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We show that the equivalence, unambiguity, and sequentiality problems are decidable for finitely ambiguous max-plus tree automata. A max-plus tree automaton is a weighted tree automaton over the max-plus semiring. A max-plus tree automaton is called finitely ambiguous if the number of accepting runs on every tree is bounded by a global constant and it is called unambiguous if there exists at most one accepting run on every tree. For the equivalence problem, we show that for two finitely ambiguous max-plus tree automata, it is decidable whether both assign the same weight to every tree. For the unambiguity and sequentiality problems, we show that for every finitely ambiguous max-plus tree automaton, both the existence of an equivalent unambiguous automaton and the existence of an equivalent deterministic automaton are decidable. [ABSTRACT FROM AUTHOR]

Weighted tree automata (WTA) extend classical weighted automata (WA) to the non-linear structure of trees. The expressive power of WA with varying degrees of ambiguity has been extensively studied. Unambiguous, finitely ambiguous, and polynomially ambiguous WA over the tropical (as well as the arctic) semiring strictly increase in expressive power. The recently developed pumping results of Mazowiecki and Riveros (STACS 2018) are lifted to trees in order to achieve the same strict hierarchy for WTA over the tropical (as well as the arctic) semiring. [ABSTRACT FROM AUTHOR]

A new version of ambiguity function (AF) associated with the offset linear canonical transform (OLCT) is considered in this paper. This new version of AF coined as the k -AF associated with the OLCT (k -AFOL) is defined based on the OLCT and the fractional instantaneous auto-correlation. A natural magnification effect characterized by the extra degrees of freedom of the OLCT and by a factor k on the frequency axis enables the k -AFOL to have flexibility to be used in cross-term reduction. Firstly, we defined the k -AF associated with the OLCT (k -AFOL), and establish its relationship with the k -Wigner distribution in OLCT domain. Later on, we define the basic properties including the scaling, conjugate-symmetry, shifting, marginal and Moyal's formulae of k -AFOL in depth. The results show that k -AFOL can be viewed as one of the generalizations of the classical AF which has elegance, simplicity and flexibility in the frequency marginal property. The novelty of our paper lies in applications part, where we have shown how the proposed transform is used for the detection of single-component and bi-component linear frequency-modulated (LFM) signals. [ABSTRACT FROM AUTHOR]

Facial expression recognition (FER) plays a vital role in the field of human-computer interaction. To achieve automatic FER, various approaches based on deep learning (DL) have been presented. However, most of them lack for the extraction of discriminative expression semantic information and suffer from the problem of annotation ambiguity. In this paper, we propose an elaborately designed end-to-end recognition network with contrastive learning and uncertainty-guided relabeling, to recognize facial expressions efficiently and accurately, as well as to alleviate the impact of annotation ambiguity. Specifically, a supervised contrastive loss (SCL) is introduced to promote inter-class separability and intra-class compactness, thus helping the network extract fine-grained discriminative expression features. As for the annotation ambiguity problem, we present an uncertainty estimation-based relabeling module (UERM) to estimate the uncertainty of each sample and relabel the unreliable ones. In addition, to deal with the padding erosion problem, we embed an amending representation module (ARM) into the recognition network. Experimental results on three public benchmarks demonstrate that our proposed method facilitates the recognition performance remarkably with 90.91% on RAF-DB, 88.59% on FERPlus and 61.00% on AffectNet, outperforming current state-of-the-art (SOTA) FER methods. Code will be available at http//github.com/xiaohu-run/fer_supCon. [ABSTRACT FROM AUTHOR]

Rule-based classifiers use a collection of high-quality rules to classify new data instances. They can be categorized according to the adopted classification strategy: Classifiers based on a single rule, and classifiers based on multiple rules. Many works were proposed in this field. However, most of them do not handle imperfect data. In this study, we focus on the issue of multi-rules-based classification for evidential data, i.e., data where imperfection is modeled via the belief functions theory. In this respect, we introduce a new algorithm called PWEviRC. This latter involves a two-level pruning technique to remove redundant and noisy rules. Finally, it applies the Dempster rule of combination to fuse the selected rules and make the final decision. To evaluate the proposed method, we carried out extensive experiments on several benchmark data sets. The performance study showed interesting results in comparison to existing methods. [ABSTRACT FROM AUTHOR]

