On the accuracy of phase-type approximations of heavy-tailed risk models

Numerical evaluation of ruin probabilities in the classical risk model is an important problem. If claim sizes are heavy-tailed, then such evaluations are challenging. To overcome this, an attractive way is to approximate the claim sizes with a phase-type distribution. What is not clear though is how many phases are enough in order to achieve a specific accuracy in the approximation of the ruin probability. The goals of this paper are to investigate the number of phases required so that we can achieve a pre-specified accuracy for the ruin probability and to provide error bounds. Also, in the special case of a completely monotone claim size distribution we develop an algorithm to estimate the ruin probability by approximating the excess claim size distribution with a hyperexponential one. Finally, we compare our approximation with the heavy traffic and heavy tail approximations.Comment: 24 pages, 13 figures, 8 tables, 38 reference

Overall survival of patients with recurrent pancreatic cancer treated with systemic therapy: a retrospective study

BACKGROUND: Only a few patients with pancreatic ductal adenocarcinoma (PDAC) recurring after curative resection and peri-operative (neoadjuvant and adjuvant) therapy are included in clinical trials of metastatic PDAC. As such, there is a paucity of data to guide treatment after relapse, and patients are treated similarly to those with de novo metastatic PDAC (mPDAC). We evaluated the patterns of chemotherapy use and over-all survival (OS) in patients with recurrent PDAC (rPDAC) following curative therapy. METHODS: In this retrospective study, the Indiana University pancreatic cancer database was used to identify patients with PDAC who underwent curative resection and subsequently developed recurrence. Demographics, tumor and treatment characteristics were collected. Patients were broadly divided into those who received chemotherapy for rPDAC and those who did not. Patients in the former category were further subdivided into those who received single agent therapy, any standard combination therapy (5-fluorouracil/irinotecan/oxaliplatin combination or gemcitabine/nab-paclitaxel) and those who received non-standard combinations. Survival analysis was performed by the Kaplan-Meier method. Log rank tests were used to determine differences in survival between treated rPDAC patients and those not treated. Cox regression analysis was employed to evaluate factors associated with OS. RESULTS: We identified 435 patients with resected PDAC treated between 2008 and 2014. Two hundred and twenty-three patients (51.2%) were diagnosed with rPDAC. Of these, 140 patients (63%) received chemotherapy whereas 71 patients (32%) did not receive chemotherapy. The 74 patients (53%) who received any standard, approved multiagent combination regimen had a median OS of 14 months compared to 8 months for the 47 patents (34%) who received other non-standard combinations and the 19 (13%) who received single agent therapy (P = 0.029). Multivariate cox regression analysis showed that margin negative resection, peri-operative therapy, radiotherapy and the use of any chemotherapy for rPDAC were associated with improved OS. CONCLUSION: Our findings support the use of standard approved multi-agent therapy in rPDAC. Patients derive significant benefit from these standard combination therapies with median OS that is comparable to what is observed with treatment for de novo mPDAC

Corrected phase-type approximations of heavy-tailed queueing models in a Markovian environment

Significant correlations between arrivals of load-generating events make the numerical evaluation of the workload of a system a challenging problem. In this paper, we construct highly accurate approximations of the workload distribution of the MAP/G/1 queue that capture the tail behavior of the exact workload distribution and provide a bounded relative error. Motivated by statistical analysis, we consider the service times as a mixture of a phase-type and a heavy-tailed distribution. With the aid of perturbation analysis, we derive our approximations as a sum of the workload distribution of the MAP/PH/1 queue and a heavy-tailed component that depends on the perturbation parameter. We refer to our approximations as corrected phase-type approximations, and we exhibit their performance with a numerical study.Comment: Received the Marcel Neuts Student Paper Award at the 8th International Conference on Matrix Analytic Methods in Stochastic Models 201

Clustering outdoor soundscapes using fuzzy ants

A classification algorithm for environmental sound recordings or "soundscapes" is outlined. An ant clustering approach is proposed, in which the behavior of the ants is governed by fuzzy rules. These rules are optimized by a genetic algorithm specially designed in order to achieve the optimal set of homogeneous clusters. Soundscape similarity is expressed as fuzzy resemblance of the shape of the sound pressure level histogram, the frequency spectrum and the spectrum of temporal fluctuations. These represent the loudness, the spectral and the temporal content of the soundscapes. Compared to traditional clustering methods, the advantages of this approach are that no a priori information is needed, such as the desired number of clusters, and that a flexible set of soundscape measures can be used. The clustering algorithm was applied to a set of 1116 acoustic measurements in 16 urban parks of Stockholm. The resulting clusters were validated against visitor's perceptual measurements of soundscape quality

Adaptation | a Reflection on Contemporary Chinese Architecture (in Four Case-studies)

Reflecting upon a decade of engaging with, researching, writing, curating and discussing critical and contemporary Chinese architectural developments (profession and projects), the author presents ‘adaptation' as a modus operandus for Chinese architects to bypass both rapid cultural changes as well as a volatile and demanding building construction climate. Seeking to understand the underlying concepts, methods and motives behind selected projects of four distinct contemporary practices (Amateur Architecture Studio, Atelier Chen Haoru, ZAO/standardarchitecture, Zhao Yang studio) the author discusses how these adapt to progress. Besides, the aforementioned practices encompass in China three distinct generations of architects, all practicing, to a large extent, in a similar spatial, social and economical environment. Focusing on the passage of time and the progress of the profession, rather than pointing out a figure or structure frozen in time, and through case-studies linked to the authors' exhibition ‘ADAPTATION – architecture and change in China' (Venice Architecture Biennale 2014), the paper seeks to discuss how architects effectively adapt and transform their thinking, practice and design in relation to ongoing demands and insights. Relating these to professional discourse, use of local materials and knowledge, to the volatility of clients, governments and markets, these alternative practices (alternative to the dominance of design institutes, to generic solutions and to Western, modernist, theories and practice) aspire to keep control over the design process. Across the four discussed practices, similarities in approach, materiality, methodology, educational and environmental concerns are contrasted with differences in architect-client relation, public appreciation, public and personal influence, laws, academic discourse. Through the lens of understanding how architects transform their modus operandi, tentatively the concept of ‘in(ter)depedent practices and projects' (or mutual reliance between different generations of independent architects) can be explored

Quantum Kagome antiferromagnet ZnCu3(OH)6Cl2

The frustration of antiferromagnetic interactions on the loosely connected kagome lattice associated to the enhancement of quantum fluctuations for S=1/2 spins was acknowledged long ago as a keypoint to stabilize novel ground states of magnetic matter. Only very recently, the model compound Herbersmithite, ZnCu3(OH)6Cl2, a structurally perfect kagome antiferromagnet, could be synthesized and enables a close comparison to theories. We review and classify various experimental results obtained over the past years and underline some of the pending issues.Comment: 23 pages, 16 figures, invited paper in J. Phys. Soc. Jpn, special topics issue on "Novel States of Matter Induced by Frustration", to be published in Jan. 201