Selective Sampling Using the Query by Committee Algorithm

We analyze the query by committee algorithm, a method for filtering informative queries from a random stream of inputs. We show that if the two-member committee algorithm achieves information gain with positive lower bound, then the prediction error decreases exponentially with the number of queries. We show that, in particular, this exponential decrease holds for query learning of perceptrons.     

Linear Interval Tolerance Problem and Linear Programming Techniques

In this paper, we consider the linear interval tolerance problem, which consists of finding the largest interval vector included in ([A], [b]) = {x R ⁿ | A [A], b [b], Ax = b}. We describe two different polyhedrons that represent subsets of all possible interval vectors in ([A], [b]), and we provide a new definition of the optimality of an interval vector included in ([A], [b]). Finally, we show how the Simplex algorithm can be applied to find an optimal interval vector in ([A], [b]).     

Query processing with quality control in the World Wide Web

Recent research on integrating database and World Wide Web (WWW) technologies has changed the navigation approach to searching information in the Web. People now can issue queries via a simple query interface or a databaselike query language to retrieve information from semistructured WWW data sources. However, the quality of query processing in the WWW is still low due to many factors such as unpredictable response time, irrelevant results, and outofdate data. Such lowquality query processing is intolerable to either users or service providers. In this paper, we present a qualitycontrolled query processing method in the WWW. Quality parameters that users can specify with their queries are introduced. Distance functions that are used to evaluate the goodness of query quality parameters are defined. A query processing model with quality control is introduced. A quality control protocol in query processing is presented. Qualitycontrolled query scheduling algorithms including admission scheduling, promotion/demotion scheduling and execution scheduling are proposed. Other relevant issues such as query classification, system parameter estimation, and query queue management are also discussed. Query processing with quality control is a promising way to solve the uncertain and lowquality query processing problems in the WWW.     

Search Algorithms for Subdatatype-Based Multimedia Retrieval

Recently, researchers have mainly been interested only in the search for data content that are globally similar to the query and not in the search for inside data items. This paper presents an algorithm, called a generalized virtual node (GVN) algorithm, to search for data items where parts (subdatatype) are similar to the incoming query. We call this subdatatype-based multimedia retrieval. Each multimedia datatype, such as image and audio is represented in this paper as a k-dimensional signal in the spatio-temporal domain. A k-dimensional signal is transformed into characteristic features and these features are stored in a hierarchical multidimensional structure, called the k-tree. Each node on the k-tree contains partial content corresponding to the spatial and/or temporal positions in the data. The k-tree structure allows us to build a unified retrieval model for any types of multimedia data. It also eliminates unnecessary comparisons of cross-media querying. The experimental results of the use of the new GVN algorithm for subaudio and subimage retrievals show that it takes much less retrieval times than other earlier algorithms such as brute-force and the partial-matching algorithm, while the accuracy is acceptable.     

Query answering via cooperative data inference

This paper proposes the use of accessible information (data/knowledge) to infer inaccessible data in a distributed database system. Inference rules are extracted from databases by means of knowledge discovery techniques. These rules can derive inaccessible data due to a site failure or network partition in a distributed system. Such query answering requires combining incomplete and partial information from multiple sources. The derived answer may be exact or approximate. Our inference process involves two phases to reason with reconstructed information. One phase involves using local rules to infer inaccessible data. A second phase involves merging information from different sites. We shall call such reasoning processes cooperative data inference. Since the derived answer may be incomplete, new algebraic tools are developed for supporting operations on incomplete information. A weak criterion called toleration is introduced for evaluating the inferred results. The conditions that assure the correctness of combining partial results, known as sound inference paths, are developed. A solution is presented for terminating an iterative reasoning process on derived data from multiple knowledge sources. The proposed approach has been implemented on a cooperative distributed database testbed, CoBase, at UCLA. The experimental results validate the feasibility of this proposed concept and can significantly improve the availability of distributed knowledge base/database systems.List of notation Mapping - --< Logical implication - = Symbolic equality - ==< Inference path - Satisfaction - Toleration - Undefined (does not exist) - Variable-null (may or may not exist) - ^* Subtuple relationship - ^* s-membership - s-containment - Open subtuple - Open s-membership - Open s-containment - _P Open base - P Program - I Interpretation - DIP Data inference program - t Tuples - R Relations - Ø Empty interpretation - Open s-union - Open s-interpretation - Set of mapping from the set of objects to the set of closed objects - W Set of attributes - _W Set of sound inference paths on the set of attributes W - Set of relational schemas in a DB that satisfy MVD - ⁺ Range closure of W wrt      

