We introduce here and investigate the notion of an alternative tree of decomposition. We show (Theorem 5) a general method of finding out all non-alternative trees of the alternative tree determined by a diagram of decomposition.

We report on progress and an unsolved problem in our attempt to obtain a clear rationale for relevance logic via semantic decomposition trees. Suitable decomposition rules, constrained by a natural parity condition, generate a set of directly acceptable formulae that contains all axioms of the well-known system R, is closed under substitution and conjunction, satisfies the letter-sharing condition, but is not closed under detachment. To extend it, a natural recursion is built into the procedure for constructing decomposition (...) trees. The resulting set of acceptable formulae has many attractive features, but it remains an open question whether it continues to satisfy the crucial letter-sharing condition. (shrink)

We propose in this article an indexing and retrieval approach applied on outline shapes. Models of objects are stored in a database using the textual descriptors of their silhouettes. We extract from the textual description a set of efficient similarity measures to index the silhouettes. The extracted features are the geometric quasi-invariants that vary slightly with the small change in the viewpoint. We use a textual description and quasi-invariant features to minimize the storage space and to achieve an efficient indexing (...) process. We also use the quad-tree structure to improve processing time during indexing. Using both geometric features and quad-tree decomposition facilitates recognition and retrieval processes. Our approach is applied on the outline shapes of three-dimensional objects. Experiments conducted on two well-known databases show the efficiency of our method in real-world applications, especially for image indexing and retrieval. (shrink)

C-minimality is a variant of o-minimality in which structures carry, instead of a linear ordering, a ternary relation interpretable in a natural way on set of maximal chains of a tree. This notion is discussed, a cell-decomposition theorem for C-minimal structures is proved, and a notion of dimension is introduced. It is shown that C-minimal fields are precisely valued algebraically closed fields. It is also shown that, if certain specific ‘bad’ functions are not definable, then algebraic closure has (...) the exchange property, and for definable sets dimension coincides with the rank obtained from algebraic closure. (shrink)

The Feferman–Vaught theorem provides a way of evaluating a first order sentence \(\varphi \) on a disjoint union of structures by producing a decomposition of \(\varphi \) into sentences which can be evaluated on the individual structures and the results of these evaluations combined using a propositional formula. This decomposition can in general be non-elementarily larger than \(\varphi \). We introduce a “tree” generalization of the prenex normal form (PNF) for first order sentences, and show that for (...) an input sentence in this form having a fixed number of quantifier alternations, a Feferman–Vaught decomposition can be obtained in time elementary in the size of the sentence. The sentences in the decomposition are also in tree PNF, and further have the same number of quantifier alternations and the same quantifier rank as the input sentence. We extend this result by considering binary operations other than disjoint union, in particular sum-like operations such as join, ordered sum and NLC-sum, that are definable using quantifier-free translation schemes. (shrink)

Let κ be a singular cardinal. Karp's notion of a chain model of size κ is defined to be an ordinary model of size κ along with a decomposition of it into an increasing union of length cf. With a notion of satisfaction and -isomorphism such models give an infinitary logic largely mimicking first order logic. In this paper we associate to this logic a notion of a dynamic EF-game which gauges when two chain models are chain-isomorphic. To this (...) game is associated a tree which is a tree of size κ with no κ-branches -branches). The measure of how non-isomorphic the models are is reflected by a certain order on these trees, called reduction. We study the collection of trees of size κ with no κ-branches under this notion and prove that when cf = ω this collection is rather regular; in particular it has universality number exactly κ+. Such trees are then used to develop a descriptive set theory of the space cf κ. The main result of the paper gives in the case of κ strong limit singular an exact connection between the descriptive set-theoretic complexity of the chain isomorphism orbit of a model, the reduction order on the trees and winning strategies in the corresponding dynamic EF games. In particular we obtain a neat analog of the notion of Scott watershed from the Scott analysis of countable models. (shrink)

Our goal is to articulate a clear rationale for relevance-sensitive propositional logic. The method: truth-trees. Familiar decomposition rules for truth-functional connectives, accompanied by novel ones for the for the arrow, together with a recursive rule, generate a set of ‘acceptable’ formulae that properly contains all theorems of the well-known system R and is closed under substitution, conjunction, and detachment. We conjecture that it satisfies the crucial letter-sharing condition.

