Elimination Rules Research Articles

A Safe Feature Elimination Rule for L1-Regularized Logistic Regression.

The L1-regularized logistic regression (L1-LR) is popular for classification problems. To accelerate its training speed for high-dimensional data, techniques named safe screening rules have been proposed recently. They can safely delete the inactive features in data so as to greatly reduce the training cost of L1-LR. The screening power of these rules is determined by their corresponding safe regions, which is also the core technique of safe screening rules. In this paper, we introduce a new safe feature elimination rule (SFER) for L1-LR. Compared to existing safe rules, the safe region of SFER is improved in two aspects: (1) a smaller sphere region is constructed by using the strong convexity of dual L1-LR twice; (2) multiple half-spaces, which correspond to the potential active constraints, are added for further contraction. Both improvements can enhance the screening ability of SFER. As for the complexity of SFER, an iterative filtering framework is given by decomposing the safe region into multiple "domes". In this way, SFER admits a closed form solution and the identified features will not be scanned repeatedly. Experiments on ten benchmark data sets demonstrate that SFER gives superior performance than existing methods on training efficiency.

Removing inessential points in [formula omitted]-and [formula omitted]-optimal design

A design point is inessential when it does not contribute to an optimal design, and can therefore be safely discarded from the design space. We derive three inequalities for the detection of such inessential points in c-optimal design: the first two are direct consequences of the equivalence theorem for c-optimality; the third one is derived from a second-order cone programming formulation of c-optimal design. Elimination rules for A-optimal design are obtained as a byproduct. When implemented within an optimization algorithm, each inequality gives a screening test that may provide a substantial acceleration by reducing the size of the problem online. Several examples are presented with a multiplicative algorithm to illustrate the effectiveness of the approach.

Finite Class Bayesian Inference System for Circle and Linear Walking Gait Event Recognition Using Inertial Measurement Units.

Accurate and fast human motion pattern recognition is the key to ensuring lower limb assistive devices' appropriate assistance. The research on human motion pattern recognition of lower limb assistive devices mainly focuses on sagittal gait. The motion pattern such as circular walking (CW) is asymmetric about the sagittal plane of the body. CW is common in daily living. However, the recognition algorithm of CW is rarely reported. Since lower limb assistive devices interact with humans, lacking the capability of recognizing CW is dangerous. Thus, to realize the accurate and fast recognition of CW, this article proposed a finite class Bayesian interference system (FC-BesIS). FC-BesIS is designed to recognize walking activities (linear walking and CW) and gait events (heel contact, load response, mid stance, terminal stance, pre-swing, initial swing, mid swing, and terminal swing). A finite class method which reduces the number of potential classes according to elimination rules before decision-making is introduced. Elimination rules are designed based on likelihood estimation and sensor information. The experiments show that walking activities and gait events can be accurately and fastly recognized by FC-BesIS. The experiments also show that the performance of FC-BesIS in mean recognition accuracy (MRA) and mean decision time (MDT) is improved compared with BesIS. The MRA of walking activities and gait events are 100% and 97.38%, respectively. The MDT of walking activities and gait events are 28.19 ms and 33.94 ms, respectively. Overall, FC-BesIS has been proved to be an accurate and fast recognition algorithm for human motion patterns using wearable sensors.

Recovering non-monotonicity problems of voting rules

A social choice rule (SCR) is monotonic if raising a single alternative in voters’ preferences while leaving the rankings otherwise unchanged is never detrimental to the prospects for winning of the raised alternative. Monotonicity is rather weak but well-known to discriminate against scoring elimination rules, such as plurality with a run off and single transferable vote. We define the minimal monotonic extension of an SCR as its unique monotonic supercorrespondence that is minimal with respect to set inclusion. After showing the existence of the concept, we characterize, for every non-monotonic SCR, the alternatives that its minimal monotonic extension must contain. As minimal monotonic extensions can entail coarse SCRs, we address the possibility of refining them without violating monotonicity provided that this refinement does not diverge from the original SCR more than the divergence prescribed by the minimal monotonic extension itself. We call these refinements monotonic adjustments and identify conditions over SCRs that ensure unique monotonic adjustments that are minimal with respect to set inclusion. As an application of our general findings, we consider plurality with a runoff, characterize its minimal monotonic extension as well as its (unique) minimal monotonic adjustment. Interestingly, this adjustment is not coarser than plurality with a runoff itself, hence we suggest it as a monotonic substitute to plurality with a runoff.

