The transform likelihood ratio method for rare event simulation with heavy tails

We present a novel method, called the transform likelihood ratio (TLR) method, for estimation of rare event probabilities with heavy-tailed distributions. Via a simple transformation ( change of variables) technique the TLR method reduces the original rare event probability estimation with heavy tail distributions to an equivalent one with light tail distributions. Once this transformation has been established we estimate the rare event probability via importance sampling, using the classical exponential change of measure or the standard likelihood ratio change of measure. In the latter case the importance sampling distribution is chosen from the same parametric family as the transformed distribution. We estimate the optimal parameter vector of the importance sampling distribution using the cross-entropy method. We prove the polynomial complexity of the TLR method for certain heavy-tailed models and demonstrate numerically its high efficiency for various heavy-tailed models previously thought to be intractable. We also show that the TLR method can be viewed as a universal tool in the sense that not only it provides a unified view for heavy-tailed simulation but also can be efficiently used in simulation with light-tailed distributions. We present extensive simulation results which support the efficiency of the TLR method.

Improved algorithms for rare event simulation with heavy tails

The estimation of P(S-n > u) by simulation, where S, is the sum of independent. identically distributed random varibles Y-1,..., Y-n, is of importance in many applications. We propose two simulation estimators based upon the identity P(S-n > u) = nP(S, > u, M-n = Y-n), where M-n = max(Y-1,..., Y-n). One estimator uses importance sampling (for Y-n only), and the other uses conditional Monte Carlo conditioning upon Y1,..., Yn-1. Properties of the relative error of the estimators are derived and a numerical study given in terms of the M/G/1 queue in which n is replaced by an independent geometric random variable N. The conclusion is that the new estimators compare extremely favorably with previous ones. In particular, the conditional Monte Carlo estimator is the first heavy-tailed example of an estimator with bounded relative error. Further improvements are obtained in the random-N case, by incorporating control variates and stratification techniques into the new estimation procedures.

Hitting and returning to rare events for all alpha-mixing processes

We prove that for any a-mixing stationary process the hitting time of any n-string A(n) converges, when suitably normalized, to an exponential law. We identify the normalization constant lambda(A(n)). A similar statement holds also for the return time. To establish this result we prove two other results of independent interest. First, we show a relation between the rescaled hitting time and the rescaled return time, generalizing a theorem of Haydn, Lacroix and Vaienti. Second, we show that for positive entropy systems, the probability of observing any n-string in n consecutive observations goes to zero as n goes to infinity. (c) 2010 Elsevier B.V. All rights reserved.

Mutations in exon 3 of the beta-catenin gene are rare in melanoma cell lines

Mutations in exon 3 of the CTNNB1 gene encoding beta-catenin have been reported in colorectal cancer cell lines and tumours. Although one study reported mutations or deletions affecting beta-catenin in 20% of melanoma cell lines, subsequent reports detected a much lower frequency of aberrations in uncultured melanomas. To determine whether this difference in mutation frequency reflected an in vitro culturing artefact, exon 3 of CTNNB1 was screened in a panel of 62 melanoma cell lines. In addition, reverse transcription-polymerase chain reaction (RT-PCR) was performed to detect intragenic deletions affecting exon 3. One out of 62 (1.6%) cell lines was found to carry a mutation, indicating that aberration of the Wnt-l/wingless pathway through activation of beta-catenin is a rare event, even in melanoma cell lines. (C) 2002 Lippincott Williams Wilkins.

A rare non-Robertsonian translocation involving chromosomes 15 and 21

CONTEXTO:Translocações robertsonianas (TR) estão entre os rearranjos estruturais balanceados mais comuns em humanos e compreendem a fusão da cromatina completa do braço longo de dois cromossomos acrocêntricos. No entanto, são raras as translocações não Robertsonianas envolvendo esses cromossomos.RELATO DE CASO:Nós descrevemos uma translocação não balanceada de novo envolvendo os cromossomos 15 e 21. A recém-nascida era filha de uma mãe de 29 anos e de um pai de 42 anos, casal não consanguíneo. Os achados clínicos levaram ao diagnóstico de síndrome de Down (SD) com defeitos cardíacos congênitos graves (persistência do canal arterial e defeito do septo atrioventricular completo), além de baixos comprimento e peso ao nascimento (< 5o e < 10o percentil em curvas de medidas específicas para SD, respectivamente). A análise citogenética convencional revelou o cariótipo 46,XX,der(15)(15pter→15q26.2

