Minus Operations Research Articles

A notch-mask and dual-prism system for snapshot spectral imaging

In this paper, we present a notch-mask and dual-prism based system for snapshot spectral imaging. Different from traditional spectrometers that utilize band-pass filters or narrow slits to prevent spectral overlap, losing most of the light emitted from the scene, the main idea of our system is to design a spatial notch mask that only occludes the light of sparsely distributed spectral samplings, and introduce a dual-prism architecture to form a non-dispersive RGB measurement on the detector, resulting in the system’s superiority of high light efficiency and high spatial resolution within the snapshot. Then, we develop a model-based algorithm to reconstruct a high-resolution spectral image from the captured RGB measurement, which is of high tolerance to calibration noise since the spectral information can be directly calculated by a minus operation. Simulated experiments have been conducted to verify the effectiveness of the proposed method, and we also build up a prototype system to further demonstrate the practical application and feasibility of our scheme.

Polar Codes for the Deletion Channel: Weak and Strong Polarization

This paper presents the first proof of polarization for the deletion channel with a constant deletion rate and a regular hidden-Markov input distribution. A key part of this work involves representing the deletion channel using a trellis and describing the plus and minus polar-decoding operations on that trellis. In particular, the plus and minus operations can be seen as combining adjacent trellis stages to yield a new trellis with half as many stages. Using this viewpoint, we prove a weak polarization theorem for standard polar codes on the deletion channel. To achieve strong polarization, we modify this scheme by adding guard bands of repeated zeros between various parts of the codeword. This gives a scheme whose rate approaches the mutual information and whose probability of error decays exponentially in the cube-root of the block length. We conclude by showing that this scheme can achieve capacity on the deletion channel by proving that the capacity of the deletion channel can be achieved by a sequence of regular hidden-Markov input distributions.

A Novel Approach Using Non-Synonymous Materialized Queries for Data Warehousing

Data from multiple sources are loaded into the organization data warehouse for analysis. Since some OLAP queries are quite frequently fired on the warehouse data, their execution time is reduced by storing the queries and results in a relational database, referred as materialized query database (MQDB). If the tables, fields, functions, and criteria of input query and stored query are the same but the query criteria specified in WHERE or HAVING clause do not match, then they are considered non-synonymous to each other. In the present research, the results of non-synonymous queries are generated by reusing the existing stored results after applying UNION or MINUS operations on them. This will reduce the execution time of non-synonymous queries. For superset criteria values of input query, UNION operation is applied, and for subset values, MINUS operation is applied. Incremental result processing of existing stored results, if required, is performed using Data Marts.

Norton Algebras of the Hamming Graphs via Linear Characters


 
 
 The Norton product is defined on each eigenspace of a distance regular graph by the orthogonal projection of the entry-wise product. The resulting algebra, known as the Norton algebra, is a commutative nonassociative algebra that is useful in group theory due to its interesting automorphism group. We provide a formula for the Norton product on each eigenspace of a Hamming graph using linear characters. We construct a large subgroup of automorphisms of the Norton algebra of a Hamming graph and completely describe the automorphism group in some cases. We also show that the Norton product on each eigenspace of a Hamming graph is as nonassociative as possible, except for some special cases in which it is either associative or equally as nonassociative as the so-called double minus operation previously studied by the author, Mickey, and Xu. Our results restrict to the hypercubes and extend to the halved and/or folded cubes, the bilinear forms graphs, and more generally, all Cayley graphs of finite abelian groups.
 
 

Nonassociativity of the Norton Algebras of Some Distance Regular Graphs

A Norton algebra is an eigenspace of a distance regular graph endowed with a commutative nonassociative product called the Norton product, which is defined as the projection of the entrywise product onto this eigenspace. The Norton algebras are useful in finite group theory as they have interesting automorphism groups. We provide a precise quantitative measurement for the nonassociativity of the Norton product on the eigenspace of the second largest eigenvalue of the Johnson graphs, Grassman graphs, Hamming graphs, and dual polar graphs, based on the formulas for this product established in previous work of Levstein, Maldonado and Penazzi. Our result shows that this product is as nonassociative as possible except for two cases, one being the trivial vanishing case while the other having connections with the integer sequence A000975 on OEIS and the so-called double minus operation studied recently by Huang, Mickey, and Xu.

Reducing Query Processing Time for Non-Synonymous Materialized Queries With Differed Criteria

Results of OLAP queries for strategic decision making are generated using warehouse data. For frequent queries, processing overhead increases as same results are generated by traversing through huge volume of warehouse data. Authors suggest saving time for frequent queries by storing them in a relational database referred as MQDB, along with its result and metadata information. Incremental updates for synonymous materialized queries are done using data marts. This article focusses on saving processing time for non-synonymous queries with differed criteria. Criteria is the query condition specified with ‘where' or a ‘having' clause apart from equijoin condition. Defined rules will determine if new results can be derived from existing stored results. If criteria of fired query are a subset of criteria in stored query, results are extracted from existing results using MINUS operation. When criteria are a superset of stored query criteria, new results are appended to existing results using the UNION operation.