CUT ELIMINATION AND NORMALIZATION FOR GENERALIZED SINGLE AND MULTI-CONCLUSION SEQUENT AND NATURAL DEDUCTION CALCULI

AbstractAny set of truth-functional connectives has sequent calculus rules that can be generated systematically from the truth tables of the connectives. Such a sequent calculus gives rise to a multi-conclusion natural deduction system and to a version of Parigot’s free deduction. The elimination rules are “general,” but can be systematically simplified. Cut-elimination and normalization hold. Restriction to a single formula in the succedent yields intuitionistic versions of these systems. The rules also yield generalized lambda calculi providing proof terms for natural deduction proofs as in the Curry–Howard isomorphism. Addition of an indirect proof rule yields classical single-conclusion versions of these systems. Gentzen’s standard systems arise as special cases.

A Hypersequent Solution to the Inferentialist Problem of Modality

The standard inferentialist approaches to modal logic tend to suffer from not being able to uniquely characterize the modal operators, require that introduction and elimination rules be interdefined, or rely on the introduction of possible-world like indexes into the object language itself. In this paper I introduce a hypersequent calculus that is flexible enough to capture many of the standard modal logics and does not suffer from the above problems. It is therefore an ideal candidate to underwrite an inferentialist theory of meaning for modal operators. Here I treat specifically the modal logics K, D, T, S4, B, and S5. I show that the calculi are adequate for each set of models, and show that they meet a large set of criteria that are generally thought necessary for a calculus to underwrite a theory of meaning.

Application of grey clusters in the development of a Synthetic Model of the goals of Polish family enterprises' successors

PurposeThe knowledge of goals of the successor, who is preparing to take over the business, is extremely important for the succession process and further operation of a family enterprise. The aim of this study is to structure the goals of Polish family enterprises’ successors and to develop a Synthetic Model of the goals of Polish family enterprises' successors with the application of grey clustering evaluation models.Design/methodology/approachResearch into the specifics of the diagnosis and assessment of the goals set for the successors of the first succession in family businesses in Poland was carried out in the third quarter of 2016 at two stages using two research methods: in-depth group interview and individual interview. The main aim of the first stage was the extraction of subjectively identified goals by family enterprises' successors (based on their succession experience). The statements were open and obtained during two in-depth group interviews (2 FGI) with successors being in the process of succession at its various stages (total, n = 14). The respondents presented their experiences connected with the succession process along with emotions that are associated with it. In one of the interview stages, the respondents were asked to enumerate their individual goals they set for themselves in the context of upcoming changes. Next, the group agreed on the most frequently mentioned goals by creating their verbal interpretation. The obtained list of 20 goals was recorded and discussed, and thanks to the application of the elimination rule in the collective decision-making process, that list was reduced to 10 goals, which was approved by all participating successors.FindingsThe results show the developed Synthetic Model of the goals of family enterprises’ successors. The study singled out four groups of successors: (1) successors who do not work in the family enterprise yet, (2) successors holding lower-level positions, (3) successors holding managerial positions, (4) successors who manage the entire company. As a result of the calculations, the developed Synthetic Model of the goals of family enterprises' successors was positively verified for successors working in higher-level positions and successors managing the entire family enterprise.Research limitations/implicationsIn order to use the results of clustering, e.g. for conducting studies on large samples with the use of statistical tools, a reduced number of goals should be taken into account. A thorough study of three goals may bring results similar to the study of the original ten successors of Polish family enterprises in the process of succession. The aim of future research is to develop a mathematical model using optimization functions that enable selection of elements representing individual clusters in such a way that it leads to the extraction of the elements with the highest value in relation to the accepted criterion for assessing their value.Originality/valueIn the future, conducting family business research in accordance with the developed methodology requires a look at the proposed list of successor goals obtained during the Focus Group Interview (FGI) as it could be shortened using the Cluster of Grey Incidence method. Shortening the list of goals has its analytic and practical justifications. The study of the full list of goals in subsequent (and numerous further studies) could lead to errors related to, for example, different interpretation of goals among the investigated successors. Furthermore, the full list of goals would increase costs and extend research time.