Generally, in every decision-making process under the fuzzy domain, ranking of fuzzy numbers is indispensable. Although such approaches are abundant, yet a universally accepted approach is not apparent. Hence, newer methodologies have been developed since its inception. In many instances, defuzzification techniques are being criticized as these methodologies are based on intuition and the geometry of the fuzzy numbers. Furthermore, in many instances the reasonable properties that a ranking method should follow are not being verified. However, in the current study, a novel defuzzification technique is being developed with the notion of value and multiple of a ambiguity inclusion-exclusion function, , with ambiguity at various decision levels. The current method perfectly obeys the intuition and the geometry of the fuzzy numbers. Adding to this, it should be emphasized that the current methodology follows all the reasonable properties of a ranking method. Furthermore, new properties are stated and proved which illustrate the novelty of the present method. Furthermore, the shortcomings and drawbacks of the existing methods are overcome by the current methodology. Noteworthy, the current method ranks the fuzzy numbers and their corresponding images consistently, which was not evident in most of the existing methods. [ABSTRACT FROM AUTHOR]

We show that, after resolving what was thought to be an ambiguity in the Higgs coupling, the FSM gives, apart from two extra terms (i) and (ii) to be specified below, an effective action in the standard sector which has the same form as the SM action, the two differing only in the values of the mass and mixing parameters of quarks and leptons which the SM takes as Γinputs from experiment while the FSM obtains as a result of a fit with a few parameters. Hence, to the accuracy that these two sets of parameters agree in value, and they do to a good extent as shown in earlier work,1 the FSM should give the same result as the SM in all the circumstances where the latter has been successfully applied, except for the noted modifications due to (i) and (ii). If so, it would be a big step forward for the FSM. The correction terms are: (i) a mixing between the SM's γ − Z with a new vector boson in the hidden sector, (ii) a mixing between the standard Higgs with a new scalar boson also in the hidden sector. And these have been shown a few years back to lead to (i ′ ) an enhancement of the W mass over the SM value,2 and (ii ′ ) effects consistent with the g − 2 and some other anomalies,3 precisely the two deviations from the SM reported by experiments4,5 recently much in the news. [ABSTRACT FROM AUTHOR]

This paper reviews various approaches for localizing submerged acoustic sources under adverse conditions. It is essential to obtain data of the highest possible quality when there are adverse conditions, such as uncertainties in the environment, source motion, and low signal-to-noise ratio. Focalization is an approach in which the source location and environmental parameters are treated as unknowns. Due to a parameter hierarchy in which source location outranks environmental parameters, there may be many realizations of the environment that bring the source into focus; the ambiguity in the environment can be an advantage if the primary objective is to localize the source. Environmental uncertainty is often associated with environmental complexity, which can be an advantage by reducing the ambiguity of the source location. Obtaining a high-quality estimate of the covariance matrix may be difficult when there is source motion, but the complexity of the received field from a moving source is another factor that can reduce ambiguity. It may be possible to localize a source that is buried in noise when an estimate of the noise covariance matrix is available. During the development of approaches for localizing submerged sources, much of the focus has been on one-dimensional vertical arrays. An extension of the multi-valued Bartlett processor to the case of a rectangular array was designed to take advantage of the extra dimension of the array and appears to have the potential to be the most powerful combination of hardware and signal processing to date. [ABSTRACT FROM AUTHOR]

Due to the complexity of the problem in the actual group management decision, the ambiguity of the information of all parties and the uncertainty of the decision environment, it is often difficult for decision-makers to describe the decision information by quantitative methods, but to give uncertain linguistic variables. Based on the analysis of previous research results, this paper proposes a group management decision-making aggregation model based on relative entropy and norm operator. First, the model uses the operation of T -norm and new T -norm operator to make the fuzzy set satisfy the ranking rate and contradiction rate. Then, based on the reliability of relative entropy, the attribute weights of different expert decisions are obtained, and the optimal assembly model of the corresponding group decision is established, respectively. The optimal solution and decision algorithm are given for each optimization model. The last example of the algorithm proves the validity and feasibility of the model, and can effectively avoid the distortion and distortion in the process of group management decision preference aggregation. [ABSTRACT FROM AUTHOR]

The estimation of various components in science always faces with errors and inaccuracies that are presented in the form of an uncertainty in identifying the considered components. This uncertainty can be represented in different shapes, one of which is the representation of estimated components in the form of fuzzy numbers. In a situation where a shortage of information or ambiguity in the studied system can be seen, fuzzy numbers can be used to express the ambiguity available in the components. In this study, we will introduce new approach for the formation of type-2 fuzzy numbers in which the mean and standard deviations of data are used to determine the uncertainty zone. Finally, with proposed type-2 fuzzy numbers, in proportion to any situation we have, we face with the claims related to the mean and assess with the subject of the statistical hypothesis test with fuzzy approach. [ABSTRACT FROM AUTHOR]

