algorithm at low temperature. In particular, we show that such a slowing down can occur in the absence of a physical phase transition.Comment: 5 pages, 6 EPS figures, REVTeX; additional information at http://wol.ra.phy.cam.ac.uk/mackay/exac

From elongated spanning trees to vicious random walks

Given a spanning forest on a large square lattice, we consider by combinatorial methods a correlation function of $k$ paths ($k$ is odd) along branches of trees or, equivalently, $k$ loop--erased random walks. Starting and ending points of the paths are grouped in a fashion a $k$--leg watermelon. For large distance $r$ between groups of starting and ending points, the ratio of the number of watermelon configurations to the total number of spanning trees behaves as $r^{-\nu} \log r$ with $\nu = (k^2-1)/2$. Considering the spanning forest stretched along the meridian of this watermelon, we see that the two--dimensional $k$--leg loop--erased watermelon exponent $\nu$ is converting into the scaling exponent for the reunion probability (at a given point) of $k$ (1+1)--dimensional vicious walkers, $\tilde{\nu} = k^2/2$. Also, we express the conjectures about the possible relation to integrable systems.Comment: 27 pages, 6 figure