We consider actions of completely metrisable groups on simplicial trees in the context of the Bass—Serre theory. Our main result characterises continuity of the amplitude function corresponding to a given action. Under fairly mild conditions on a completely metrisable group G, namely, that the set of elements generating a non-discrete or finite subgroup is somewhere dense, we show that in any decomposition as a free product with amalgamation, G = A * C B, the amalgamated groups A, B and (...) C are open in G. (shrink)

Brain-computer interface multi-modal fusion has the potential to generate multiple commands in a highly reliable manner by alleviating the drawbacks associated with single modality. In the present work, a hybrid EEG-fNIRS BCI system—achieved through a fusion of concurrently recorded electroencephalography and functional near-infrared spectroscopy signals—is used to overcome the limitations of uni-modality and to achieve higher tasks classification. Although the hybrid approach enhances the performance of the system, the improvements are still modest due to the lack of availability of computational (...) approaches to fuse the two modalities. To overcome this, a novel approach is proposed using Multi-resolution singular value decomposition to achieve system- and feature-based fusion. The two approaches based up different features set are compared using the KNN and Tree classifiers. The results obtained through multiple datasets show that the proposed approach can effectively fuse both modalities with improvement in the classification accuracy. (shrink)

Let H n be the linear heptagonal networks with 2 n heptagons. We study the structure properties and the eigenvalues of the linear heptagonal networks. According to the Laplacian polynomial of H n, we utilize the method of decompositions. Thus, the Laplacian spectrum of H n is created by eigenvalues of a pair of matrices: L A and L S of order numbers 5 n + 1 and 4 n + 1 n! / r! n − r!, respectively. On the (...) basis of the roots and coefficients of their characteristic polynomials of L A and L S, we get not only the explicit forms of Kirchhoff index but also the corresponding total number of spanning trees of H n. (shrink)

Words like well, oh, and you know have long been observed and studied in spontaneous speech. With the proliferation of on-line dialogues, such as instant messaging between friends or back-and-forth postings at websites, there are increasing opportunities to observe them in spontaneous writing. In Experiment 1, the interpretation of discourse markers in on-line debates was compared to proposed functions of those markers identified in other settings. In Experiment 2, the use of discourse markers in spontaneous speech was compared to their (...) uses in spontaneous writing. Results support the conclusion that although they vary in frequency in spoken versus written domains, discourse markers are used similarly across domains, but with particular communicative functions that make them non-interchangeable. (shrink)

The discourse marker use of the word like is considered by many to be superfluously sprinkled into talk, a bad habit best avoided. But a comparison of the use of like in successive tellings of stories demonstrates that like can be anticipated in advance and planned into stories. In this way, like is similar to other words and phrases tellers recycle during story telling. The anticipation of like contrasted with the uses of other discourse markers such as oh, you know, (...) and well, which almost never re-occurred in similar locations across tellings. Um and uh did sometimes re-occur; these uses are contrasted with like. Although discourse markers are generally used on the fly to handle various issues that come up in coordinating talk as it unfolds, like can be used as an integral part of the story -a marked contrast to the prevalent idea that likes are speech tics. (shrink)

We explored the differential impact of auditory information and written contextual information on the recognition of verbal irony in spontaneous speech. Based on relevance theory, we predicted that speakers would provide acoustic disambiguation cues when speaking in situations that lack other sources of information, such as a visual channel. We further predicted that listeners would use this information, in addition to context, when interpreting the utterances. People were presented with spontaneously produced ironic and nonironic utterances from radio talk shows in (...) written or auditory form, with or without written contextual information. When the utterances were read without written contextual information, all utterances were rated as equally ironic. But when they were heard as opposed to read, or when they were presented in irony-biasing contexts, originally ironic utterances were rated as more sarcastic than originally nonironic utterances. This evidence suggests both acoustic and contextual information are used when inferring ironic intent in spontaneous speech, and validates previous manipulations of intonation in studies of irony understanding. (shrink)