In the context of precise measurements in some of the CKM elements and angles of the unitarity triangle coupled with latest theoretical improvements of lattice QCD calculations of "hadronic factors," we have explored the implication of these and unitarity on some of the CKM parameters which are ridden with ambiguities. In particular, we have undertaken a thorough scrutiny of the implications of the precise measurements of the angles of the unitarity triangle along with the element | V u s | , on the | V u b | , | V t d | , | V t s | , as well as the CP violating parameter K . Interestingly, we find a unitarity-based analysis while unambiguously favoring | V u b | exclusive-over-inclusive value which is also in agreement with the present data pertaining to K , | V t d | , | V t s | , Δ M d / Δ M s , etc. The present analysis also shows that the presence of NP in K − K ̄ and B d − B d ¯ systems, if any, would be less than a few percent only. [ABSTRACT FROM AUTHOR]

When specifying user requirements, not only is it critical to ensure correct and unambiguous specification of functional requirements, but also that of Non-Functional Requirements (NFRs). A critical success factor in Requirements Engineering (RE) involves recognizing conflicts among NFRs specified by multiple stakeholders having differing concerns, priorities, and responsibilities. There indeed are numerous attempts made in the literature to resolve the conflicts between two NFRs, with the traditional view of considering the two NFRs different from each other e.g. security conflicting with the availability. In this paper, however, we propose that to introduce fine-grained conflict resolution – by also focusing on those situations where one NFR conflicts with another NFR of the same type. For ease of understanding, we propose to differentiate such conflicts by coining the term intra-conflicts. Thus, we propose fine-grained conflict resolution – by focusing on the notion of resolving conflicts between two NFRs of the same type. Needless to say, non-detection of any conflict between two NFRs – whether the NFRs are of the same type or not – at an early stage of RE, leads to higher costs for changes. The process of conflict resolution is essentially intuitive and hence is iterative. Our proposal hence is motivated by a view that differentiating the inter-conflicts with intra-conflicts, helps one in better focusing on the conflict resolution. We also propose an approach that allows a requirements analyst to semi-automatically identify intra-conflicts among NFRs at an early stage of RE using natural language processing, machine learning, and ontology-based semantic analysis. The controlled experiments, conducted on five publicly available datasets, achieve an average recall, precision, and F-measure of 0.57, 0.77, and 0.65 respectively. [ABSTRACT FROM AUTHOR]

Fractal analysis of time series is an important tool for describing complex systems and solving nonlinear problems based on time series datebases, of which the core is believed that the geometric bodies composed of various parts of the system have self-similarity and scale invariance. Supply chain management uses integrated thinking, from the perspective of system, to design, plan and control the logistics, capital flow, and information flow in the supply chain for minimizing internal consumption, improving competitiveness or welfare levels, and achieving win–win cooperation. Whether or not the supply chain enterprises cooperate is essentially a game between the enterprises; according to the game theory, the profit of an enterprise depends not only on its own behavior, but also on the behavior of another enterprise with which it deals. On basis of summarizing and analyzing of previous research works, this paper expounded the current research status and significance of the game model of supply chain management, elaborated the development background, current status, and future challenges of the fractal analysis of time series, introduced the methods and principles of fractal dimension calculation and replicator dynamic equation, established a game model of supply chain management based on the fractal analysis of time series including scale-free area determination and model optimization solution, and conducted the fractal analysis of the game model of supply chain management and discussed the equilibrium and statistical similarity of this proposed model. The final simulation experiment showed that the game model of supply chain management based on the fractal analysis of time series applied the phase space reconstruction principle to the data sample selection of fractal prediction algorithm in supply chain, which solved the problem of low similarity between data samples taken by fractal prediction objects with fuzzy self-similar characteristics and periodic ambiguity, and improved the prediction accuracy of the fractal prediction algorithm when predicting objects in the game model of supply chain management. [ABSTRACT FROM AUTHOR]

Taking videos as nodes in a graph, graph matching is an effective technique for unsupervised video-based person re-identification (re-ID). However, most of existing methods are sensitive to noisy training data and mainly only focus on visual content relations between query and gallery videos, which may introduce large amount of false positives. To enhance the robustness to training data and alleviate the visual ambiguity, a Dynamic Hybrid Graph Matching (DHGM) method is proposed, which jointly considers both content and context information for person re-ID in an iterative manner. The content relations between video nodes are obtained by metric learning, based on which the context relation is acquired by encoding the bidirectional feature of each probe node relative to its graph neighbors. The model is iteratively updated during the process of graph construction for promoted distance measurement and further better matching performance. Experimental results on the PRID 2011 and iLIDS-VID datasets demonstrate the superiority of the DHGM. [ABSTRACT FROM AUTHOR]