Оценка радиационной опасности пребывания населения и ведения хозяйственной деятельности в районе расположения выработанного уранового месторождения

Purpose: To analize radiation situation in the vicinity of mine number one of the Lermontov Production Association “Almaz” in the areas of the public residence and economic activities.
 Material and methods: During the study, methods of pedestrian gamma surveys with a portable spectrometric complex MKS-01A “Multirad-M” and short-term measurements of radon equivalent equilibrium concentration with aerosol alpha radiometer RAA-20P2 “Poisk” were used.
 Results: Along the main roads used by the population for walks and rest, the values of the gamma ambient dose equivalent rate vary within the range between 0.10 and 0.86 μSv/h. Local areas with excess of the remediation criterion (0.6 μSv / h), established by the Sanitary Rules for elimination, conservation and changing functions of facilities for radioactive ore mining and milling (SP LKP-91), are located on the ascent of Beshtau Mountain from the side of the Town of Pyatigorsk (near tunnels and dumps). Along other routes, the remediation criteria are met. External effective doses to the population in a single passage of the routes vary from 1.0 to 1.6 µSv. The highest contribution to the dose from manmade radiation does not exceed 30 %. The highest external doses (4.3 μSv at the contribution of manmade radiation about 70 %) can be realized when resting near the most contaminated parts of the dumps or tunnel mouths. 
 The equivalent equilibrium concentrations of radon progenies in air along the routes did not exceed 60 Bq/m3. The effective internal dose due to inhalation intake of radon and its progenies will not exceed 3 μSv when single passing routes.
 Conclusions: In the main areas of the residence and economic activity of the population in the vicinity of mine number 1 , the radiation situation at some locations does not comply with the requirements of the SP LKP-9, however, it does not pose a threat to public health.

Typal Heterogeneous Equality Types

The usual homogeneous form of equality type in Martin-Löf Type Theory contains identifications between elements of the same type. By contrast, the heterogeneous form of equality contains identifications between elements of possibly different types. This short note introduces a simple set of axioms for such types. The axioms are shown to be equivalent to the combination of systematic elimination rules for both forms of equality, albeit with typal (also known as “propositional”) computation properties, together with Streicher’s Axiom K, or equivalently, the principle of uniqueness of identity proofs.

Development of Indonesian Stemming Algorithms through Modification of Grouping, Sequencing and Removing of Affixes Based on Morphophonemic

Text documents stored on the system in an unstructured form, so that the information inside cannot be extracted directly. To be able to extract it, it takes text processing which is first carried out initial processing (preprocessing text) to convert text documents into more structured by selecting words that used as indexes. The smaller the index value, the more text documents are recognized on the system and the information is more easily extracted. The size of the index determined by the number of groups of words formed. To avoid forming many groups of words, then each word is changed to become a basic word first before grouping. The process of changing of affix word into a basic word using certain rules is called stemming. This research aims to produce a new Indonesian stemming algorithm named UG18 Stemmer algorithm, which can reduce or eliminate stemming errors such as over-stemming and under-stemming on existing stemming algorithms including the Enhanced Confix Stripping (ECS) Stemmer algorithm and the New Enhanced Confix Stripping (NECS) stemming algorithm. The method used is the morphophonemic process approach, which sees affixes as bound morphemes that experience phoneme changes, phoneme addition, and phoneme removal. The three processes are mapped, and Finite State Automata was made to obtain new affixed groups, sequences and new deletion methods that form the basis of the development of the UG18 Stemmer algorithm. This algorithm developed not using a list of decapitation rules used in pre-existing algorithms. Decapitation rules replaced with morphophonemic based elimination rules. Based on the evaluation results and testing of the UG18 Stemmer algorithm, it has a lower error rate compared to the results of stemming using NESC Stemmer. The result can be seen from the randomized test of 2500 word using Relevance Judgment validated by Indonesian language experts, from 1.48% over-stemming and 16.69% under-stemming using the NECS stemmer algorithm down to 0.12% overstemming and 0% understemming using the UG18 algorithm stemmer. Also, the UG18 Stemmer algorithm can improve the speed performance process in the information retrieval-based document similarity measurement application of 45.47% compared to using the ECS stemmer algorithm.

