Safe Compositional Specification of Network Systems With Polymorphic, Constrained Types

In the framework of iBench research project, our previous work created a domain specific language TRAFFIC [6] that facilitates specification, programming, and maintenance of distributed applications over a network. It allows safety property to be formalized in terms of types and subtyping relations. Extending upon our previous work, we add Hindley-Milner style polymorphism [8] with constraints [9] to the type system of TRAFFIC. This allows a programmer to use for-all quantifier to describe types of network components, escalating power and expressiveness of types to a new level that was not possible before with propositional subtyping relations. Furthermore, we design our type system with a pluggable constraint system, so it can adapt to different application needs while maintaining soundness. In this paper, we show the soundness of the type system, which is not syntax-directed but is easier to do typing derivation. We show that there is an equivalent syntax-directed type system, which is what a type checker program would implement to verify the safety of a network flow. This is followed by discussion on several constraint systems: polymorphism with subtyping constraints, Linear Programming, and Constraint Handling Rules (CHR) [3]. Finally, we provide some examples to illustrate workings of these constraint systems.National Science Foundation (CCR-0205294

Wright-Fisher diffusion with a continuum of seed-banks

This paper aims to extend the strong seed-bank model introduced in arXiv:1411.4747 to allow for more general dormancy time distributions, such as a type of Pareto distribution. To achieve this, the Wright-Fisher diffusion with a continuum of seed-banks (also referred to as ``continuum seed-bank diffusion'') along with its coalescent process which is referred to as ``continuum seed-bank coalescent" are introduced. First, the corresponding infinite-dimensional stochastic differential equation, which is equivalent to a non-Markovian stochastic Volterra equation, is proved to have a unique strong solution. The solution is a strong Markov process in both the cases when the state space is endowed with the original and the weak$^{\star}$ topology. Then, a discrete-time Wright-Fisher type model is constructed, in which the scaling limit of the allele frequency process is the continuum seed-bank diffusion in the weak$^{\star}$ topology setting. Finally, by establishing a duality relation between the continuum seed-bank diffusion and a Markov jump process, the continuum seed-bank coalescent process is obtained, which is exactly the scaling limit of the ancestral process in the above discrete-time Wright-Fisher type model.Comment: 40 pages, 2 figure

Simulation and Measurement of Optical Aberrations of Injection Molded Progressive Addition Lenses

Engineering: 1st Place (The Ohio State University Edward F. Hayes Graduate Research Forum)Injection molding is an important mass production tool in optical industry. In this research our aim is to develop a process of combining ultraprecision diamond turning and injection molding to create a unique low cost manufacturing process for progressive addition lenses or PALs. In industry, it is a well-known fact that refractive index variation and geometric deformation of injection molded lenses due to polymers’ rheological properties will distort their optical performances. To address this problem, we developed a method of determining the optical aberrations of the injection molded PALs. This method involves reconstructing the wavefront pattern in the presence of uneven refractive index distribution and surface warpage using a finite element method. In addition to numerical modeling, a measurement system based on a Shack-Hartmann wavefront sensor was used to verify the modeling results. The measured spherocylindrical powers and aberrations of the PALs were in good agreement with the model. Consequently, the optical aberrations of injection molded PALs were successfully predicted by finite element modeling. In summary, it was demonstrated in this study that numerical based optimization for PALs manufacturing is feasible.National Science FoundationNo embarg

Simple, safe, and efficient memory management using linear pointers

Efficient and safe memory management is a hard problem. Garbage collection promises automatic memory management but comes with the cost of increased memory footprint, reduced parallelism in multi-threaded programs, unpredictable pause time, and intricate tuning parameters balancing the program's workload and designated memory usage in order for an application to perform reasonably well. Existing research mitigates the above problems to some extent, but programmer error could still cause memory leak by erroneously keeping memory references when they are no longer needed. We need a methodology for programmers to become resource aware, so that efficient, scalable, predictable and high performance programs may be written without the fear of resource leak. Linear logic has been recognized as the formalism of choice for resource tracking. It requires explicit introduction and elimination of resources and guarantees that a resource cannot be implicitly shared or abandoned, hence must be linear. Early languages based on linear logic focused on Curry-Howard correspondence. They began by limiting the expressive powers of the language and then reintroduced them by allowing controlled sharing which is necessary for recursive functions. However, only by deviating from Curry-Howard correspondence could later development actually address programming errors in resource usage. The contribution of this dissertation is a simple, safe, and efficient approach introducing linear resource ownership semantics into C++ (which is still a widely used language after 30 years since inception) through linear pointer, a smart pointer inspired by linear logic. By implementing various linear data structures and a parallel, multi-threaded memory allocator based on these data structures, this work shows that linear pointer is practical and efficient in the real world, and that it is possible to build a memory management stack that is entirely leak free. The dissertation offers some closing remarks on the difficulties a formal system would encounter when reasoning about a concurrent linear data algorithm, and what might be done to solve these problems

Nonlinearity compensation using dispersion-folded digital backward propagation

A computationally efficient dispersion-folded (D-folded) digital backward propagation (DBP) method for nonlinearity compensation of dispersion-managed fiber links is proposed. At the optimum power level of long-haul fiber transmission, the optical waveform evolution along the fiber is dominated by the chromatic dispersion. The optical waveform and, consequently, the nonlinear behavior of the optical signal repeat at locations of identical accumulated dispersion. Hence the DBP steps can be folded according to the accumulated dispersion. Experimental results show that for 6,084 km single channel transmission, the D-folded DBP method reduces the computation by a factor of 43 with negligible penalty in performance. Simulation of inter-channel nonlinearity compensation for 13,000 km wavelength-division multiplexing (WDM) transmission shows that the D-folded DBP method can reduce the computation by a factor of 37

Efficient Computation And Compensation Of Linear And Nonlinear Distortion in Dispersion-Managed Fiber-Optic Transmission

In one embodiment, a method for performing nonlinearity compensation on a dispersion-managed optical signal that was transmitted over an optical communication link, the method including virtually dividing the communication link into a plurality of steps, performing lumped dispersion compensation on a recieved optical signal to obtain a waveform upon which digital backward propagation (DBP) can be performed, performing DBP by performing dispersion compensation and nonlinearity compensation for each step, and generating an estimate of the transmitted signal base upon the performed DBP