To get a more comprehensive understanding of the amount of branching in computations of a nondeterministic finite automaton (NFA), we introduce and study the string path width and depth path width measures. For a given NFA, the string path width on a string w counts the number of all complete computations on w , and the depth path width on an integer ℓ counts the number of complete computations on all strings of length ℓ. We give an algorithm to decide the finiteness of the depth path width of an NFA. Deciding finiteness of string path width can be reduced to the corresponding question on ambiguity. An NFA is nearly acyclic if any computation can pass through at most one cycle. The class of nearly acyclic NFAs consists of exactly all NFAs with finite depth path width. Using this characterization we show that the finite depth path width of an m -state NFA over a k -letter alphabet is at most (k + 1) m − 1 and that this bound is tight. The nearly acyclic NFAs recognize exactly the class of constant density regular languages. [ABSTRACT FROM AUTHOR]

In this paper we present a new approach to rough set approximations that permits to distinguish between two kinds of "imperfect" knowledge in a joint framework: on one hand, vagueness, due to imprecise knowledge and uncertainty typical of fuzzy sets, and on the other hand, ambiguity, due to granularity of knowledge originating from the coarseness typical of rough sets. The basic idea of our approach is that each concept is represented by an orthopair, that is, a pair of disjoint sets in the universe of knowledge. The first set in the pair contains all the objects that are considered as surely belonging to the concept, while the second set contains all the objects that surely do not belong to the concept. In this context, following some previous research conducted by us on the algebra of rough sets, we propose to define as rough approximation of the orthopair representing the considered concept another orthopair composed of lower approximations of the two sets in the first orthopair. We shall apply this idea to the classical rough set approach based on indiscernibility, as well as to the dominance-based rough set approach. We discuss also a variable precision rough approximation, and a fuzzy rough approximation of the orthopairs. Some didactic examples illustrate the proposed methodology. [ABSTRACT FROM AUTHOR]

This work is a study of the class of non-deterministic automata on infinite trees that are unambiguous i.e. have at most one accepting run on every tree. The motivating question asks if the fact that an automaton is unambiguous implies some drop in the descriptive complexity of the language recognised by the automaton. As it turns out, such a drop occurs for the parity index and does not occur for the weak parity index. More precisely, given an unambiguous parity automaton 𝒜 of index (i , 2 j) , we show how to construct an alternating automaton T r a n s f o r m a t i o n (𝒜) which accepts the same language, but is simpler in terms of the acceptance condition. In particular, if 𝒜 is a Büchi automaton (i = 0 , j = 1) then T r a n s f o r m a t i o n (𝒜) is a weak alternating automaton. In general, T r a n s f o r m a t i o n (𝒜) belongs to the class comp (i + 1 , 2 j) , what implies that it is simultaneously of alternating index (i , 2 j) and of the dual index (i + 1 , 2 j + 1). The transformation algorithm is based on a separation procedure of Arnold and Santocanale (2005). In the case of non-deterministic automata with the weak parity condition, we provide a separation procedure analogous to the one used above. However, as illustrated by examples, this separation procedure cannot be used to prove a complexity drop in the weak case, as there is no such drop. [ABSTRACT FROM AUTHOR]

After reviewing Gribov ambiguity of non-Abelian gauge theories, a phenomenon related to the topology of the bundle of gauge connections, we show that there is a similar feature for noncommutative QED over Moyal space, despite the structure group being Abelian, and we exhibit an infinite number of solutions for the equation of Gribov copies. This is a genuine effect of noncommutative geometry which disappears when the noncommutative parameter vanishes. [ABSTRACT FROM AUTHOR]

We introduce an extension of the restricted shuffle operator on binary words considered by Atanasiu and Teh (2016). We then derive properties on Parikh matrix equivalence of words over a binary alphabet based on this extended shuffle operator and a weak-ratio property of words. We also examine the recently introduced concept of core Parikh matrix equivalence of binary words in the context of the restricted shuffle operator. [ABSTRACT FROM AUTHOR]

This paper proposes a rumor spreading model that considers three main factors: the event importance, event ambiguity, and the publics critical sense, each of which are defined by decision makers using linguistic descriptions and then transformed into triangular fuzzy numbers. To calculate the resultant force of these three factors, the transmission capacity and a new parameter category with fuzzy variables are determined. A rumor spreading model is then proposed which has fuzzy parameters rather than the fixed parameters in traditional models. As the proposed model considers the comprehensive factors affecting rumors from three aspects rather than examining special factors from a particular aspect. The proposed rumor spreading model is tested using different parameters for several different conditions on BA networks and three special cases are simulated. The simulation results for all three cases suggested that events of low importance, those that are only clarifying facts, and those that are strongly critical do not result in rumors. Therefore, the model assessment results were proven to be in agreement with reality. Parameters for the model were then determined and applied to an analysis of the 7.23 Yong-Wen line major transportation accident (YWMTA). When the simulated data were compared with the real data from this accident, the results demonstrated that the interval for the rumor spreading key point in the model was accurate, and that the key point for the YWMTA rumor spread fell into the range estimated by the model. [ABSTRACT FROM AUTHOR]