Implementation of a square‐root filtering approach in marginalized particle filters for mixed linear/nonlinear state‐space models

SummaryMarginalized particle filter (MPF) takes advantage of both Kalman filter and particle filter frameworks to estimate nonlinear state‐space models with reduced number of calculations in comparison to particle filter. However, due to existence of Kalman filter framework inside MPF, some limitations are introduced in implementation of MPF especially in embedded systems with finite numerical accuracies. In this paper, for the first time, we propose a novel square‐root filtering strategy for MPFs to alleviate these restrictions using modified factorization. Typical square‐root Kalman filters cannot be employed inside MPF due to the presence of minus operations in some equations of MPF. However, our method can be easily implemented inside the MPF structure. The proposed method can be used in any application that employs MPFs to estimate the mixed linear/nonlinear state‐space models. In order to demonstrate its usefulness, we employed the proposed square‐root filtering method inside a marginalized particle extended Kalman filter (MP‐EKF) structure, which was specifically designed for ECG denoising. The experimental results showed that, in the field of ECG denoising, the square‐root MP‐EKF performs more consistently than MP‐EKF in white Gaussian noises.

A double-threshold technique for fast time-correspondence imaging

We present a robust imaging method based on time-correspondence imaging and normalized ghost imaging (GI) that sets two thresholds to select the reference frame exposures for image reconstruction. This double-threshold time-correspondence imaging protocol always gives better quality and signal-to-noise ratio than previous GI schemes, and is insensitive to surrounding noise. Moreover, only simple add and minus operations are required while less data storage space and computing time are consumed; thus, faster imaging speeds are attainable. The protocol offers a general approach applicable to all GI techniques and marks a further step forward towards real-time practical applications of correlation imaging.

Set Reconciliation via Counting Bloom Filters

In this paper, we study the set reconciliation problem, in which each member of a node pair has a set of objects and seeks to deliver its unique objects to the other member. How could each node compute the set difference, however, is challenging in the set reconciliation problem. To address such an issue, we propose a lightweight but efficient method that only requires the pair of nodes to represent objects using a counting Bloom filter (CBF) of size $(O(d))$ and exchange with each other, where $(d)$ denotes the total size of the set differences. A receiving node then subtracts the received CBF from its local one via minus operation proposed in this paper. The resultant CBF can approximately represent the union of the set differences and thus the set difference to each node can be identified after querying the resultant CBF. In this paper, we propose a novel estimator through which each node can accurately estimate not only the value of $(d)$ but also the size of the set difference to each node. Such an estimation result can be used to optimize the parameter setting of the CBF to achieve less false positives and false negatives. Comprehensive analysis and evaluation demonstrates that our method is more efficient than prior BF-based methods in terms of achieving the same accuracy with less communication cost. Moreover, our reconciliating method needs no prior context logs and it is very useful in networking and distributed applications.

The axiomatization of override and update

There are only very few natural ways in which arbitrary functions can be combined. One composition operator is override: for arbitrary functions f and g, f ▷ g is the function with domain dom ( f ) ∪ dom ( g ) that behaves like f on dom ( f ) and like g on dom ( g ) ∖ dom ( f ) . Another operator is update: f [ g ] has the same domain as f, behaves like f on dom ( f ) ∖ dom ( g ) , and like g on dom ( f ) ∩ dom ( g ) . These operators are widely used, especially within computer science, where for instance f [ g ] may denote the new state that results when in state f the updates given as g are applied. It is therefore surprising that thus far no axiomatization of these operators has been proposed in the literature. As an auxiliary operator we consider the minus operator: f − g is the restriction of f to the domain dom ( f ) ∖ dom ( g ) . The update operator can be defined in terms of override and minus. We present five equations that together constitute a sound and complete axiomatization of override and minus. As part of our completeness proof, we infer a large number of useful derived laws using the proof assistant Isabelle. With the help of the SMT solver Yices, we establish independence of the axioms. Thus, our axiomatization is also minimal. Finally, we establish that override and minus are functionally complete in the sense that any operation on general functions that corresponds to a valid coloring of a Venn diagram can be described using just these two operations.