To generate empathy in the care of vulnerable older persons requires care providers to reflect critically on their care practices. Ethics education and training must provide them with tools to accomplish such critical reflection. It must also create a pedagogical context in which good care can be taught and cultivated. The care-ethics lab ‘sTimul’ originated in 2008 in Flanders with the stimulation of ethical reflection in care providers and care providers in training as its main goal. Also in 2008, sTimul (...) commenced the organization of empathy sessions as an attempt to achieve this goal by simulation. The empathy session is a practical and fairly straightforward way of working to provoke care providers and care providers in training to engage in ethical reflection. Characteristic of the empathy session in the care-ethics lab is the emphasis on experience as a basis for ethical reflection. (shrink)

Observing others in conversation is a common format for comprehending language, yet little work has been done to understand dialog comprehension. We tested whether overhearers use addressee backchannels as predictive cues for how to integrate information across speaker turns during comprehension of spontaneously produced collaborative narration. In Experiment 1, words that followed specific backchannels were recognized more slowly than words that followed either generic backchannels or pauses. In Experiment 2, we found that when the turn after the backchannel was a (...) continuation of the narrative, specific backchannels prompted the fastest verification of prior information. When the turn after was an elaboration, they prompted the slowest, indicating that overhearers took specific backchannels as cues to integrate preceding talk with subsequent talk. These findings demonstrate that overhearers capitalize on the predictive relationship between backchannels and the development of speakers’ talk, coordinating information across conversational roles. (shrink)

The COVID-19 pandemic has presented a global threat to physical and mental health worldwide. Research has highlighted adverse impacts of COVID-19 on wellbeing but has yet to offer insights as to how wellbeing may be protected. Inspired by developments in wellbeing science and guided by our own theoretical framework, we examined the role of various potentially protective factors in a sample of 138 participants from the United Kingdom. Protective factors included physical activity, tragic optimism, gratitude, social support, and nature connectedness. (...) Initial analysis involved the application of one-sample t-tests, which confirmed that wellbeing in the current sample was significantly lower compared to previous samples. Protective factors were observed to account for up to 50% of variance in wellbeing in a hierarchical linear regression that controlled for a range of sociostructural factors including age, gender, and subjective social status, which impact on wellbeing but lie beyond individual control. Gratitude and tragic optimism emerged as significant contributors to the model. Our results identify key psychological attributes that may be harnessed through various positive psychology strategies to mitigate the adverse impacts of hardship and suffering, consistent with an existential positive psychology of suffering. (shrink)

This article discusses ways to operationalise the concept of culturally appropriate computer-mediated communication, utilising information systems (IS) development methodologies and adopting a postmodern and postcolonial perspective. By way of illustration, it describes progress on the participative development of the Ieramugadu Cultural Information System. This project is designed to develop and evaluate innovative procedures for elicitation, analysis, storage and communication of indigenous cultural heritage information. It is investigating culturally appropriate IS design techniques, multimedia approaches and ways to ensure protection of secret/sacred (...) information. Ethical issues are foregrounded. (shrink)

There has been little previous scholarship regarding the aims, options and impact of ethics education on residential care‐givers. This manuscript details findings from a pragmatic cluster trial evaluating the impact of three different approaches to ethics education. The focus of the article is on one of the interventions, an immersive simulation experience. The simulation experience required residential care‐givers to assume the profile of elderly care‐recipients for a 24‐hr period. The care‐givers were student nurses. The project was reviewed favourably by a (...) university ethics committee, and participants provided informed consent. Data from six postsimulation experience focus groups were analysed thematically and three themes were identified: the experience of vulnerability, dignity in care and the organisation of care. Findings suggest that the immersive simulation experience had a powerful immediate impact as participants described epiphanous insights relating to their care experiences. It is suggested that reflecting on and recording epiphanous events has the potential to sustain ethical care practices. Further research is required to evaluate the impact of different ethics education interventions in different cultural contexts. Exploration is also required regarding the meaning and significance of care epiphanies, those “most delicate and evanescent of moments,” for the sustainability of ethical care. (shrink)

