Showing papers on "Hierarchy (mathematics) published in 1995"

Method and apparatus for processing natural language with a hierarchy of mapping routines

Abstract: A method and apparatus for processing natural language and deducing meaning from a natural language input characterized by the steps of (a) receiving an ordered string of word objects having a natural language meaning, (b) selecting a word window length, and (c) successively moving the word window along the ordered string and analyzing the meaning of a substring of word objects that fall within the word window. The substring is removed from the ordered string if the substring has a recognized meaning, until all substrings of the ordered string that fit within the window have been analyzed. In a step (d), the word window length is reduced and step (c) is repeated until only an unrecognized residual of the ordered string remains. The meaning of the substring is analyzed by mapping the substring against a database using one or more mapping routines. The mapping routines are preferably arranged in a hierarchy, wherein a successive mapping routine is used to analyze the substring when a previous mapping routine in the hierarchy cannot map the substring. A computer-implemented task is determined from the recognized substrings and performed by the computer system. The apparatus of the present invention implements the method on a pen-based computer system, and the ordered string is preferably received from strokes entered by a stylus on a display screen of the pen-based computer or from a microphone receiving speech input.

An object-oriented computer environment and related method

Abstract: An object-oriented computer environment is managed by storing, in a plurality of repositories accessible during the life cycles of objects, information required to initiate object operations. The repositories can contain location information identifying the storage location of system objects or information indicating preferences for a preselected manner of performing object operations. In another preferred form, the repositories can be assigned to different levels of a hierarchy to control the distribution of stored information.

Flexible distributed network database containing configuration information for a network divided into domains

Abstract: A network database. The network database is arranged in a plurality of domains in a logical hierarchy. Each domain of the hierarchy represents a body of information associated with a logically related group of users or related group of computers. A relative naming scheme is implemented in which a domain stores the names of only its parent domain and child domains. This permits reconfiguration of the network to be accomplished without changing the database structure. Each domain stores information in a hierarchical structure known as a "directory." Each directory consists of a list of zero or more "properties," each having an associated name and ordered list of values.

New Collapse Consequences of NP Having Small Circuits

Abstract: We show that if a self-reducible set has polynomial-size circuits, then it is low for the probabilistic class ZPP(NP) As a consequence we get a deeper collapse of the polynomial-time hierarchy PH to ZPP(NP) under the assumption that NP has polynomial-size circuits This improves on the well-known result of Karp, Lipton, and Sipser (1980) stating a collapse of PH to its second level σ 2 P under the same assumption As a further consequence, we derive new collapse consequences under the assumption that complexity classes like UP, FewP, and C=P have polynomial-size circuits

On the Complexity of Min-Max Optimization Problems and their Approximation

Abstract: The computational complexity of optimization problems of the min-max form is naturally characterized by ∏ 2 P , the second level of the polynomial-time hierarchy. We present a number of optimization problems of this form and show that they are complete for the class ∏ 2 P . We also show that the constant–factor approximation versions of some of these optimization problems are also complete for ∏ 2 P .

A hierarchy of totally ordered multicasts

Abstract: The increased interest in protocols that provide a total order on message delivery has led to several different definitions of total order. In this paper we investigate these different definitions and propose a hierarchy that helps to better understand the implications of the different possibilities in terms of guarantees and communication cost. We identify two definitions: weak total order and strong total order, which are at the extremes of the proposed hierarchy, and incorporate them into a consistent design. Finally, we propose high-level algorithms based on a virtually synchronous communication environment that implement the given definitions.

Efficient Radiosity in Dynamic Environments

Abstract: A method of determining radiosity in an environment containing moving objects, is described. This method uses the hierarchical techniques of Hanrahan et al. to obtain a static solution. Hanrahan’s techniques efficiently create a hierarchical meshing of the environments geometry, and create links from element to element based on the magnitude of the form-factor between the elements. These ideas extend naturally to a dynamic environment, as only three atomic editing operations are required to update a hierarchy when an object moves: a link can be moved up or down the hierarchy, or a link can be occluded. Our algorithm exploits these simple editing processes to maintain the hierarchy, and then uses an iterative technique to solve the resulting linear system. The approach is extremely efficient, requiring little work between frames.