Regular expressions are often ambiguous. We present a novel method based on Brzozowski's derivatives to aid the user in diagnosing ambiguous regular expressions. We introduce a derivative-based finite state transducer to generate parse trees and minimal counter-examples. The transducer can be easily customized to either follow the POSIX or Greedy disambiguation policy and based on a finite set of examples it is possible to examine if there are any differences between POSIX and Greedy. [ABSTRACT FROM AUTHOR]

We continue our research and extend the class of finite BRST-anti-BRST transformations with odd-valued parameters , , introduced in these works. In doing so, we evaluate the Jacobians induced by finite BRST-anti-BRST transformations linear in functionally-dependent parameters, as well as those induced by finite BRST-anti-BRST transformations with arbitrary functional parameters. The calculations cover the cases of gauge theories with a closed algebra, dynamical systems with first-class constraints, and general gauge theories. The resulting Jacobians in the case of linearized transformations are different from those in the case of polynomial dependence on the parameters. Finite BRST-anti-BRST transformations with arbitrary parameters induce an extra contribution to the quantum action, which cannot be absorbed into a change of the gauge. These transformations include an extended case of functionally-dependent parameters that implies a modified compensation equation, which admits nontrivial solutions leading to a Jacobian equal to unity. Finite BRST-anti-BRST transformations with functionally-dependent parameters are applied to the Standard Model, and an explicit form of functionally-dependent parameters is obtained, providing the equivalence of path integrals in any 3-parameter -like gauges. The Gribov-Zwanziger theory is extended to the case of the Standard Model, and a form of the Gribov horizon functional is suggested in the Landau gauge, as well as in -like gauges, in a gauge-independent way using field-dependent BRST-anti-BRST transformations, and in -like gauges using transverse-like non-Abelian gauge fields. [ABSTRACT FROM AUTHOR]

We perform a comprehensive study of the ability of the Deep Underground Neutrino Experiment (DUNE) to answer outstanding questions in the neutrino sector. We consider the sensitivities to the mass hierarchy, the octant of and to CP violation using data from beam and atmospheric neutrinos. We evaluate the dependencies on the precision with which will be measured by reactor experiments, on the detector size, beam power and exposure time, on detector magnetization, and on the systematic uncertainties achievable with and without a near detector. We find that a 35 kt far detector in DUNE with a near detector will resolve the eightfold degeneracy that is intrinsic to long baseline experiments and will meet the primary goals of oscillation physics that it is designed for. [ABSTRACT FROM AUTHOR]

This paper deals with one-way and two-way weighted automata. When the semiring of weights is commutative, we prove that unambiguous one-way automata, unambiguous two-way automata and deterministic two-way automata realize the same (rational) power series. If the semiring of weights is not commutative, unambiguous one-way automata and deterministic two-way automata realize the same rational power series, but unambiguous two-way automata may realize non rational power series. [ABSTRACT FROM AUTHOR]

We prove new decidability and undecidability results concerning the finite-ambiguity problem in acceptors, and the finite-valuedness and lossiness problems in transducers. The acceptors and transducers we study have infinite memory. [ABSTRACT FROM AUTHOR]

Cross-lingual document clustering is the task of automatically organizing a large collection of multi-lingual documents into a few clusters, depending on their content or topic. It is well known that language barrier and translation ambiguity are two challenging issues for cross-lingual document representation. To this end, we propose to represent cross-lingual documents through statistical word senses, which are automatically discovered from a parallel corpus through a novel cross-lingual word sense induction model and a sense clustering method. In particular, the former consists in a sense-based vector space model and the latter leverages on a sense-based latent Dirichlet allocation. Evaluation on the benchmarking datasets shows that the proposed models outperform two state-of-the-art methods for cross-lingual document clustering. [ABSTRACT FROM AUTHOR]

In this paper, a new rumor spreading model which quantifies a specific rumor spreading feature is proposed. The specific feature focused on is the important role the event ambiguity plays in the rumor spreading process. To study the impact of this event ambiguity on the spread of rumors, the probability p(t) that an individual becomes a rumor spreader from an initially unaware person at time t is built. p(t) reflects the extent of event ambiguity, and a parameter c of p(t) is used to measure the speed at which the event moves from ambiguity to confirmation. At the same time, a principle is given to decide on the correct value for parameter c A rumor spreading model is then developed with this function added as a parameter to the traditional model. Then, several rumor spreading model simulations are conducted with different values for c on both regular networks and ER random networks. The simulation results indicate that a rumor spreads faster and more broadly when c is smaller. This shows that if events are ambiguous over a longer time, rumor spreading appears to be more effective, and is influenced more significantly by parameter c in a random network than in a regular network. We then determine parameters of this model through data fitting of the missing Malaysian plane, and apply this model to an analysis of the missing Malaysian plane. The simulation results demonstrate that the most critical time for authorities to control rumor spreading is in the early stages of a critical event. [ABSTRACT FROM AUTHOR]

