2134196
Counting Structures in Grid Graphs, Cylinders and Tori Using Transfer Matrices: Survey and New Results
There is a very large literature devoted to counting structures, e.g., spanning trees, Hamiltonian cycles, independent sets, acyclic orientations, in the n×m grid graph G(n,m). In particular the problem of counting the number of structures in fixed height graphs, i.e., fixing m and letting n grow, has been, for different types of structures, attacked independently by many different authors, using a transfer matrix approach. This approach essentially permits showing that the number of structures in G(n,m) satisfies a fixed-degree constant-coefficient recurrence relation in n. In contrast there has been surprisingly little work done on counting structures in grid-cylinders (where the left and right, or top and bottom, boundaries of the grid are wrapped around and connected to each other) or in grid-tori (where the left edge of the grid is connected to the right and the top edge is connected to the bottom one). The goal of this paper is to demonstrate that, with some minor modifications, the transfer matrix technique can also be easily used to count structures in fixed height grid-cylinders and tori.
14088697
Approximate shortest paths in anisotropic regions
Our goal is to find an approximate shortest path for a point robot moving in a planar subdivision with <i>n</i> vertices. Let ρ ≥ 1 be a real number. Distances in each face of this subdivision are measured by a convex distance function whose unit disk is contained in a concentric unit Euclidean disk, and contains a concentric Euclidean disk with radius 1/ρ. Different convex distance functions may be used for different faces, and obstacles are allowed. These convex distance functions may be asymmetric. For all ε ∈ (0, 1), and for any two points <i>v<inf>s</inf></i> and <i>v<inf>d</inf></i>, we give an algorithm that finds a path from <i>v<inf>s</inf></i> to <i>v<inf>d</inf></i> whose cost is at most (1 + ε) times the minimum cost. Our algorithm runs in <i>O</i> (ρ<sub>2</sub>logρ/ε<sup>2</sup>n<sup>3</sup> log (ρn/ε)) time. This bound does not depend on any other parameters; in particular, it does not depend on the minimum angle in the subdivision. We give applications to two special cases that have been considered before: the weighted region problem and motion planning in the presence of uniform flows. For the weighted region problem with weights in [1, ρ] ∪ {∞}, the time bound of our algorithm improves to <i>O</i> (ρ<sub>2</sub>logρ/εn<sup>3</sup> log (ρn/ε)).
1333188
Querying approximate shortest paths in anisotropic regions
We present a data structure for answering approximate shortest path queries ina planar subdivision from a fixed source. Let ρ ≥ 1 be a real number.Distances in each face of this subdivision are measured by a possiblyasymmetric convex distance function whose unit disk is contained in aconcentric unit Euclidean disk, and contains a concentric Euclidean disk withradius 1/ρ. Different convex distance functions may be used for differentfaces, and obstacles are allowed. Let ε be any number strictly between 0and 1. Our data structure returns a (1+ε)approximation of the shortest path cost from the fixed source to a querydestination in O(logρn/ε) time. Afterwards, a(1+ε)-approximate shortest path can be reported in time linear in itscomplexity. The data structure uses O(ρ<sup>2</sup> n<sup>4</sup>/ε<sup>2</sup> log ρn/ε) space and can be built in O((ρ<sup>2</sup> n<sup>4</sup>)/(ε<sup>2</sup>)(log ρn/ε)<sup>2</sup>) time. Our time and space bounds do not depend onany geometric parameter of the subdivision such as the minimum angle.
38202538
Infix-free Regular Expressions and Languages
We study infix-free regular languages. We observe the structural properties of finite-state automata for infix-free languages and develop a polynomial-time algorithm to determine infix-freeness of ...
17974516
G-Networks and the Modeling of Adversarial Agents
As a result of the structure and content transformation of an evolving society, many large scale autonomous systems emerged in diverse areas such as biology, ecology or finance. Inspired by the desire to better understand and make the best out of these systems, we propose an approach which builds stochastic mathematical models, in particular G-networks models, that allow the efficient representation of systems of agents and offer the possibility to analyze their behavior using mathematics. This approach is capable of modelling the system at different abstraction levels, both in terms of the number of agents and the size of the geographical location. We demonstrate our approach with some urban military planning scenarios and the results suggest that this approach has tackled the problem in modelling autonomous systems at low computational cost. Apart from offering the numerical estimates of the outcome, the approach helps us identify the characteristics that impact the system most and allows us to compare alternative strategies.