Restricted flows of the Ablowitz-Ladik hierarchy and their continuous limits

Abstract: It is studied here how the Ablowitz-Ladik (AL) hierarchy and their restricted flows are related to the AKNS hierarchy and to their restricted flows in the continuous limit. It is shown that restricted flows of the AL hierarchy yield discrete maps approximating restricted flows of the AKNS hierarchy. Integrals of motion and Lax representation for restricted flows of the AL hierarchy as well as a discrete zero-curvature representation for the AL hierarchy with sources are given.

General rational reductions of the KP hierarchy and their symmetries

Abstract: [ O m L m , O n L n ] = 0 , O n = O / O t n . (5) In this form the "hierarchy" of the KP equation is an infinite system of equations for infinitely many unknown functions depending on infinitely many variables. The KP hierarchy was defined in [3] as a system of commuting evolution equations on the space of infinite tuples u i ( x ) , i = 1 ,2 , . . . , of functions of one variable. The corresponding equations are equivalent to the Lax equations o . ~ = [ ~ ; , q (6) for the pseudodifferential operator

The complexity of reconfiguring network models

Abstract: This paper concerns some of the theoretical complexity aspects of the reconfigurable network model. The computational power of the model is investigated under several variants, depending on the type of switches (or switch operations) assumed by the network nodes. Computational power is evaluated by focusing on the set of problems computable in constant time in each variant. A hierarchy of such problem classes corresponding to different variants is shown to exist and is placed relative to traditional classes of complexity theory.

The symmetry structure of the anti-self-dual Einstein hierarchy

Abstract: An important example of a multi‐dimensional integrable system is the anti‐self‐dual Einstein equations. By studying the symmetries of these equations, a recursion operator is found and the associated hierarchy constructed. Owing to the properties of the recursion operator one may construct a hierarchy of symmetries and find the algebra generated by them. In addition, the Lax pair for this hierarchy is constructed.

Lamé potentials and the stationary (m)KdV hierarchy

Abstract: A new method of constructing elliptic finite-gap solutions of the stationary Korteweg-de Vries (KdV) hierarchy, based on a theorem due to PICARD, is illustrated in the concrete case of the Lame-Ince potentials -s(s + 1) ρ(z), se (ρ() the elliptic Weierstrass function) Analogous results are derived in the context of the stationary modified Korteweg-de Vries (mKd V) hierarchy for the first time

An infinite hierarchy of symmetries associated with hyperbolic surfaces

Abstract: A subclass of hyperbolic surfaces defined by the requirement that the negative Gaussian curvature be a function of one asymptotic coordinate only is considered. Thus, these Bianchi surfaces generalize pseudo-spherical surfaces governed by the classical sine-Gordon equation. It is shown that the modified Korteweg-de Vries (MKDV) hierarchy associated with the latter equation may be used to construct an infinite hierarchy of coordinate-dependent symmetries of the corresponding Bianchi system. Accordingly, an extension of the well-known MKDV recursion operator is presented.

The Adler–Shiota–van Moerbeke formula for the BKP hierarchy

Abstract: We study the BKP hierarchy and prove the existence of an Adler–Shiota–van Moerbeke formula. This formula relates the action of the BW1+∞ algebra on tau functions to the action of the ‘‘additional symmetries’’ on wave functions.

Efficient management of time-evolving databases

Abstract: Efficiently managing the history of a time-evolving system is one of the central problems in many database environments, like database systems that incorporate versioning, or object-oriented databases that implicitly or explicitly maintain the history of persistent objects. In this paper we propose algorithms that reconstruct past states of an evolving system for two general cases, i.e., when the system's state is represented by a set or by a hierarchy (a forest of trees). Sets are widely used as a canonical form of representing information in databases or program states. For more complex applications, like schema evolution in object-oriented databases, it becomes necessary to manage the history of data structures that have the form of forests or even graphs. The proposed algorithms use minimal space (proportional to the number of changes occurring in the evolution) and have the advantage of being on-line (in the amortized sense). Any past system state s(t) is reconstructed in time O. >

