Binary Rules Research Articles

Preferences, actions and voting rules

In this paper we address several issues related to collective dichotomous decision-making by means of quaternary voting rules, i.e., when voters may choose between four actions: voting yes, voting no, abstaining and not turning up-which are aggregated by a voting rule into a dichotomous decision: acceptance or rejection of a proposal. In particular we study the links between the actions and preferences of the actors. We show that quaternary rules (unlike binary rules, where only two actions -yes or no- are possible) leave room for “manipulability” (i.e., strategic behaviour). Thus a preference profile does not in general determine an action profile. We also deal with the notions of success and decisiveness and their ex ante assessment for quaternary voting rules, and discuss the role of information and coordination in this context.

Convergence and Smoothness of Nonlinear Lane–Riesenfeld Algorithms in the Functional Setting

We investigate the Lane–Riesenfeld subdivision algorithm for uniform B-splines, when the arithmetic mean in the various steps of the algorithm is replaced by nonlinear, symmetric, binary averaging rules. The averaging rules may be different in different steps of the algorithm. We review the notion of a symmetric binary averaging rule, and we derive some of its relevant properties. We then provide sufficient conditions on the nonlinear binary averaging rules used in the Lane–Riesenfeld algorithm that ensure the convergence of the algorithm to a continuous function. We also show that, when the averaging rules are C 2 with uniformly bounded second derivatives, then the limit is a C 1 function. A canonical family of nonlinear, symmetric averaging rules, the p-averages, is presented, and the Lane–Riesenfeld algorithm with these averages is investigated.

Structural properties of continuous representations of Boolean functions for gene network modelling

This paper recaps and extends a new method for the parameter identification of Boolean models with continuous valued data. The proposed Zhegalkin identification method with constraints allows us to include a priori known qualitative properties of the system formulated as binary rules. One rule is especially investigated, i.e. the canalizing property—because of its relevance in gene network modelling from which an application example is given.

Adaptive index models for marker-based risk stratification

We use the term "index predictor" to denote a score that consists of K binary rules such as "age > 60" or "blood pressure > 120 mm Hg." The index predictor is the sum of these binary scores, yielding a value from 0 to K. Such indices as often used in clinical studies to stratify population risk: They are usually derived from subject area considerations. In this paper, we propose a fast data-driven procedure for automatically constructing such indices for linear, logistic, and Cox regression models. We also extend the procedure to create indices for detecting treatment-marker interactions. The methods are illustrated on a study with protein biomarkers as well as a large microarray gene expression study.

Phase Portrait Analysis for Multiresolution Generalized Gradient Vector Flow

We propose a modification of the generalized gradient vector flow field techniques based on multiresolution analysis and phase portrait techniques. The original image is subjected to mutliresolutional analysis to create a sequence of approximation and detail images. The approximations are converted into an edge map and subsequently into a gradient field subjected to the generalized gradient vector flow transformation. The procedure removes noise and extends large gradients. At every iteration the algorithm obtains a new, improved vector field being filtered using the phase portrait analysis. The phase portrait is applied to a window with a variable size to find possible boundary points and the noise. As opposed to previous phase portrait techniques based on binary rules our method generates a continuous adjustable score. The score is a function of the eigenvalues of the corresponding linearized system of ordinary differential equations. The salient feature of the method is continuity: when the score is high it is likely to be the noisy part of the image, but when the score is low it is likely to be the boundary of the object. The score is used by a filter applied to the original image. In the neighbourhood of the points with a high score the gray level is smoothed whereas at the boundary points the gray level is increased. Next, a new gradient field is generated and the result is incorporated into the iterative gradient vector flow iterations. This approach combined with multiresolutional analysis leads to robust segmentations with an impressive improvement of the accuracy. Our numerical experiments with synthetic and real medical ultrasound images show that the proposed technique outperforms the conventional gradient vector flow method even when the filters and the multiresolution are applied in the same fashion. Finally, we show that the proposed algorithm allows the initial contour to be much farther from the actual boundary than possible with the conventional methods.