The quantization of Yang-Mills theories relies on the gauge-fixing procedure. However, in the non-Abelian case this procedure leads to the well-known Gribov ambiguity. In order to solve the ambiguity a modification of the functional integral formula must be introduced. As a consequence of this, the Green functions get deep modifications in the infrared. We consider, in particular, the (N) case and show that in the pure gauge case the ghost propagator is enhanced, while the gluon propagator is suppressed in this limit, therefore the study of the Gribov ambiguity may shed some light on the mass gap problem and on color confinement. We discuss some recent developments on the subject in the case of a curved background. We argue that the concurrent presence of a spacetime curvature and the Gribov ambiguity may introduce further modifications to the Green functions in the infrared. [ABSTRACT FROM AUTHOR]

The class of languages captured by Constrained Automata (CA) that are unambiguous is shown to possess more closure properties than the provably weaker class captured by deterministic CA. Problems decidable for deterministic CA are nonetheless shown to remain decidable for unambiguous CA, and testing for regularity is added to this set of decidable problems. Unambiguous CA are then shown incomparable with deterministic reversal-bounded machines in terms of expressivity, and a deterministic model equivalent to unambiguous CA is identified. [ABSTRACT FROM AUTHOR]

The concept of possibilistic mean value and variance of fuzzy numbers has been applied to investment decisions by using a nonlinear type of fuzzy numbers called adaptive fuzzy numbers. In this paper, by extending the notion of adaptive fuzzy number, we propose a more flexible methodology. Our aim is to allow decision maker more flexibility in dealing with ambiguity and uncertainty. To illustrate the use of our approach and its ability in dealing with ambiguity and imprecision we analyze, as an application, the fuzzy net present value of future cash flows and give some numerical results. [ABSTRACT FROM AUTHOR]

Parikh matrix mapping or Parikh matrix of a word has been introduced in the literature to count the scattered subwords in the word. Several properties of a Parikh matrix have been extensively investigated. A picture array is a two-dimensional connected digitized rectangular array consisting of a finite number of pixels with each pixel in a cell having a label from a finite alphabet. Here we extend the notion of Parikh matrix of a word to a picture array and associate with it two kinds of Parikh matrices, called row Parikh matrix and column Parikh matrix. Two picture arrays A and B are defined to be Mequivalent if their row Parikh matrices are the same and their column Parikh matrices are the same. This enables to extend the notion of M-ambiguity to a picture array. In the binary and ternary cases, conditions that ensure M-ambiguity are then obtained. [ABSTRACT FROM AUTHOR]

In recent years codes that are not Uniquely Decipherable ( UD) were studied partitioning them in classes that localize the ambiguities of the code. A natural question is how we can extend the notion of maximality to codes that are not UD. In this paper we give an answer to this question. To do this we introduce a partial order in the set of submonoids of a free monoid showing the existence, in this poset, of maximal elements that we call full monoids. Then a set of generators of a full monoid is, by definition, a maximal set. We show how this definition extends, in a natural way, the existing definition concerning UD codes and we find a characteristic property of a monoid generated by a maximal UD code. Finally we generalize some properties of UD codes. [ABSTRACT FROM AUTHOR]

Gene insertion and deletion are the operations that occur commonly in DNA processing and RNA editing. Based on these evolutionary transformations, a computing model has been formulated in formal language theory known as insertion-deletion systems. In this paper, we study about the ambiguity issues of insertion systems. First, we define six levels of ambiguity for insertion systems based on the components used in the derivation such as axiom, contexts and strings. Next, we show that there are inherently i-ambiguous insertion languages which are j-unambiguous for the combinations (i, j) ∈ {(5,0), (5,4), (4,3), (4,2), (3,1),(2,1), (1,0), (0,1)}. Finally, we prove an important result that the ambiguity problem of insertion systems is undecidable. [ABSTRACT FROM AUTHOR]

In this study, we propose to use two corpus-driven linguistic approaches for a sense prediction study. We will concentrate on the character similarity clustering approach and the concept similarity clustering approach to predict the senses of non-assigned words by using corpora and tools, such as the Chinese Gigaword Corpus and HowNet. In this study, we will evaluate sense predictions via the sense divisions of Chinese Wordnet (CWN) and Xiandai Hanyu Cidian ( Xian Han). Using these corpora, we will determine the clusters of our four target words - chi1 "eat", wan2 "play", huan4 "change", and shao1 "burn" - in order to predict all possible senses and then evaluate them. This process will demonstrate the viability of the corpus-based approaches. [ABSTRACT FROM AUTHOR]