Somatic CEBPA mutations are a frequent second event in families with germline CEBPA mutations and familial acute myeloid leukemia

PURPOSE: The transcription factor CCAAT/enhancer binding protein-alpha (CEBPA) is crucial for normal myeloid differentiation. Mutations in the CEBPA gene are found in subsets of patients with acute myeloid leukemia (AML). Recently, three families were reported in whom several family members had germline CEBPA mutations and subsequently developed AML. Whereas familial AML is considered a rare event, the frequency of CEBPA germline mutations in AML is not known. PATIENTS AND METHODS: In this study, we screened 187 consecutive AML patients for CEBPA mutations at diagnosis. We detected 18 patients (9.6%) with CEBPA mutations. We then analyzed remission samples and constitutive DNA from these patients. RESULTS: We found that two (11.1%) of 18 AML patients with CEBPA mutations carried a germline N-terminal frameshift CEBPA mutation. Interestingly, additional members in the families of both of these patients have been affected by AML, and the germline CEBPA mutations were also observed in these patients. Additional somatic mutations in AML patients with germline CEBPA mutations in the two families comprised in-frame C-terminal CEBPA mutations in two patients, two nonsilent CEBPA point mutations in one patient, and monosomy 7 in one patient. CONCLUSION: This study shows, for the first time to our knowledge, that germline CEBPA mutations are frequently observed among AML patients with CEBPA mutations. Including the families with germline CEBPA mutations reported previously, additional somatic CEBPA mutations represent a frequent second event in AML with germline CEBPA mutations. Our data strongly indicate that germline CEBPA mutations predispose to AML and that additional somatic CEBPA mutations contribute to the development of the disease.

Stochastic simulation of rare events

Stochastic simulation is an important and practical technique for computing probabilities of rare events, like the payoff probability of a financial option, the probability that a queue exceeds a certain level or the probability of ruin of the insurer's risk process. Rare events occur so infrequently, that they cannot be reasonably recorded during a standard simulation procedure: specifc simulation algorithms which thwart the rarity of the event to simulate are required. An important algorithm in this context is based on changing the sampling distribution and it is called importance sampling. Optimal Monte Carlo algorithms for computing rare event probabilities are either logarithmic eficient or possess bounded relative error.

Spinous Process Osteochondroma as a Rare Cause of Lumbar Pain

We present a case of a 5th Lumbar Vertebra (L5) spinous process osteochondroma as a rare cause of lumbar pain in an old patient. A 70-year-old male presented with progressive and disabling lower lumbar pain. Tenderness over the central and left paraspinal area of the lower lumbar region and a palpable mass were evident. CT scan showed a mass arising from the spinous process of L5. Marginal resection of the tumor was performed through a posterior approach. The histological study revealed an osteochondroma. After surgery, pain was completely relieved. After one year there was no evidence of local recurrence or symptoms. Osteochondromas rarely involve the spine, but when they do symptoms like pain, radiculopathy/myelopathy, or cosmetic deformity may occur. The imagiologic exam of election for diagnosis is CT scan. When symptomatic the treatment of choice is surgical resection. The most concerning complication of osteochondromas is malignant transformation, a rare event.

Menstrual and hormonal alterations in juvenile systemic lupus erythematosus

Menstrual cycles of 30 patients with juvenile systemic lupus erythematosus (JSLE) were compared with 30 age-matched controls. The mean age of patients with JSLE and controls was similar (17.4 +/- 3.2 vs 17.06 +/- 2.08 years, P = 0.66). The mean menarche age was higher in JSLE than controls (13.13 +/- 1.4 vs 11.56 +/- 1.5 years, P = 0.0008). On the contrary, the mean maternal menarche age was similar in both groups (P = 0.62). Menstrual abnormalities and longer length cycles were more frequently observed in JSLE than controls (63% vs 10%, P = 0.0001; 23% vs 0%, P = 0.0105, respectively). The median of follicle stimulating hormone was significantly higher in patients with JSLE compared with controls (4.6 vs 3.4 IU/L, P = 0.0207), and the median of progesterone was lower (32.5 vs 70 ng/mL, P = 0.0033). The median Of luteinizing hormone was lower in patients with JSLE with menstrual abnormalities versus normal cycles (2.9 vs 5.5 IU/L, P = 0.019) and both had a high percentage of decreased progesterone levels (63% vs 73%, P = 0.70). Our findings support the notion that menstrual disturbances are frequent and may be associated with pituitary dysfunction leading to a decreased progesterone production. We also reported that in spite of premature ovarian failure being a rare event in JSLE the follicular reserve seems to be low regardless of intravenous cyclophosphamide treatment. Lupus (2009) 18, 38-43.