Shallow circuits and concise formulae for multiple addition and multiplication

A theory is developed for the construction of carry-save networks with minimal delay, using a given collection of carry-save adders each of which may receive inputs and produce outputs using several different representation standards.The construction of some new carry-save adders is described. Using these carry-save adders optimally, as prescribed by the above theory, we get {, , }-circuits of depth 3.48 log₂ n and {, , }-circuits of depth 4.95 log₂ n for the carry-save addition ofn numbers of arbitrary length. As a consequence we get multiplication circuits of the same depth. These circuits put out two numbers whose sum is the result of the multiplication. If a single output number is required then the depth of the multiplication circuits increases respectively to 4.48 log₂ n and 5.95 log₂ n.We also get {, , }-formulae of sizeO (n ^3.13) and {, }-formulae of sizeO (n ^4.57) for all the output bits of a carry-save addition ofn numbers. As a consequence we get formulae of the same size for the majority function and many other symmetric Boolean functions.     

A New Class of Depth-Size Optimal Parallel Prefix Circuits

Given n values x₁, x₂, ... ,x_n and an associative binary operation o, the prefix problem is to compute x₁ox₂o··· ox_i, 1in. Many combinational circuits for solving the prefix problem, called prefix circuits, have been designed. It has been proved that the size s(D(n)) and the depth d(D(n)) of an n-input prefix circuit D(n) satisfy the inequality d(D(n))+s(D(n))2n–2; thus, a prefix circuit is depth-size optimal if d(D(n))+s(D(n))=2n–2. In this paper, we construct a new depth-size optimal prefix circuit SL(n). In addition, we can build depth-size optimal prefix circuits whose depth can be any integer between d(SL(n)) and n–1. SL(n) has the same maximum fan-out lgn+1 as Snir's SN(n), but the depth of SL(n) is smaller; thus, SL(n) is faster. Compared with another optimal prefix circuit LYD(n), d(LYD(n))+2d(SL(n))d(LYD(n)). However, LYD(n) may have a fan-out of at most 2 lgn–2, and the fan-out of LYD(n) is greater than that of SL(n) for almost all n12. Because an operation node with greater fan-out occupies more chip area and is slower in VLSI implementation, in most cases, SL(n) needs less area and may be faster than LYD(n). Moreover, it is much easier to design SL(n) than LYD(n).     

Logic of Change: Semantics of Object Systems with Active Relations

In traditional approaches to object-oriented programming, objects are active, while relations between them are passive. The activeness of an object reveals itself when the object invokes a method (function) as a reaction to a message from another object (or itself). While this model is suitable for some tasks, like arranging interactions between windows, widgets and the end-user in a typical GUI environment, it's not appropriate for others. Business applications development is one of the examples. In this domain, relations between conceptual objects are at least as important as objects themselves and the more appropriate model for this field would be the one where relations are active while objects are passive. A version of such a model is presented in the paper. The model considers a system as consisting of a set of objects, a code of laws, and a set of connectors, each connector hanging on a group of objects that must obey a certain law. The formal logical semantics of this model is presented as a way of analyzing the set of all possible trajectories of all possible systems. The analysis allows to differentiate valid trajectories from invalid ones. The procedural semantics is presented as a state machine that given an initial state, generates all possible trajectories that can be derived from this state. This generator can be considered as a model of a connectors scheduler that allows various degrees of parallelism, from sequential execution to the maxim possible parallelism. In conclusion, a programming language that could be appropriate for the proposed computer environment is discussed, and the problems of applying the model to the business domain are outlined.     

Invariant Structures of the Subdivision and Their Some Applications

Studies are made of recursive structures used for the solution of classical problems for stones, constructions of invariant subdivisions for polynomials, and also some other applications of the obtained results.     

Separating complexity classes related to bounded alternating ω-branching programs

We develop a theory of communication within branching programs that provides exponential lower bounds on the size of branching programs that are bounded alternating. Our theory is based on the algebraic concept of -branching programs, : , a semiring homomorphism, that generalizes ordinary branching programs, -branching programs [M2] andMOD _p-branching programs [DKMW].Due to certain exponential lower and polynomial upper bounds on the size of bounded alternating -branching programs we are able to separate the corresponding complexity classesN _ba ,co-N _{ba ba} , andMOD _p - _ba ,p prime, from each other, and from that classes corresponding to oblivious linear length-bounded branching programs investigated in the past.     