In Memoriam: Ralph L. Vanderslice and Gunnar Fant

RALPH L. VANDERSLICE, who contributed to many areas of phonetics, died on 24 August 2008, aged 78, in Portland, Oregon. He was born on 2 January 1930 in South Bend, Indiana. He received his B.A. and his M.Sc. in speech and theatre from Michigan State College (now Michigan State University) in 1951 and 1954, respectively. He subsequently taught at the Universities of Vermont and Hawai'i. He moved to UCLA where, in 1968, he obtained his Ph.D. His dissertation, Synthetic Elocution (http://repositories.cdlib.org/uclaling/wpp/No8/), was an exploration of the character and some of the specifics of the rules that would be necessary to implement the prosodic aspects of synthesized speech produced by a reading machine. Peter Ladefoged was the chair of his dissertation committee and Victoria Fromkin one of the other members. While still a student at UCLA Ralph Vanderslice was an expert witness testifying against the validity of ‘voiceprints’ (the use of spectrographic displays of speech to identify suspects in criminal trials). He was very much a ‘hands-on’ person, skilled in many of the mechanical and electronic arts, one manifestation of this being his invention of the ‘crico-thyrometer’, a device that could track vertical larynx movement in connected speech. He subsequently taught at City University of New York and Yale University. He published many papers on speech prosody, notably ‘Binary suprasegmental features and transformational word-accentuation rules’ (1972, Language, with Peter Ladefoged). His colleagues, including this author, his office-mate in the UCLA Phonetics Lab, remember him for his erudition, wit, and generosity in helping others with everything from providing references to the seventeenth- and eighteenth-century works on phonetics (which he was steeped in) to repairing a shorted circuit in an amplifier. His salutary influence continues.

On the computability of quasi-transitive binary social choice rules in an infinite society and the halting problem

This paper investigates the computability problem of the existence of a vetoer and an oligarchy for quasi-transitive binary social choice rules (Mas-Colell and Sonnenschein in Rev Econ Stud 39:185–192, 1972) in a society with an infinite number of individuals (infinite society) according to the computable calculus (or computable analysis) by Aberth (Computable analysis, McGraw-Hill, New York, 1980; Computable calculus, Academic Press, Dublin, 2001). We will show the following results. The problem whether a quasi-transitive binary social choice rule which satisfies Pareto principle and independence of irrelevant alternatives (IIA) has a vetoer or has no vetoer in an infinite society is a nonsolvable problem, that is, there exists no ideal computer program for a quasi-transitive binary social choice rule which satisfies Pareto principle and IIA that decides whether it has a vetoer or has no vetoer. And it is equivalent to nonsolvability of the halting problem. We also show that if for any quasi-transitive binary social choice rule there exists an oligarchy in an infinite society, whether it is finite or infinite is a nonsolvable problem. A vetoer is an individual such that if he strictly prefers an alternative to another alternative, then the society prefers the former to the latter or is indifferent between them regardless of the preferences of other individuals, and an oligarchy is the minimal set of individuals which has dictatorial power and its each member is a vetoer. It will be shown that an oligarchy is a set of vetoers if it exists.

RISE OF THE CENTRIST: FROM BINARY TO CONTINUOUS OPINION DYNAMICS

We propose a model that extends the binary "united we stand, divided we fall" opinion dynamics of Sznajd-Weron to handle continuous and multi-state discrete opinions on a linear chain. Disagreement dynamics are often ignored in continuous extensions of the binary rules, so we make the most symmetric continuum extension of the binary model that can treat the consequences of agreement (debate) and disagreement (confrontation) within a population of agents. We use the continuum extension as an opportunity to develop rules for persistence of opinion (memory). Rules governing the propagation of centrist views are also examined. Monte Carlo simulations are carried out. We find that both memory effects and the type of centrist significantly modify the variance of average opinions in the large timescale limits of the models. Finally, we describe the limit of applicability for Sznajd-Weron's model of binary opinions as the continuum limit is approached. By comparing Monte Carlo results and long time-step limits, we find that the opinion dynamics of binary models are significantly different to those where agents are permitted more than 3 opinions.