Firewall Policy Queries

Firewalls are crucial elements in network security, and have been widely deployed in most businesses and institutions for securing private networks. The function of a firewall is to examine each incoming and outgoing packet and decide whether to accept or to discard the packet based on its policy. Due to the lack of tools for analyzing firewall policies, most firewalls on the Internet have been plagued with policy errors. A firewall policy error either creates security holes that will allow malicious traffic to sneak into a private network or blocks legitimate traffic and disrupts normal business processes, which in turn could lead to irreparable, if not tragic, consequences. Because a firewall may have a large number of rules and the rules often conflict, understanding and analyzing the function of a firewall has been known to be notoriously difficult. An effective way to assist firewall administrators to understand and analyze the function of their firewalls is by issuing queries. An example of a firewall query is "Which computers in the private network can receive packets from a known malicious host in the outside Internet?rdquo Two problems need to be solved in order to make firewall queries practically useful: how to describe a firewall query and how to process a firewall query. In this paper, we first introduce a simple and effective SQL-like query language, called the Structured Firewall Query Language (SFQL), for describing firewall queries. Second, we give a theorem, called the Firewall Query Theorem, as the foundation for developing firewall query processing algorithms. Third, we present an efficient firewall query processing algorithm, which uses decision diagrams as its core data structure. Fourth, we propose methods for optimizing firewall query results. Finally, we present methods for performing the union, intersect, and minus operations on firewall query results. Our experimental results show that our firewall query processing algorithm is very efficient: it takes less than 10 milliseconds to process a query over a firewall that has up to 10,000 rules.

An alternative semantics for quantified relevant logic

AbstractThe quantified relevant logic RQ is given a new semantics in which a formula ∀xA is true when there is some true proposition that implies all x-instantiations of A. Formulae are modelled as functions from variable-assignments to propositions, where a proposition is a set of worlds in a relevant model structure. A completeness proof is given for a basic quantificational system QR from which RQ is obtained by adding the axiom EC of ‘extensional confinement’: ∀x(A ⋁ B) → (A ⋁ ∀xB), with x not free in A. Validity of EC requires an additional model condition involving the boolean difference of propositions. A QR-model falsifying EC is constructed by forming the disjoint union of two natural arithmetical structures in which negation is interpreted by the minus operation.

NEW APPROACH TO KNOWLEDGE REPRESENTATION FOR ADVANCED MANUFACTURING MODES

A new approach to knowledge representation for advanced manufacturing modes based on knowledge mesh (KM) and agent mesh (AM) is proposed to solve the self-reconfiguration problem of knowledgeable manufacturing systems. First, the definition of KMs is given and the relationships between KMs and AMs are presented. The multiple set and its mapping relationships onto the KM are then defined. The union, intersection and minus operations on the multiple sets of KMs are also defined and their related properties are presented. Physical meanings of properties of operations on the multiple sets are studied. Properties of operations on the multiple sets are compared with those of operations on the classical sets. Then the perfectness of a KM, the cut set between the two KMs, and the multiple cut set on the cut set are defined. On the basis of those above, the relational-database-based realization and the inference engine of KMs are studied. The self-reconfiguration methods based on both KMs and AMs are presented through two examples of self-reconfiguration of knowledgeable manufacturing systems, which verifies the validity of these methods.

A new complicated-knowledge representation approach based on knowledge meshes

This paper presents a new complicated-knowledge representation method for the self-reconfiguration of complex systems such as complex software systems, complex manufacturing systems, and knowledgeable manufacturing systems. Herein, new concepts of a knowledge mesh (KM) and an agent mesh (AM) are proposed along with a new KM-based approach to complicated-knowledge representation. KM is the representation of such complicated macroknowledge as an advanced manufacturing mode, focusing on knowledge about the structure, functions, and information flows of an advanced manufacturing system. The multiple set, KM, and the mapping relationships between both, are then formally defined. The union, intersection, and minus operations on the multiple sets are proposed, and their properties proved. Then, the perfectness of a KM, the redundancy set between the two KMs, and the multiple redundancy set on the redundancy set are defined. Three examples are provided to illustrate the concepts of the KM, multiple set, multiple redundancy set, and logical operations. On the basis of the above, the KM-based inference engine is presented. In logical operations on KMs, each KM is taken as an operand. A new KM obtained by operations on KM multiple sets can be mapped into an AM for automatic reconfiguration of complex software systems. Finally, the combination of two real management modes is exemplified for the effective application of the new KM-based method to the self-reconfiguration of complex systems. It is worth mentioning that KM multiple sets can also be taken as a new formal representation of software systems if their corresponding AMs are the real software systems.

A study on self-reconfiguration of a knowledgeable manufacturing system

This paper deals with a new approach to the self-reconfiguration of the knowledgeable manufacturing system (KMS), which is based on knowledge meshes and agent meshes. To this end, new concepts of a knowledge mesh (K-M) and an agent mesh (A-M) are proposed as well as a new K-M and A-M based approach to knowledge representation for advanced manufacturing modes. A multiple set on the K-M is also formally defined as well as the mapping relationships between the multiple sets and the K-M. The union, intersection and minus operations on the multiple sets and the algorithms of K-M operations are proposed. In addition, preprocessing rules and the mapping between the multiple sets and the new K-M are explored in detail. On the basis of these, the relational database-based realizations of the K-M and its multiple sets are presented. Functional structure and realization of the self-reconfiguration subsystem of KMS are also presented. Finally, the self-reconfiguration method based on the K-M and A-M is exemplified by the self-reconfiguration of the management information system (MIS) software used in a vehicle body plant at Nanjing in China, which shows the method to be very effective.