A correction algorithm for token-passing sequences in mobile communication networks

We present a distributed approximation algorithm for the Traveling Salesman Problem (TSP) in networks that use a broadcast, multiaccess communication channel. The application for which the algorithm was originally designed is maintaining a short token-passing path (which means low scheduling overhead) in radio networks with mobile nodes.The algorithm is adaptive in the sense that it shifts gradually between performing a slight correction of an existing tour and recomputing one from scratch. It can thus be viewed as a generalization, or extension, of conventional TSP algorithms. The proposed algorithm guarantees the same worst-case tour length as the one guaranteed by any conventional from scratch algorithm, yet it is capable of taking advantage of certain node layouts (e.g., geographically clustered nodes) to reduce the cost of computing the path.The correction algorithm is suitable for dynamic graphs with slowly changing edge weights, and for which a Traveling Salesman tour (optimal or approximate) has previously been computed and is deteriorating with time due to the weight changes. The algorithm can be used to refresh the tour whenever it deteriorates beyond a given level, and thus maintain a reasonable average tour length at relatively low computation and communication costs. For a Euclidean graph withn nodes laid out in a bounded area with diameterD, the maximal length of the tour produced by the algorithm is proportional toDn, like the maximal length of an optimal tour in that graph (the two differ by a factor of 2 at the worst case).This work was supported in part by NSF Grant No. ECS-8307186 and in part by ARO Grant No. DAAG29-85-K-0044. Part of this work was done while Y. Gold was with the Department of Electrical Engineering and Computer Science, University of Connecticut, USA. Part of this work was done while S. Moran was with IBM Thomas J. Watson Research Center, Yorktown Heights, NY, USA.     

Approximate syllogisms – on the logic of everyday life

Since Aristotle it is recognised that a valid syllogism cannot have two particular premises. However, that is not how a lay person sees it; at least as long as the premises read many, most etc, instead of a plain some. The lay people are right if one considers that these syllogisms do not have strict but approximate (Zadeh) validity. Typically there are only particular premises available in everyday life and one is dependent on such syllogisms. – Some rules on the usage of particular premises are given below.     

The Relative Entropy of Entanglement of Schmidt Correlated States and Distillation

We show that a mixed state = _mna_mn|mn| can be realized by an ensemble of pure states {p_k, |_k} where . Employing this form, we discuss the relative entropy of entanglement of Schmidt correlated states. Also, we calculate the distillable entanglement of a class of mixed states. PACS: 03.67.-a; 03.65.Bz; 03.65.Ud     

Specification and verification of database dynamics

Summary A framework is proposed for the structured specification and verification of database dynamics. In this framework, the conceptual model of a database is a many sorted first order linear tense theory whose proper axioms specify the update and the triggering behaviour of the database. The use of conceptual modelling approaches for structuring such a theory is analysed. Semantic primitives based on the notions of event and process are adopted for modelling the dynamic aspects. Events are used to model both atomic database operations and communication actions (input/output). Nonatomic operations to be performed on the database (transactions) are modelled by processes in terms of trigger/reaction patterns of behaviour. The correctness of the specification is verified by proving that the desired requirements on the evolution of the database are theorems of the conceptual model. Besides the traditional data integrity constraints, requirements of the form Under condition W, it is guaranteed that the database operation Z will be successfully performed are also considered. Such liveness requirements have been ignored in the database literature, although they are essential to a complete definition of the database dynamics.

Notation

Classical Logic Symbols (Appendix 1) for all (universal quantifier) - exists at least once (existential quantifier) - ¬ no (negation) - implies (implication) - is equivalent to (equivalence) - and (conjunction) - or (disjunction) Tense Logic Symbols (Appendix 1) G always in the future - G ₀ always in the future and now - F sometime in the future - F ₀ sometime in the future or now - H always in the past - H ₀ always in the past and now - P sometime in the past - P ₀ sometime in the past or now - X in the next moment - Y in the previous moment - L always - M sometime Event Specification Symbols (Sects. 3 and 4.1) (x) means immediately after the occurrence of x - (x) means immediately before the occurrence of x - (x) means x is enabled, i.e., x may occur next - { } ({w ₁} x{w ₂}) states that if w ₁ holds before the occurrence of x, then w ₂ will hold after the occurrence of x (change rule) - [ ] ([oa₁, ..., oa_n]x) states that only the object attributes oa₁, ..., oa _n are modifiable by x (scope rule) - {{ }} ({{w}}x) states that if x may occur next, then w holds (enabling rule) Process Specification Symbols (Sects. 5.3 and 5.4) :: for causal rules - for behavioural rules Transition-Pattern Composition Symbols (Sects. 5.2 and 5.3) ; sequential composition - ¦ choice composition - parallel composition - :| guarded alternative composition Location Predicates (Sect. 5.2) (z) means immediately after the occurrence of the last event of z (after) - (z) means immediately before the occurrence of the first event of z (before) - (z) means after the beginning of z and before the end of z (during) - ( z) means before the occurrence of an event of z (at)     