We study a coherent version of the entropic risk measure, both in the law-invariant case and in a situation of model ambiguity. In particular, we discuss its behavior under the pooling of independent risks and its connection with a classical and a robust large deviations bound. [ABSTRACT FROM AUTHOR]

We investigate the number of occurrences of a word u as a (scattered) subword of a word w. The notion of a Parikh matrix, recently introduced, is a basic tool in this investigation. In general, several words are associated with a Parikh matrix. The ambiguity can be resolved by associating a unique word called the Lyndon image to each Parikh matrix. In this paper we will investigate properties of Lyndon images and the corresponding questions of ambiguity. We give an exhaustive characterization in the case of a binary alphabet. Our main results in the general case deal with the comparison of unambiguous words and Lyndon images, algorithms for constructing Lyndon images, as well as classes of words with the same Parikh matrix, obtained by circular variance. [ABSTRACT FROM AUTHOR]

Searching for a pattern in an Arabic text raises various problems due to the association of vocalization characters with alphabetical letters of Arabic words. This feature causes a problem for existing searching algorithms. They either fail to find all partial matches of a pattern or they may suffer from performance degradation when they are simply modified to ignore these vocalization characters. This paper presents a new coding schema for Arabic vocalization characters that will facilitate and improve the performance of searching for vocalized and unvocalized patterns in any Arabic text (vocalized or unvocalized). This schema is based on repositioning the vocalization characters at the end of each word. We present in this paper the coding and decoding algorithms needed to support our new coding schema. In addition, we explain the modifications to the Boyer-Moore algorithm that take advantage of our improved coding schema together with the complexity analysis. [ABSTRACT FROM AUTHOR]

In the algebraic study of words and languages it is often convenient to analyze words as numerical quantities. One such now-famous example is the study of words by using their attached Parikh mapping (or vector). However, the Parikh vector abstracts away too much of the structure of the word. Parikh matrices were introduced as a means to obtain more than just the number of occurrences of single letters. When studying properties of words, an important property is that a word is uniquely determined by the number of occurrences of certain predetermined subwords. In the context of Parikh matrices, the problem is translated in finding which words are completely characterized by their associated Parikh matrix. This paper links this problem with that of the print of a word, i.e. the word obtained by considering consecutive occurrences of the same letter as only one letter. We obtain results regarding finiteness and context-freeness of such classes of words. [ABSTRACT FROM AUTHOR]

Restarting automata can be considered as a machine model as well as regulated rewriting systems. We introduce a measure of ambiguity for restarting automata which recognizes a language as a projection of its characteristic language (containing also auxiliary—non-input—symbols) into its input alphabet. Based on this measure we define an ambiguity measure of languages. This measure can be considered as a measure of non-determinism of languages. We show that there is an infinite hierarchy with respect to the degree of ambiguity even inside linear languages and that there are linear languages with a linear ambiguity. [ABSTRACT FROM AUTHOR]

In this paper, the human fingerprint, which is independent of rotation and scaling, is recognized. The multiple classification technique, based on wavelet and fractal analysis, is used. It is shown that systematic incorporation of decision from various classifiers leads to a better decision rather than simply fusing them. Multiple classifiers can serve as a means of enhancing the performance of pattern recognition problems. Multiple classifier system design involves the problem of classifier fusion. This paper deals with multi-classifier systems in which each classifier uses its own representation of the input pattern, based on features collected from multiple sources. The multiple feature sources considered here are multi-fractals, wavelets and fast Fourier transforms coefficients. A clustering algorithm is used to observe the efficacy of the feature sources. The multiple sources were graded according to their effectiveness of providing more non-overlapping clusters for different groups into which the samples are to be separated. This approach first considers the best source for the feature parameters. If this feature classifies the test sample into more than one cluster, then the feature next to the best is summoned to finish up the remaining part of the classification process. The continuation of this process along with the judicious selection of classifiers succeeds in identifying a single cluster for the test sample. The results obtained after the experiments on a set of fingerprint images shows that this novel technique can go a long way in avoiding ambiguity and thus limiting the need for use of soft-computing tools for making decisions. Our method provides a hard, concrete and accurate solution to pattern recognition problems employing multiple classifiers. [ABSTRACT FROM AUTHOR]

We study a fundamental combinatorial problem on morphisms in free semigroups: With regard to any string α over some alphabet we ask for the existence of a morphism σ such that σ(α) is unambiguous, i.e. there is no morphism τ with τ(i) ≠ σ(i) for some symbol i in α and, nevertheless, τ(α) = σ(α). As a consequence of its elementary nature, this question shows a variety of connections to those topics in discrete mathematics which are based on finite strings and morphisms such as pattern languages, equality sets and, thus, the Post Correspondence Problem. Our studies demonstrate that the existence of unambiguous morphic images essentially depends on the structure of α: We introduce a partition of the set of all finite strings into those that are decomposable (referred to as prolix) in a particular manner and those that are indecomposable (called succinct). This partition, that is also known to be of major importance for the research on pattern languages and on finite fixed points of morphisms, allows to formulate our main result according to which a string α can be mapped by an injective morphism onto an unambiguous image if and only if α is succinct. [ABSTRACT FROM AUTHOR]