On the computability of binary social choice rules in an infinite society and the halting problem

This paper investigates the computability problem of the Arrow impossibility theorem [K.J. Arrow, Social Choice and Individual Values, second ed., Yale University Press, 1963] of social choice theory in a society with an infinite number of individuals (infinite society) according to the computable calculus (or computable analysis) by Aberth [O. Aberth, Computable Analysis, McGraw-Hill, 1980, O. Aberth, Computable Calculus, Academic Press, 2001]. We will show the following results. The problem whether a transitive binary social choice rule satisfying Pareto principle and independence of irrelevant alternatives (IIA) has a dictator or has no dictator in an infinite society is a nonsolvable problem, that is, there exists no ideal computer program for a transitive binary social choice rule satisfying Pareto principle and IIA that decides whether the binary social choice rule has a dictator or has no dictator. And it is equivalent to nonsolvability of the halting problem. A binary social choice rule is a function from profiles of individual preferences to social preferences, and a dictator is an individual such that if he strictly prefers an alternative to another alternative, then the society must also strictly prefer the former to the latter.

Pareto violations of parliamentary voting systems

It has been known for a long time that many binary voting rules can select a Pareto dominated outcome, that is an outcome such that there exists some other alternative which is preferred by every voter. In this paper, we show that some of these rules can select an outcome Pareto dominated in a much stronger sense. Furthermore, our main results are concerned with the evaluation of the likelihood of Pareto dominated outcomes under four social choice rules commonly used in Parliaments or in committees. Given a set of four alternatives and a set of n individuals, we assume anonymous profiles and using analytical methods we compute the proportion of profiles at which the Pareto criterion is violated. Our results show that one should not be especially worried about the existence of the possibility as such.

Gene Expression From Random Libraries of Yeast Promoters

Genomewide techniques to assay gene expression and transcription factor binding are in widespread use, but are far from providing predictive rules for the function of regulatory DNA. To investigate more intensively the grammar rules for active regulatory sequence, we made libraries from random ligations of a very restricted set of sequences. Working with the yeast Saccharomyces cerevisiae, we developed a novel screen based on the sensitivity of ascospores lacking dityrosine to treatment with lytic enzymes. We tested two separate libraries built by random ligation of a single type of activator site either for a well-characterized sporulation factor, Ndt80, or for a new sporulation-specific regulatory site that we identified and several neutral spacer elements. This selective system achieved up to 1:10(4) enrichment of the artificial sequences that were active during sporulation, allowing a high-throughput analysis of large libraries of synthetic promoters. This is not practical with methods involving direct screening for expression, such as those based on fluorescent reporters. There were very few false positives, since active promoters always passed the screen when retested. The survival rate of our libraries containing roughly equal numbers of spacers and activators was a few percent that of libraries made from activators alone. The sequences of approximately 100 examples of active and inactive promoters could not be distinguished by simple binary rules; instead, the best model for the data was a linear regression fit of a quantitative measure of gene activity to multiple features of the regulatory sequence.

The Unique Intermediate Logic Whose Every Rule is Archetypal

Informally, we can say that an inference rule is archetypal if any other rule can be transformed to it (up to suitable equivalence) via some substitution for the propositional variables. It was shown by L. Humberstone that, in the case of classical propositional logic, every non-degenerate binary rule is archetypal and conjectured that this result holds also for all rules in the full language. In this paper we provide a proof of this conjecture and show that it is the unique intermediate logic with this property.

