Categorical ML — Category-theoretic modular programming

We consider an extension of the functional programming language Standard ML with a modular structure based upon concepts in category theory such as categories, functors, natural transformations and adjunctions. In essence, we are following the categorical imperative of considering arrows as well as objects. This is intended to enforce a certain mathematical rigour on the programmer, so that the only programs that can be expressed are those with a categorical significance. The essentially algebraic nature of category theory means that we may generate equational correctness conditions for the modular structure of programs, thus separating the correctness of individual functions from that of modules. We describe this programming language, give examples of its use, and explain how it is implemented in a type system.     

Mean-square stability for discrete bilinear systems in Hilbert space

A discrete system is uniformly mean-square stable if uniform convergence is preserved between input and state correlation sequences, and if nuclearity is preserved between the input and state correlation limits. This paper supplies a contraction-free condition ensuring mean-square stability for infinite-dimensional bilinear systems evolving in a separable Hilbert space.     

Development and implementation of a NURBS curve motion interpolator

This paper deals with the issues of development and implementation of a real-time NURBS interpolator for a six-axis robot. Using an open-architecture controller system as a testbed, a real-time NURBS curve interpolator was developed, implemented and tested. Sample runs were conducted with the resulting trajectories measured in real-time during robot motion. The resulting trajectories are analyzed, discussed and compared with those from a commonly used point-to-point approximation technique. The real-time NURBS curve interpolator's feasibility, advantages and related issues are also discussed.     

Nonnegative integral subset representations of integer sets

We consider an integer-subset representation problem motivated by a medical application in radiation therapy. We prove NP-completeness, derive nontrivial bounds, and report on the performance of a greedy heuristic.     

Information cut for clustering using a gradient descent approach

We introduce a new graph cut for clustering which we call the Information Cut. It is derived using Parzen windowing to estimate an information theoretic distance measure between probability density functions. We propose to optimize the Information Cut using a gradient descent-based approach. Our algorithm has several advantages compared to many other graph-based methods in terms of determining an appropriate affinity measure, computational complexity, memory requirements and coping with different data scales. We show that our method may produce clustering and image segmentation results comparable or better than the state-of-the art graph-based methods.     

A method for the efficient prioritization of infrastructure renewal projects

The infrastructure renewal program at MIT consists of a large number of projects with an estimated budget that could approach $1 billion. Infrastructure renewal at the Massachusetts Institute of Technology (MIT) is the process of evaluating and investing in the maintenance of facility systems and basic structure to preserve existing campus buildings. The selection and prioritization of projects must be addressed with a systematic method for the optimal allocation of funds and other resources. This paper presents a case study of a prioritization method utilizing multi-attribute utility theory. This method was developed at MIT's Department of Nuclear Engineering and was deployed by the Department of Facilities after appropriate modifications were implemented to address the idiosyncrasies of infrastructure renewal projects and the competing criteria and constraints that influence the judgment of the decision-makers. Such criteria include minimization of risk, optimization of economic impact, and coordination with academic policies, programs, and operations of the Institute. A brief overview of the method is presented, as well as the results of its application to the prioritization of infrastructure renewal projects. Results of workshops held at MIT with the participation of stakeholders demonstrate the feasibility of the prioritization method and the usefulness of this approach.     

Vibrational Mode in Two-Dimensional Dust Monolayer with Finite Size Dust Grains

Vibrational mode in a two-dimensional dust monolayer is investigated by considering the finite size of dust grains. Each dust grain is assumed to be a negative point charge and a dipole moment due to the inhomogeneous charge distribution on its surface. The dispersion relation of the vibrational mode is derived. Both the self-excited and externally excited cases are discussed. It is shown that the mode is sensitive to the direction of the dipole moment.     

啮合型同向旋转双螺杆挤出螺槽非充满的熔融理论研究 Ⅱ.模型的求解

根据啮合型同向旋转双螺杆挤出非充满熔融的理论模型，对描述非充满熔融过程的主要物理量：固相高度变化函数、熔融速率及熔融区总长等进行了计算分析，并对有关影响因素进行了讨论。     

THE APPLICATION OF COKELET''''S WAVE THEORY IN THE CALCULATION OF WAVE-CURRENT FIELD

By using Cokelet's wave theory,the limiting wave height and the relative waveangular frequency in wave-current field were calculated in this paper.It is indicated by numeri-cal calculation that if the water depth is not too small,the result given by authors'calculationare very close to the results of limiting wave height by Dalrymple(1975)and to the data of rel-ative wave angular frequency by linear wave theory;but if water depth is rather small,thereare some discrepancy,