A Family of non-Gaussian Martingales with Gaussian Marginals

We construct a family of non-Gaussian martingales the marginals of which are all Gaussian. We give the predictable quadratic variation of these processes and show they do not have continuous paths. These processes are Markovian and inhomogeneous in time, and we give their infinitesimal generators. Within this family we find a class of piecewise deterministic pure jump processes and describe the laws of jumps and times between the jumps.Comment: 16 pages, 2 figure

Limit theorems for multi-type general branching processes with population dependence

A general multi-type population model is considered, where individuals live and reproduce according to their age and type, but also under the influence of the size and composition of the entire population. We describe the dynamics of the population density as a measure-valued process and obtain its asymptotics, as the population grows with the environmental carrying capacity. "Density" in this paper generally refers to the population size as compared to the carrying capacity. Thus, a deterministic approximation is given, in the form of a Law of Large Numbers, as well as a Central Limit Theorem. Migration can also be incorporated. This general framework is then adapted to model sexual reproduction, with a special section on serial monogamic mating systems

Convergence of the age structure of general schemes of population processes

We consider a family of general branching processes with reproduction parameters depending on the age of the individual as well as the population age structure and a parameter $K$, which may represent the carrying capacity. These processes are Markovian in the age structure. In a previous paper the Law of Large Numbers as $K\to\infty$ was derived. Here we prove the Central Limit Theorem, namely the weak convergence of the fluctuation processes in an appropriate Skorokhod space. We also show that the limit is driven by a stochastic partial differential equation

On the Digital Holographic Interferometry of Fibrous Material, I. Optical Properties of Polymer and Optical Fibers

The digital holographic interferometry (DHI) was utilized for investigating the optical properties of polymer and optical fibers. The samples investigated here were polyvinylidene fluoride (PVDF) polymer fiber and graded-index (GRIN) optical fiber. The phase shifting Mach-Zehnder interferometer was used to obtain five phase-shifted holograms, in which the phase difference between two successive holograms is pi/2, for each fiber sample. These holograms were recorded using a CCD camera and were combined to gain a complex wavefield, which was numerically reconstructed using the convolution approach into amplitude and phase distributions. The reconstructed phase distribution was used to determine the refractive index, birefringence and refractive index profile of the studied samples. The mean refractive index has been measured with accuracy up to 4 {\times} 10-4. The main advantage of DHI is to overcome the manual focusing limitations by means of the numerical focusing. The results showed accurate measurements of the optical properties of fibers.Comment: abstract, reference

Rethinking Baloch Secularism: What the Data Say

Since 1947, Baloch have resisted inclusion into the Pakistan and have waged several waves of ethno-nationalist insurgency against the state. Scholars and Baloch nationalist leaders alike generally assert that Baloch are more secular than other Pakistanis, more opposed to the political Islamist policies pursued by the state, and less supportive of Islamist militancy in the country. However, these claims lack empirical support. We employ data derived from a large national survey of Pakistanis from 2012 to evaluate these conventional wisdoms. Contrary to claims in the literature, we find that Baloch resemble Pakistanis generally with few important exceptions

On Verifying Causal Consistency

Causal consistency is one of the most adopted consistency criteria for distributed implementations of data structures. It ensures that operations are executed at all sites according to their causal precedence. We address the issue of verifying automatically whether the executions of an implementation of a data structure are causally consistent. We consider two problems: (1) checking whether one single execution is causally consistent, which is relevant for developing testing and bug finding algorithms, and (2) verifying whether all the executions of an implementation are causally consistent. We show that the first problem is NP-complete. This holds even for the read-write memory abstraction, which is a building block of many modern distributed systems. Indeed, such systems often store data in key-value stores, which are instances of the read-write memory abstraction. Moreover, we prove that, surprisingly, the second problem is undecidable, and again this holds even for the read-write memory abstraction. However, we show that for the read-write memory abstraction, these negative results can be circumvented if the implementations are data independent, i.e., their behaviors do not depend on the data values that are written or read at each moment, which is a realistic assumption.Comment: extended version of POPL 201

An Audit of 6 years of Oral and Maxillofacial Surgical Conditions admitted for Interventional Treatment at Muhimbili National Hospital, Dar es Salaam – Tanzania

Background: The world wide pattern of OMFS conditions has been rarely reported despite its significance in the head and neck medicine; maxillofacial trauma and tumors. The main objective of this study was to audit oral and maxillofacial surgical (OMFS) conditions admitted for interventional treatment at Muhimbili National Hospital. Methods: Patients presenting to the OMFS unit with oral and maxillofacial pathological conditions between January 2003 - January 2009 were studied prospectively. Data for analysis were obtained from the daily operation list and includes age, sex, location, diagnosis of the pathological lesion, surgical procedure and date of procedure. Results: During the study period, the unit offered specialized services to 454 patients. Among them, 222 were males and 232 females. The mean age of the patients was 31.7 and the range was 79 years. Patient aged 21-30 years were mostly affected. Of the pathological lesions attended, benign tumors were the most common 255(56.2%) followed by fractures 58(12.8%), cysts 46(10.1%), malignant tumors 36(7.9%) and chronic infections 17(3.7%). Of the 255 cases of benign tumors 155(60.8%) were located on the mandible and 64 (25.1%) on the maxilla. Malignant tumors were 36 cases in which 11(30.6%) were located on the mandible. Maxillofacial fractures accounted 58 cases in which 31(53.4%) cases were located on the mandible. Cysts were 46 cases of which 17(37%) were located on the floor of the mouth, 10(21.7%) on the mandible and 7(15.2%) on the maxilla. Tumor excision was the commonest procedure performed 119(26.2%), followed by Tumor excision + reconstruction 89(19.6%), ORIF+IMF 51(11.2%), Fistulectomy 45(9.9%), Tumor enucleation 45(9.9%), Wide surgical excision 27(5.9%), Sinusectomy 16(3.5%) and Sequestrectomy 15(3.3%). Conclusion: There is a significant burden of OMFS conditions attended at MNH. We suggest that the government enhance the state of medical infrastructure in the local hospitals in terms of manpower and facilities for the diagnosis and treatment of simpler OMFS disease as well as timely referral on to regional center for the more complex issues. This will reduce the burden of OMF conditions experienced by this hospital and improve OMF services country wide