Winnebago Accent and Dorsey's Law

Abstract: Parallelism is the property of Optimality Theory (Prince and Smolensky 1993, McCarthy and Prince 1993a) which distinguishes it from other constraintbased theories of phonology In Optimality Theory (OT), the candidate set provided by Gen is evaluated in parallel with respect to the constraint hierarchy of a given language This means that best satisfaction with respect to the constraint hierarchy is computed over all the members of the candidate set Furthermore, parallelism significantly contributes to the restrictiveness of OT Derivational models permit a wide array of machinery, eg repair strategies and restructuring algorithms, which effectively negate fair consequences of other phonological rules There is no room, however, for such derivational devices in a theory that directly pairs an input with the optimal output

System and method for parameter-based image synthesis using hierarchical networks

Abstract: Synthesis of novel images from example images is achieved by interpolating among example images based on user selection of parameter values in a hierarchy of networks referred to as parent networks and child networks Child networks describe distinct physical characteristics of the image, such as thickness of eyebrows Parent networks describe more general or abstract characteristics related to the image, such as emotional states expressed by the image

An explicit expression for the Korteweg-de Vries hierarchy

Abstract: Several constructions and an explicit expression for the right-hand side of the KdV hierarchy are presented.

Information classifying system that discovers the hierarchical structure of keywords by comparing link numbers

Abstract: A system classifies the information added with keywords by discovering the hierarchy relation with respect to all of keywords. There is generated a relation composed of a total link number and links to other keywords and information, each for keyword. The total link numbers of two relations with links are compared with each other thereby determining a high level relation having a larger total link number and a low level relation having a lower total link number, and a hierarchy structure can be discovered by making the link from the low level relation to the high level relation ineffective.

Weight hierarchy of a product code

Abstract: Formulas to compute the first members of the weight hierarchy of a product code are given and proved. Basic patterns for the supports of subcodes in which the minimum cardinalities can be found are presented. Hence, formulas for every term of the hierarchy can be given, and the proof for each case will be a generalization of the proofs shown here. >

Continuous limits for the Kac-Van Moerbeke hierarchy and for their restricted flows

Abstract: The continuous limit for the Kac-Van Moerbeke (KvM) hierarchy, for their bi-Hamiltonian formulation, recursion relation and square eigenfunction relation is studied. A new family of integrable symplectic maps (ISM) are reduced from the KvM hierarchy via constraint for a higher flow of the hierarchy in terms of square eigenfunctions. Their integrability is deduced from the discrete zero-curvature representation of the KvM hierarchy. It is shown that these ISMs provide maps which approximate many well known integrable mechanical systems (e.g. Neumann, Garnier) embedded into the KdV hierarchy as their restricted flows.

Image processing apparatus for editing a dynamic image having a first and a second hierarchy classifying and synthesizing plural sets of: frame images displayed in a tree structure

Abstract: Scenes having arbitrary sizes can be collectively edited. Dynamic image data is managed by a tree structure in accordance with scenes. An array of scenes belonging to a higher order hierarchy than a reference hierarchy by one level is displayed in a scene display area, an array of scenes belonging to the reference hierarchy is displayed in a scene display area, and an array of scenes belonging to a given scene and having an order hierarchy lower by one level than the given scene which is designated by an operator and selected from scenes displayed in the reference hierarchy is displayed in a scene display area. An arbitrary scene displayed in the scene display area is designated, and processing (copy, move, divide, and synthesize) for the designated scene is designated. A tree structure portion of the designated scene is modified in accordance with the designated processing.

Hierarchy of negative order equation and its Lax pair

Abstract: A simple method is presented to construct the hierarchy of a negative order equations from a given eigenvalue problem. The hierarchy of the negative order equation we obtained is the natural continuation of a corresponding hierarchy of a higher order equation, although most of the negative order equations are complicated; we give their Lax representations. Three examples are discussed to illustrate the effectiveness of our method.

Structural complexity of ω-automata

Abstract: In this paper we relate expressiveness of ω-automata to their complexity. Expressiveness is related to the different subclasses of the ω-regular languages that are accepted by automata that arise by restrictions on the acceptance conditions used. For example, different subclasses of the ω-regular languages arise from identifying the ω-languages with different classes and levels in the Borel hierarchy. Within the class of ω-regular languages, Wagner and Kaminski identified a strict hierarchy of languages induced by restricting the number of pairs allowed in a deterministic Rabin automaton (DRA).