A framework for the Saudi universities governance to achieve competitive advantage in decision making according to the aspirations of Vision 2030

The study aimed at identifying the degree of applying the visual management strategies and the obstacles of applying them in the public universities in Riyadh region in light of the vision of the Kingdom in 2030. In addition, it aimed at identifying the statistical significance differences on the implementation of the visual management strategies from the point of view of department heads according to the variables of gender, Years of service). The researcher followed the descriptive approach. The study community is composed of all department directors at the public universities in Riyadh, specifically King Saud University, Princess Norah Bint Abdul Rahman University, and Saudi Electronic University. The sample of the study was limited to a randomly selected sample of 137 department heads in the public universities under study. The tool consisted of a two-pronged questionnaire, namely the degree of application of the visual management strategies. It includes three sub-axes (rules of operation, disinfection, and elimination of waste), the second axis: obstacles to the implementation of visual management strategies. The results of the study came out with a number of results, the most important of which were: After the implementation of the business rules strategy, a total average of (3.74 of 5) was achieved with a grade of (large), followed by the clearance strategy with an average of (3.61 of 5) (3.53). The results indicated that there were statistically significant differences between the respondents' responses to the implementation of the visual management strategies of the heads of departments In the universities in question are due to the variables (gender, female favor, In addition to the number of years of experience and for the benefit of their experience 5 years than less. In addition, there were statistically significant differences between the responses of the sample members on the obstacles of visual administration in the heads of departments at King Saud University, Princess Nora University, In the Riyadh region in view of the vision of the Kingdom in 2030 due to the gender variable. And for the benefit of males. There were no statistically significant differences between the responses of the sample members on the obstacles of visual administration in the heads of departments due to the variable (years of experience, qualification). In the light of the results, a set of recommendations and proposals were presented to activate the implementation of the visual management strategies in the public universities in Riyadh and other Saudi universities in light of the vision of the Kingdom in 2030.

A Binary Quantifier for Definite Descriptions in Intuitionist Negative Free Logic: Natural Deduction and Normalisation

This paper presents a way of formalising definite descriptions with a binary quantifier ℩, where ℩x[F, G] is read as `The F is G'. Introduction and elimination rules for ℩ in a system of intuitionist negative free logic are formulated. Procedures for removing maximal formulas of the form ℩x[F, G] are given, and it is shown that deductions in the system can be brought into normal form.

Duplicate File Detection and Elimination

The problem of detecting and eliminating duplicated file is one of the major problems in the broad area of data cleaning and data quality in system. Many times, the same logical real world entity may have multiple representations in the data warehouse. Duplicate elimination is hard because it is caused by several types of errors like typographical errors, and different representations of the same logical value. The main objective of this research work is to detect exact and inexact duplicates by using duplicate detection and elimination rules. This approach is used to improve the efficiency of the data. The importance of data accuracy and quality has increased with the explosion of data size. In the duplicate elimination step, only one copy of exact duplicated records or file are retained and eliminated other duplicate records or file. The elimination process is very important to produce a cleaned data. Before the elimination process, the similarity threshold values are calculated for all the records which are available in the data set. The similarity threshold values are important for the elimination process.

Multi-parameter safe sample elimination rule for accelerating nonlinear multi-class support vector machines

K-SVCR and Twin-KSVC are two novel algorithms to deal with multi-class problems. They have achieved good performance since they evaluate all training samples into a “1-versus-1-versus-rest” structure. But they are extremely time consuming, so it remains challenging to apply them into large-scale problems directly. Inspired by the sparse solution of SVMs, in this paper, we propose a safe sample elimination rule (SSE) for multi-class classifiers K-SVCR and Twin-KSVC, termed as SSE-K-SVCR and SSE-T-KSVC, to reduce computation time. With our rule, many redundant samples of all classes can be identified and deleted before actually solving the problem, so the scale of dual problems can be reduced a lot. And our methods are safe, i.e., they can derive identical optimal solutions as K-SVCR and Twin-KSVC, respectively. So the testing accuracy keeps unchanged. Besides, the methods can be embedded into grid search method to accelerate the whole training process, and they are effective both for penalty parameter and kernel parameter. Finally, a fast algorithm clipDCD is introduced to reduce the computation time for larger datatset. Experimental results on one artificial dataset and seventeen benchmark datasets demonstrate the effectiveness and safety of our proposed methods.

A logic for best explanations

ABSTRACTEfforts to formalize qualitative accounts of inference to the best explanation (IBE) confront two obstacles: the imprecise nature of such accounts and the unusual logical properties that explanations exhibit, such as contradiction-intolerance and irreflexivity. This paper aims to surmount these challenges by utilising a new, more precise theory that treats explanations as expressions that codify defeasible inferences. To formalise this account, we provide a sequent calculus in which IBE serves as an elimination rule for a connective that exhibits many of the properties associated with the behaviour of the English expression ‘That…best explains why…’. We first construct a calculus that encodes these properties at the level of the turnstile, i.e. as a metalinguistic expression for classes of defeasible consequence relations. We then show how this calculus can be conservatively extended over a language that contains a best-explains-why operator.