New Point-of-Care test identifies diabetic ketoacidosis in triage

Study objectives: Diabetic ketoacidosis (DKA) is a common, life-threatening complication of diabetes. Immediate treatment is necessary to avoid rapid clinical deterioration and the need for higher levels of care. Patients presenting with elevated blood glucose levels have become so common in the emergency department (ED) that clinical suspicion of DKA may not be sufficient to discriminate the true metabolic emergency from less serious hyperglycemic conditions. Treatment delays are common because of nonclassic presentation and the need for laboratory test results to make the diagnosis of DKA. The diagnosis of DKA relies on signs and symptoms plus laboratory findings of blood glucose level greater than 250 mg/dL, an anion gap greater than 15 mmol/L, and carbon dioxide (CO 2 ) level less than 20 mmol/L, excluding other, less common causes of anion gap acidosis. We compared the results of a point-of-care test for the ketone β-hydroxybutyrate (β-OHB) with standard measures for accuracy in predicting the diagnosis of DKA. Methods: After providing informed consent, 101 patients who presented with blood glucose greater than 250 mg/dL or clinical signs of DKA underwent testing for β-OHB at Barnes-Jewish Hospital ED triage using the Precision Xtra meter (Abbott Laboratories, North Chicago, IL). Additional diagnostic evaluation followed clinical guidelines but included a measured glucose and electrolyte panel in all cases. The diagnosis of DKA was made by experienced clinicians using standard clinical criteria. Logistic regression was used to identify clinical indicators of DKA, and χ 2 analysis was used to evaluate binary decision rules. Results: Demographics of the study group include mean age 46.4±16.3 years (range 20 to 83 years); 45.1% female patients; 83.3% black patients, and 16.6% white patients (including 1 Asian and 1 Hispanic patient). The mean blood glucose level was 511±265 mg/dL (range 76 to 1,340 mg/dL); creatinine level 1.76±1.56 mg/dL (range 0.5 to 9.8 mg/dL); and anion gap level 15.7±8.7 mmol/L. A clinical diagnosis of DKA was made in 37 patients. Values of β-OHB ranged between 0 and 6 mmol/L (mean 1.86±2.12 mmol/L). The β-OHB values correlated with anion gap (0.614 mmol/L, P 2 (–0.603 mmol/L, P P 1.5 mmol/L, patient at high risk for DKA; β-OHB from 0.6 to 1.5 mmol/L with blood glucose >250 mg/dL, patient at intermediate risk of DKA). This decision rule was significantly related to DKA status (χ 2 =38.176, P 2 ), implied a complex decision rule with sensitivity of .949 and specificity of .919. Additional logistic regression analysis, using only information available at triage (β-OHB and BG), showed that blood glucose level added little to classification of patients. Therefore, an alternate decision rule using only β-OHB was tested, in which β-OHB greater than 1.1 mmol/L was used as an indicator of DKA status. This decision rule left diagnostic sensitivity at .949, reduced specificity to .806, and provided an overall correct classification rate of .861 (χ 2 =54.66, P Conclusion: The point-of-care test for β-OHB was as sensitive as more established clinical indicators of DKA and offers immediate preliminary diagnosis of patients so that timely, critical interventions can be initiated.

Automatic Generation of Composite Labels Using Part-of-Speech Tags for Parsing Korean

We propose a format of a binary phrase structure grammar with composite labels. The grammar adopts binary rules so that the dependency between two sub-trees can be represented in the label of the tree. The label of a tree is composed of two attributes, each of which is extracted from each sub-tree, so that it can represent the compositional information of the tree. The composite label is generated from part-of-speech tags using an automatic labeling algorithm. Since the proposed rule description scheme is binary and uses only part-of-speech information, it can readily be used in dependency grammar and be applied to other languages as well. In the best-1 context-free cross validation on 31,080 tree-tagged corpus, the labeled precision is 79.30%, which outperforms phrase structure grammar and dependency grammar by 5% and by 4%, respectively. It shows that the proposed rule description scheme is effective for parsing Korean.

Binary rule generation via Hamming Clustering

The generation of a set of rules underlying a classification problem is performed by applying a new algorithm called Hamming Clustering (HC). It reconstructs the AND-OR expression associated with any Boolean function from a training set of samples. The basic kernel of the method is the generation of clusters of input patterns that belong to the same class and are close to each other according to the Hamming distance. Inputs which do not influence the final output are identified, thus automatically reducing the complexity of the final set of rules. The performance of HC has been evaluated through a variety of artificial and real-world benchmarks. In particular, its application in the diagnosis of breast cancer has led to the derivation of a reduced set of rules solving the associated classification problem.

Rapid assessment of the quality of services in Rubella immunization provide d through the primary health care service network in the Polonnaruwa district

Objective: To assess the quality of services in munization provided through Primary Health Care clinics at the divisional level using the Lot Quality Assurance Sampling method. Methodology: A non-participant observation was carried out at 20 randomly selected clinics using Lot Quality Assurance Sampling (LQAS) method with a threshold level of a triage system of 80 and 50% The-defective elements (clinics) needed to reject the lot and make improvements was six. Taking into account that not only rubella immunization is provided in a clinic, ten deliveries of rubella immunization in a clinic were studied with a triage system of95 %, 75% (provider risk 1%, Consumer risk 23%), These repetitive activities were judged by LQAS10:3 binary rules. The study instrument was a pre-tested, structured observational checklist that comprised essential activities of vaccination referred to as sub-systems. Results: In the subsystem “sterility”, the hand washing procedure proved to be defective. The maintenance of sterilization chart was found to be poor. Cold chain maintenance was extremely good and none of the related activities was found to be defective. The screening of eligible clients was poor. A tegister of eligible women for rubella immunization was not maintained in any of clinics supervised. The register of immunization was completed after vaccination. In none of clinics were immunized clients totalled and categorized according to age groups at the end of sessions leading to inability to detect any unrecorded vaccinated client by comparing the number of vaccinations with the dosages of vaccines used and to calculate the vaccine wastage. Conclusion: Apart from the defective activities already mentioned, overall quality of services was satisfactory in majority of essential activities Recommendations: It is essential to carry out regular supervisions to detect and modify substandard items by supervisory staff. Steps should be taken to improve documentation during and at the end of the clinic session.