14934450
Combining Statistical and Knowledge-Based Spoken Language Understanding in Conditional Models
Spoken Language Understanding (SLU) addresses the problem of extracting semantic meaning conveyed in an utterance. The traditional knowledge-based approach to this problem is very expensive --- it requires joint expertise in natural language processing and speech recognition, and best practices in language engineering for every new domain. On the other hand, a statistical learning approach needs a large amount of annotated data for model training, which is seldom available in practical applications outside of large research labs. A generative HMM/CFG composite model, which integrates easy-to-obtain domain knowledge into a data-driven statistical learning framework, has previously been introduced to reduce data requirement. The major contribution of this paper is the investigation of integrating prior knowledge and statistical learning in a conditional model framework. We also study and compare conditional random fields (CRFs) with perceptron learning for SLU. Experimental results show that the conditional models achieve more than 20% relative reduction in slot error rate over the HMM/CFG model, which had already achieved an SLU accuracy at the same level as the best results reported on the ATIS data.
14022565
Semantic Structure Matching for Assessing Web-Service Similarity
The web-services stack of standards is designed to support the reuse and interoperation of software components on the web. A critical step in the process of developing applications based on web services is service discovery, i.e., the identification of existing web services that can potentially be used in the context of a new web application. UDDI, the standard API for publishing web-services specifications, provides a simple browsing-by-business-category mechanism for developers to review and select published services. To support programmatic service discovery, we have developed a suite of methods that utilizes both the semantics of the identifiers of WSDL descriptions and the structure of their operations, messages and data types to assess the similarity of two WSDL files. Given only a textual description of the desired service, a semantic information-retrieval method can be used to identify and order the most similar service-description files. This step assesses the similarity of the provided description of the desired service with the available services. If a (potentially partial) specification of the desired service behavior is also available, this set of likely candidates can be further refined by a semantic structure-matching step assessing the structural similarity of the desired vs. the retrieved services and the semantic similarity of their identifier. In this paper, we describe and experimentally evaluate our suite of service-similarity assessment methods.
20468093
A Multiplier Structure Based on a Novel Real-time CSD Recoding
Implementation of digital signal processing (DSP) algorithms in hardware, such as field programmable gate arrays (FPGAs), requires a large number of multiplications. In this paper, we introduce a novel multiplier structure that converts from 2's complement to canonical signed digit (CSD) representation in real time. The proposed algorithm increases the number of zero partial products (which can be simplified by shift operations) to approximately 66.7% compared with 50% for modified Booth's recoding. Also, the proposed hardware structure reduces the non-zero partial products to a minimum, and consequently the number of arithmetic operations in the carry-save structure is reduced. So, our proposed hardware decreases both the time required for multiplication and the power consumption of the multiplier. Furthermore, because the proposed structure uses real time CSD recoding, and does not require a fixed value for the multiplier input to be known a priori, the proposed multiplier can be used to implement digital filters with non-fixed filter coefficients, such as adaptive filters.
29450095
Cognitive models of the brain
The human brain is the most complicated organ in the universe and a new frontier yet to be explored in an interdisciplinary approach. Investigation of the brain is a unique problem that requires recursive mental power to explore the brain using the brain. This paper attempts to develop functional and cognitive models of the brain by using cognitive informatics and formal methodologies. This paper adopts a memory-based approach to explore the brain, and to demonstrate that memory is the foundation for any natural intelligence. Structures of memories are explored and cognitive models of the natural intelligence are proposed. Cognitive mechanisms of the brain, including hypotheses and theories on the thinking engine of the brain, long-term memory establishment, and roles of sleep in long-term memory development, are investigated. The models and theories are applied to explain a number of fundamental physiological and psychological phenomena.