SPONTANEOUS FRACTURE OF THE FEMORAL NECK FOLLOWING PFN REMOVAL

Femoral neck fracture without associated trauma following consolidation of a transtrochanteric fracture is a rare event. The authors report a case of transtrochanteric fracture that was treated with PFN and which presented fracturing of the femoral neck two weeks after removal of the device. This occurrence was treated with partial arthroplasty.

Screening of autosomal gene deletions in patients with hypogonadotropic hypogonadism using multiplex ligation-dependent probe amplification: detection of a hemizygosis for the fibroblast growth factor receptor 1

P>Objective Congenital hypogonadotropic hypogonadism with anosmia (Kallmann syndrome) or with normal sense of smell is a heterogeneous genetic disorder caused by defects in the synthesis, secretion and action of gonadotrophin-releasing hormone (GnRH). Mutations involving autosomal genes have been identified in approximately 30% of all cases of hypogonadotropic hypogonadism. However, most studies that screened patients with hypogonadotropic hypogonadism for gene mutations did not include gene dosage methodologies. Therefore, it remains to be determined whether patients without detected point mutation carried a heterozygous deletion of one or more exons. Measurements We used the multiplex ligation-dependent probe amplification (MLPA) assay to evaluate the potential contribution of heterozygous deletions of FGFR1, GnRH1, GnRHR, GPR54 and NELF genes in the aetiology of GnRH deficiency. Patients We studied a mutation-negative cohort of 135 patients, 80 with Kallmann syndrome and 55 with normosmic hypogonadotropic hypogonadism. Results One large heterozygous deletion involving all FGFR1 exons was identified in a female patient with sporadic normosmic hypogonadotropic hypogonadism and mild dimorphisms as ogival palate and cavus foot. FGFR1 hemizygosity was confirmed by gene dosage with comparative multiplex and real-time PCRs. Conclusions FGFR1 or other autosomal gene deletion is a possible but very rare event and does not account for a significant number of sporadic or inherited cases of isolated GnRH deficiency.

Successful defibrillation of a dental patient in cardiac arrest

Cardiac arrest is a very rare event in a dental patient. However, practitioners have a duty of care to their patients if ever such an event occurs. The cardiac arrest discussed in this case report occurred in an elderly person with an implanted pacemaker whilst undergoing restorative dental treatment. Cardiac arrest was diagnosed and cardiopulmonary resuscitation instituted immediately, followed within three minutes by successful defibrillation using the School's semi-automatic defibrillator.

Efficient simulation of a Tandem Jackson Network

The two-node tandem Jackson network serves as a convenient reference model for the analysis and testing of different methodologies and techniques in rare event simulation. In this paper we consider a new approach to efficiently estimate the probability that the content of the second buffer exceeds some high level L before it becomes empty, starting from a given state. The approach is based on a Markov additive process representation of the buffer processes, leading to an exponential change of measure to be used in an importance sampling procedure. Unlike changes of measures proposed and studied in recent literature, the one derived here is a function of the content of the first buffer. We prove that when the first buffer is finite, this method yields asymptotically efficient simulation for any set of arrival and service rates. In fact, the relative error is bounded independent of the level L; a new result which is not established for any other known method. When the first buffer is infinite, we propose a natural extension of the exponential change of measure for the finite buffer case. In this case, the relative error is shown to be bounded (independent of L) only when the second server is the bottleneck; a result which is known to hold for some other methods derived through large deviations analysis. When the first server is the bottleneck, experimental results using our method seem to suggest that the relative error is bounded linearly in L.

Carpogenic germination of Sclerotinia minor and potential distribution in Australia

This study confirms that Australian isolates of Sclerotinia minor can produce fertile apothecia and further demonstrates that ascospores collected from these apothecia are pathogenic to sunflower (Helianthus annuus). Sunflower is a known host of the related fungus Sclerotinia sclerotiorum and is grown in some regions where S. minor is known to occur. Head rot symptoms were produced following inoculation with S. minor ascospores. Predictive modeling using CLIMEX software suggested that conditions suitable for carpogenic germination of S. minor probably occur in Australia particularly in southern regions. Carpogenic germination is probably a rare event in northern regions and, if it does occur, probably does not coincide with anthesis in sunflower crops, therefore allowing disease escape.