Discovery of an Iron K Absorption Line in the Low-Mass X-Ray Binary GX 13+1

We report the discovery of an iron K absorption-line feature with ASCA in the spectra of the low-mass X-ray binary GX 13+1. The absorption line is detected at 7.0 keV with an equivalent width of 35 ± 8 eV, which is attributed to resonant scattering of the Kα line from Fe XXVI ions in the line of sight whose column density is larger than ~1018 cm-2. The detection of such a spectral feature from a neutron star binary rules out the hypothesis that it is unique to the Galactic superluminal jet sources. From the similarity of the line parameters to those of the superluminal sources, we infer that we view the X-ray emission through a highly ionized plasma in outer parts of the accretion disk with a relatively high inclination angle. This picture is consistent with the universal presence of such plasmas in X-ray binaries accreting through disks.

On-line learning in the Ising perceptron

On-line learning of both binary and continuous rules in an Ising space is studied. Learning is achieved by using an artificial parameter, a weight vector , which is constrained to the surface of a hypersphere (spherical constraint). In the case of a binary rule the generalization error decays to zero super-exponentially as exp (-Cα2), where α is the number of examples divided by N, the size of the input vector, and C>0. Much faster learning is obtained in the case of continuous activation functions where the generalization error decays as exp (-e|λ|α). The number of steps required for perfect learning is estimated for both scenarios and compared with simulations.

Internal Consistency and Concurrent Validity of Two Short Forms of the Visual Form Discrimination Test

The purpose of this study was to evaluate the reliability and concurrent validity of 2 short forms of the Visual Form Discrimination Test, referred to as first half (FH) and front-back (FB). Participants were a mixed sample of 225 patients seen for neuropsychological evaluations. The mean difference score between both short forms and the full form was less than 1 point. The short-total correlations were .85 and .86 for the FH and FB forms, respectively. A binary clinical decision rule, used to classify patients as normal or impaired, resulted in a 93.3% correct and a 94.7% correct classification rate for the FH and FB forms, respectively. It is concluded that the short form of the test, used in conjunction with a clinical decision rule, results in a very minor loss of accuracy.

Large scale characterization of intertidal communities using a predictive model

Abstract This research presents a methodology that combines shoreline morphology, temperature, salinity, and current (tidal stream velocity) data with biological field sampling to develop kilometer scale intertidal biotopes in the southern Strait of Georgia, British Columbia, Canada. The abiotic component of the classification was based on a geomorphological shoreline classification acquired from low level aerial video, fetch (wave exposure) estimates, as well as salinity, temperature, and current velocity predicted from a hydrodynamic model. The biotic component of the classification was based on in situ field sampling of 39 sites using a published sampling methodology. The inter-relationships between community and habitat were first explored using the two-way indicator species analysis (Twinspan) to define communities and functional groups, and then with regression tree models to determine what combinations of abiotic variables were necessary to support the communities identified by Twinspan. This methodology is predictive, and can be used to quantitatively model the occurrence of biological communities based on abiotic data. The classification presented here is composed of two parts. The first part clustered site by species data collected at 39 sites in the study area using Twinspan. Seven community types were identified by Twinspan. Using an exploratory technique termed tree-based regression, these community types were used as response variables, while abiotic data were used as predictors. The regression tree model predicted seven intertidal biotopes with an accuracy of 72%. Binary decision tree rules produced from the model were used to attach biotopes to the remainder of the 1486 km of shoreline in the study area. Results indicate that this methodology is an effective technique for assessing the broad scale biological composition of large areas of shoreline. This method will be used to assist in the identification of representative, distinct, and rare communities at scales consistent with the identification of conservation importance for site protection and management. It is expected that this methodology will be applied to the remaining 29 000 km of shoreline on Canada’s Pacific coast in the near future.