In this paper, we study the tradeoffs in descriptional complexity of NFA (nondeterministic finite automata) of various amounts of ambiguity. We say that two classes of NFA are separated if one class can be exponentially more succinct in descriptional sizes than the other. New results are given for separating DFA (deterministic finite automata) from UFA (unambiguous finite automata), UFA from MDFA (DFA with multiple initial states) and UFA from FNA (finitely ambiguous NFA). We present a family of regular languages that we conjecture to be a good candidate for separating FNA from LNA (linearly ambiguous NFA). [ABSTRACT FROM AUTHOR]

Translation ambiguity is a major problem in dictionary-based cross-language information retrieval. To attack the problem, indirect disambiguation approaches, which do not explicitly resolve translation ambiguity, rely on query-structuring techniques such as a structured Boolean model and Pirkola's method. Direct disambiguation approaches try to assign translation probabilities to translation equivalents, normally by employing co-occurrence statistics of target language terms from target documents as disambiguation clues. Thus far, translation probabilities have not been well explored in terms of statistical query translation models, query formulation, or cross-lingual retrieval models, etc. In order to study the impact of translation probabilities on retrieval effectiveness in direct disambiguation approaches, this paper empirically investigates the following issues: different disambiguation factors affecting the calculation of translation probabilities, the comparison of cross-lingual query formulation techniques involving translation probabilities, the relationship between the accuracy of translation disambiguation and retrieval effectiveness, and the relationship between top n translations and retrieval effectiveness. [ABSTRACT FROM AUTHOR]

A comparison method for discrete type-2 fuzzy values is proposed in this paper. The proposed method is based on the concept of the satisfaction function that handles the ambiguity in fuzzy comparisons using the possibility distribution of actual values. Some properties of the proposed comparison method are analyzed as well. [ABSTRACT FROM AUTHOR]

Studying comparison methods for fuzzy sets is an essential task for the good understanding of the underlying theory in this field. Most of these tools deal with fuzzy sets from the view of similarity, order relationships and so forth. In this paper however, based on a former comparison measures introduced by the authors, the so called Coherence Measures, the extension and analysis of these tools to a measurable Lebesgue set X is carried out. Furthermore we present how coherence measures could be linked to the Fishburn-Yager's ambiguity measures. Besides, two methods for constructing coherence measures, one from ambiguity measures and another from metrics on Pf(X), the set of fuzzy sets on X, are shown and exemplified by a variety of measures and metrics. Finally some illustrative examples testing the coherence measures introduced are provided. [ABSTRACT FROM AUTHOR]

We describe a part of the stimulus sentences of a German language processing ERP experiment using a context-free grammar and represent different processing preferences by its unambiguous partitions. The processing is modeled by deterministic pushdown automata. Using a theorem proven by Moore, we map these automata onto discrete time dynamical systems acting at the unit square, where the processing preferences are represented by a control parameter. The actual states of the automata are rectangles lying in the unit square that can be interpreted as cylinder sets in the context of symbolic dynamics theory. We show that applying a wrong processing preference to a certain input string leads to an unwanted invariant set in the parsers dynamics. Then, syntactic reanalysis and repair can be modeled by a switching of the control parameter — in analogy to phase transitions observed in brain dynamics. We argue that ERP components are indicators of these bifurcations and propose an ERP-like measure of the parsing model. [ABSTRACT FROM AUTHOR]

We propose a new prototype Chinese-to-Korean machine translation system called TOTAL-CK, a prototype transfer based MT system designed for the large-scale practical domain. TOTAL-CK consists of the components of analysis, transfer, and generation. In this paper, we mainly discuss the transfer issues resulting from stylistic structural differences between Chinese and Korean. The dependency grammar formalism is employed for Chinese parsed trees and their equivalent Korean parsed trees. We deal with structural transfer ambiguities that arise when a given source language syntactic pattern is potentially translated by a number of different target language syntactic patterns. Also, structural transfer ambiguities are the major complex transfer problem appearing during dependency transferring, in an SVO pattern that most frequently occurs in Chinese sentences. There are three types of structural transfer ambiguity: transitive transfer, subject-governing transfer and verb-governing transfer. They are discovered by analyzing the ambiguity and the related formalism. Finally, we present a thesaurus-based disambiguation approach for dependency structural transfer, which is adopted in TOTAL-CK. Our approach achieves 94.6% in precision for SVO sentences and 93.5% for overall sentences. [ABSTRACT FROM AUTHOR]