21906808
The Theory and Application of Rough Integration in Rough Function Model
The definition of the rough integral Pawlak proposed is improved. New notions are proposed, which are respectively the rough integral on a constant interval and the roughly integral upper limit function, and so on. By comparing with the definite integral of real functions, the properties of rough integrals are analyzed. Giving the concept of mean value of discrete functions, the mean value method for rough integration is derived. At the same time, the intermediate value theorem of rough integration is proposed and its geometric significance is analyzed, which provides a dependable theoretical tool for rough integral operation, etc.. Conclusions including the existence theorem of rough primitives and the fundamental formula of rough calculus are proposed. By the representative of discrete functions, the method of computing a primitive is given, by which basic formulas for rough integration in common use are derived, and the method of rough direct integration is obtained. There is also the method of rough integration by parts for rough integrals which is like that of definite integrals. Thus the recurrence formula for rough integration is deduced, in which the integrand of the rough integral is in the shape of the product of a rough power function and a rough exponential function. It is pointed out that integration by substitution is not applicable for rough integral operation.
452800
Rough Derivatives in Rough Function Model and Their Application
On the theory and application of rough derivatives in rough function model, the notion of generalized rough functions is defined to improve the definition of higher order rough derivatives Pawlak proposed, and analyze the functional features of roughly derived functions and higher order roughly derived functions. The rough extremum definition of discrete functions is given, Fermat theorem and Rolle theorem of roughly smooth discrete functions are proposed and proved, which complete and perfect the theoretical foundation of rough derivatives application in rough function model. The concepts that are rough monotone and rough convexity of discrete functions are defined. By comparing with the derivative application of real continuous function, a series of theorems are put forward which are the relation theorem of rough derivatives and rough monotone, the two sufficient conditions of rough extrema, the two relation theorems of rough derivatives and rough convexity. Moreover, some new results are achieved such as the sufficient condition of rough smoothing of discrete functions, etc.
5078035
Order-Based Decision Rules Acquisition in Continuous-Valued Decision Information Systems
In a continuous-valued information system, attribute values of objects represent not only the relative distances, but also the ordinal relation of objects. By considering the relative distances of objects, some discretization approaches and other approaches were proposed in previous literature, to discuss the attribute reduces of the system. This paper considers ordinal relations of objects, and utilizes dominance relation rough set model to discuss decision rules acquisition problems. Firstly, concepts of order-based decision rules and generalized order-based decision rules are introduced. Then the concept of optimal order-based decision rule is defined. In order to compute optimal order-based decision rules, the concept of reduct of the object is proposed. Lastly, discernibility functions of objects are constructed, and used to compute optimal order-based decision rules by Boolean reasoning techniques.
6225988
A global optimal algorithm for class-dependent discretization of continuous data
This paper presents a new method to convert continuous variables into discrete variables for inductive machine learning. The method can be applied to pattern classification problems in machine learning and data mining. The discretization process is formulated as an optimization problem. We first use the normalized mutual information that measures the interdependence between the class labels and the variable to be discretized as the objective function, and then use fractional programming (iterative dynamic programming) to find its optimum. Unlike the majority of class-dependent discretization methods in the literature which only find the local optimum of the objective functions, the proposed method, OCDD, or Optimal Class-Dependent Discretization, finds the global optimum. The experimental results demonstrate that this algorithm is very effective in classification when coupled with popular learning systems such as C4.5 decision trees and Naive-Bayes classifier. It can be used to discretize continuous variables for many existing inductive learning systems.
9823069
Multiple Tree Models for Occlusion and Spatial Constraints in Human Pose Estimation
Tree-structured models have been widely used for human pose estimation, in either 2D or 3D. While such models allow efficient learning and inference, they fail to capture additional dependencies between body parts, other than kinematic constraints between connected parts. In this paper, we consider the use of multiple tree models, rather than a single tree model for human pose estimation. Our model can alleviate the limitations of a single tree-structured model by combining information provided across different tree models. The parameters of each individual tree model are trained via standard learning algorithms in a single tree-structured model. Different tree models can be combined in a discriminative fashion by a boosting procedure. We present experimental results showing the improvement of our approaches on two different datasets. On the first dataset, we use our multiple tree framework for occlusion reasoning. On the second dataset, we combine multiple deformable trees for capturing spatial constraints between non-connected body parts.
37274241
Preparation of one-dimensional photonic crystal with variable period by using ultra-high vacuum electron beam evaporation
One-dimensional photonic crystal with variable period has been prepared by using the method of ultra-high vacuum electron beam evaporation. Advantage of this method is gaining variable period easily. The transmittance of the photonic crystal has been also studied.
7145981
High performance first principles method for complex magnetic properties
The understanding of metallic magnetism is of fundamental importance for a wide range of technological applications ranging from thin film disc drive read heads to bulk magnets used in motors and power generation. In this submission for the Gordon Bell Prize we use the power of massively parallel processing (MPP) computers to perform first principles calculations of large system models of non-equilibrium magnetic states in metallic magnets. The calculations are based on a new constrained local moment (CLM) model that places the recently proposed Spin-Dynamics of Antropov et al. [1] on firm theoretical foundations. The equations of constrained local spin density approximation (constrained LSDA) are solved using the massively parallel locally self-consistent multiple scattering (LSMS) method[3] extended to treat general non-collinear arrangements of the magnetic moments [4]. A general algorithm has been developed for self-consistently finding the constraining fields which are introduced into LSDA in order to maintain a prescribed magnetic moment orientation configuration. The existence of CLM states is demonstrated for 1024 atom per unit cell models of Iron above its Curie temperature. The constrained LSMS method we have developed exploits the locality in the physics of the problem to produce an algorithm that has only local and limited communications on parallel computers leading to very good scale-up to large processor counts and linear scaling of the number of operations with the number of atoms in the system. The computationally intensive step of inversion of a dense complex matrix is largely reduced to matrix-matrix multiplies which are implemented in BLAS. Throughout the code attention is paid to minimizing both the total operation count and total execution time, with primacy given to the latter. Full 64-bit arithmetic is used throughout. The code shows near linear scale-up to 1024-processing elements (PE) and attains a performance of 657 Gflops on a Cray T3E1200 LC1024 at a US Government site. Performance figures of 276 Gflops and 329 Gflops have also been obtained on T3E900 and T3E1200 LC512 machines at the National Energy Research Scientific Computing Center (NERSC), and Cray Research respectively. All performance figures include necessary I/O.
9142519
Utilizing field usage patterns for Java heap space optimization
This research studies the characteristics of field usage patterns in the SpecJVM98 benchmarks. It finds that multiple object instances of the same class often exhibit different field-usage patterns. Motivated by this observation, we designed a heap compression mechanism that classifies object instances at runtime based on their field-usage patterns and eliminates unused fields to save space. To achieve the maximum space savings while minimizing the space and time overhead, our design combines three interrelated techniques in a novel manner: runtime object instance classification, field virtualization, and bidirectional object layout. An experimental evaluation reveals that this mechanism can reduce the maximum heap occupancy of SpecJVM98 benchmarks by up to 18% and 14% on average while keeping the application execution overhead low.