A Refined Interpretation of Intuitionistic Logic by Means of Atomic Polymorphism

We study an alternative embedding of IPC into atomic system F whose translation of proofs is based, not on instantiation overflow, but instead on the admissibility of the elimination rules for disjunction and absurdity (where these connectives are defined according to the Russell–Prawitz translation). As compared to the embedding based on instantiation overflow, the alternative embedding works equally well at the levels of provability and preservation of proof identity, but it produces shorter derivations and shorter simulations of reduction sequences. Lambda-terms are employed in the technical development so that the algorithmic content is made explicit, both for the alternative and the original embeddings. The investigation of preservation of proof-reduction steps by the alternative embedding enables the analysis of generation of “administrative” redexes. These are the key, on the one hand, to understand the difference between the two embeddings; on the other hand, to understand whether the final word on the embedding of IPC into atomic system F has been said.

Logical argumentation by dynamic proof systems

In this paper we provide a proof theoretical investigation of logical argumentation, where arguments are represented by sequents, conflicts between arguments are represented by sequent elimination rules, and deductions are made by dynamic proof systems extending standard sequent calculi. The idea is to imitate argumentative movements in which certain claims are introduced or withdrawn in the presence of counter-claims. This is done by a dynamic evaluation of sequences of sequents, in which the latter are considered ‘derived’ or ‘not derived’ according to the content of the sequence. We show that decisive conclusions of such a process correspond to well-accepted consequences of the underlying argumentation framework. The outcome is therefore a general and modular proof-theoretical approach for paraconsistent and non-monotonic reasoning with argumentation systems.

The Harmony of Identity

The standard natural deduction rules for the identity predicate have seemed to some not to be harmonious. Stephen Read has suggested an alternative introduction rule that restores harmony but presupposes second-order logic. Here it will be shown that the standard rules are in fact harmonious. To this end, natural deduction will be enriched with a theory of definitional identity. This leads to a novel conception of canonical derivation, on the basis of which the identity elimination rule can be justified in a proof-theoretical manner.

How to Ekman a Crabbé-Tennant

Developing early results of Prawitz, Tennant proposed a criterion for an expression to count as a paradox in the framework of Gentzen’s natural deduction: paradoxical expressions give rise to non-normalizing derivations. Two distinct kinds of cases, going back to Crabbe and Tennant, show that the criterion overgenerates, that is, there are derivations which are intuitively non-paradoxical but which fail to normalize. Tennant’s proposed solution consists in reformulating natural deduction elimination rules in general (or parallelized) form. Developing intuitions of Ekman we show that the adoption of general rules has the consequence of hiding redundancies within derivations. Once reductions to get rid of the hidden redundancies are devised, it is clear that the adoption of general elimination rules offers no remedy to the overgeneration of the Prawitz–Tennant analysis. In this way, we indirectly provide further support for a solution to one of the two overgeneration cases developed in previous work.

The No-Show Paradox Under a Restricted Domain

The no-show paradox occurs whenever a group of identically-minded voters is better off abstaining than by voting according to its preferences. Moulin’s (J Econ Theory 45:53–64, 1988) result states that if one wants to exclude the possibility of the no-show paradox, one has to resort to procedures that do not necessarily elect the Condorcet winner when one exists. This paper examines ten Condorcet-consistent and six Condorcet-non-consistent procedures in a restricted domain, viz., one where there exists a Condorcet winner who is elected in the original profile and the profile is subsequently modified by removing a group of voters with identical preferences. The question asked is whether the no-show paradox can occur in these settings. It is found that only two of the ten Condorcet-consistent procedures investigated (Maximin and Schwartz’s procedure) are not vulnerable to the no-show paradox, whereas only two of the six non-Condorcet-consistent ranked procedures investigated (Coombs’ and the Negative Plurality Elimination Rule procedures) are vulnerable to this paradox in the restricted domain. In other words, for a no-show paradox to occur when using Condorcet-consistent procedures it is not, in general, necessary that a top Condorcet cycle exists in the original profile, while for this paradox to occur when using (ranked) non-Condorcet-consistent procedures it is, almost always, necessary that the original profile has a top cycle.