Toward a formal study of jazz chord sequences generated by Steedman’s grammar

This paper shows how to generate jazz chord sequences incrementally using Steedmans grammar by taking advantage of some formal properties. We point out the specific role played by particular chord sequences called cadential sequences. By precompiling them, one could improve the implementation of Steedmans grammar in a real-time improvisation system, and make it more reactive to the inputs of the user.I thank Mark Steedman for his comments on this text.     

The Eigenvalue Problem for the 2D Laplacian in ℋ-Matrix Arithmetic and Application to the Heat and Wave Equation

A class of matrices (-matrices) has recently been introduced by Hackbusch for approximating large and fully populated matrices arising from FEM and BEM applications. These matrices are data-sparse and allow approximate matrix operations of almost linear complexity. In the present paper, we choose a special class of -matrices that provides a good approximation to the inverse of the discrete 2D Laplacian. For these 2D -matrices we study the blockwise recursive schemes for block triangular linear systems of equations and the Cholesky and LDL^T factorization in an approximate arithmetic of almost linear complexity. Using the LDL^T factorization we compute eigenpairs of the discrete 2D Laplacian in -matrix arithmetic by means of a so-called simultaneous iteration for computing invariant subspaces of non-Hermitian matrices due to Stewart. We apply the -matrix techniques to approximate the solutions of the high-frequency 2D wave equation for smooth initial data and the 2D heat equation for arbitrary initial data by spectral decomposition of the discrete 2D Laplacian in, up to logarithmic factors, optimal complexity.     

A short note on simultaneous splitting

We show that for any alphabet there is a setL ^* such that ifC is any infinite co-infinite context-free language over , thenL splitsC (i.e., each ofL C,L , C, and is infinite).Preparation of this paper was supported in part by the National Science Foundation under Grant No. MCS77-11360.     

Quantum Algorithms for Highly Structured Search Problems

We consider the problem of identifying a base k string given an oracle which returns information about the number of correct components in a query, specifically, the Hamming distance between the query and the solution, modulo r = max{2, 6 – k}. Classically this problem requires (nlog _r k) queries. For k {2, 3, 4}, we construct quantum algorithms requiring only a single quantum query. For k > 4, we show that O(k) quantum queries suffice. In both cases the quantum algorithms are optimal. PACS: 03.67.Lx     

Musical chronology by seriation

The statistical process of seriation arranges a set of objects along a one-dimensional line so that the distance between each pair of objects reflects the dissimilarity between them. The process has recently been cast into an algorithm which makes it feasible to seriate a few tens of objects efficiently on a personal computer. This algorithm is now used for establishing a chronology of the Troubadours according to certain melodic features in their works. Other musicological uses for seriation are proposed.David Halperin is a Lecturer in the Department of Musicology, Tel Aviv University, specializing in computer-aided analysis of monophonic music. He has published articles on the Ambrosian chant and on the ancient musical notation from Ugarit. His publications include A Segmentation Algorithm and its Application to Medieval Monophonic Music,Musikometrika, 2 (1990) and Towards Deciphering the Ugaritic Musical Notation,Musikometrika, 4 (1992).This is an expanded version of a paper given at the 15th Congress of the International Musicological Society, Madrid, 1992.     

On Steiner minimal trees withLp distance

LetL _p be the plane with the distanced _p (A ₁ ,A ₂ ) = (¦x ₁ –x ₂¦ ^p + ¦y₁ –y ₂¦^p)^/1p wherex _i andy _i are the cartesian coordinates of the pointA _i . LetP be a finite set of points inL _p . We consider Steiner minimal trees onP. It is proved that, for 1 <p < , each Steiner point is of degree exactly three. Define the Steiner ratio _p to be inf{L _s (P)/L _m (P)¦PL _p } whereL _s (P) andL _m (P) are lengths of the Steiner minimal tree and the minimal spanning tree onP, respectively. Hwang showed ₁ = 2/3. Chung and Graham proved ₂ > 0.842. We prove in this paper that {} = 2/3 and (2/2)_{12 p} 3/2 for anyp.This work was supported in part by the National Science Foundation of China and the President Foundation of Academia Sinica.