Bilingualism has been identified as a potential cognitive factor linked to delayed onset of dementia as well as boosting executive functions in healthy individuals. However, more recently, this claim has been called into question following several failed replications. It remains unclear whether these contradictory findings reflect how bilingualism is defined between studies, or methodological limitations when measuring the bilingual effect. One key issue is that despite the claims that bilingualism yields general protection to cognitive processes, studies reporting putative bilingual differences (...) are often focused on domain specific experimental paradigms. This study chose a broader approach, by considering the consequences of bilingualism on a wide range of cognitive functions within individuals. We utilised 19 measures of different cognitive functions commonly associated with bilingual effects, to form a “cognitive profile” for 215 non-clinical participants. We recruited Welsh speakers, who as a group of bilinguals were highly homogeneous, as means of isolating the bilingualism criterion. We sought to determine if such analyses would independently classify bilingual/monolingual participant groups based on emergent patterns driven by collected cognitive profiles, such that population differences would emerge. Multiple predictive models were trained to independently recognise the cognitive profiles of bilinguals, older adults and higher education attainment. Despite managing to successfully classify cognitive profiles based on age and education, the model failed to differentiate between bilingual and monolingual cognitive ability at a rate greater than that of chance. Repeated modelling using alternative definitions of bilingualism, and just the older adults, yielded similar results. In all cases then, using our “bottom–up” analytical approach, there was no evidence that bilingualism as a variable indicated differential cognitive performance – as a consequence, we conclude that bilinguals are not cognitively different from their monolingual counterparts, even in older demographics. We suggest that studies that have reported a bilingual advantage could well have confounded other key variables that may be driving reported advantages. We recommend that future research refine the machine learning methods used in this study to further investigate the complex relationship between bilingualism and cognition. (shrink)

It has been recognized that design rationale is necessary for understanding and designing artifacts. In order to capture it, we focus on functional knowledge as design rationale and have developed a functional knowledge modeling tool, named SOFAST, which has been deployed in a few companies. In this paper, we aim to capture the processes related to functional knowledge which are not dealt with by the current SOFAST. We discuss a systematic description and an automatic capture system of two typical processes: (...) modification process of functional decomposition trees in the context of designer's daily jobs, and systematization processes in which functional knowledge grows. For the implementation of the system, we extended SOFAST using an ontology-based Knowledge Management framework. Through demonstration and trial use of the system, SOFAST's users positively evaluated the system's effectiveness and expectable usefulness for their daily work. (shrink)

Information is considered to be the major part of an organization. With the enhancement of technology, the knowledge level is increasing with the passage of time. This increase of information is in volume, velocity, and variety. Extracting meaningful insights is the dire need of an individual from such information and knowledge. Visualization is a key tool and has become one of the most significant platforms for interpreting, extracting, and communicating information. The current study is an endeavour toward data modelling and (...) user knowledge by using a rough set approach for extracting meaningful insights. The technique has used different rough set algorithms such as K-nearest neighbours, decision rules, decomposition tree, and local transfer function classifier for an experimental setup. The approach has found its accuracy for the optimal use of data modelling and user knowledge. The experimental setup of the proposed method is validated by using the dataset available in the UCI web repository. Results of the proposed study show that the model is effective and efficient with an accuracy of 96% for KNN, 87% for decision rules, 91% for decision trees, 85.04% for cross validation architecture, and 94.3% for local transfer function classifier. The validity of the proposed classification algorithms is tested using different performance metrics such as F-score, precision, accuracy, recall, specificity, and misclassification rates. For all these performance metrics, the KNN classifier outperformed, and this high performance shows the applicability of the KNN classifier in the proposed problem. (shrink)

Security has become one of the important factors for any network communication and transmission of data packets. An organization with an optimal security system can lead to a successful business and can earn huge profit on the business they are doing. Different network devices are linked to route, compute, monitor, and communicate various real-time developments. The hackers are trying to attack the network and want to draw the organization’s significant information for its own profits. During the communication, if an intrusion (...) or eavesdropping occurs, it will lead to a severe disfigurement of the whole communication network, and the data will be controlled by wrong malicious users. Identification of attack is a way to identify the security violations and analyze the measures in a computer network. An identification system, which is effective and accurate, can add security to the existing system for secure and smooth communication among end to end nodes and can work efficiently in the identification of attack on data packets. The role of information security is to design and protect the entire data of networks and maintain its confidentiality, integrity, and availability for their right users. Therefore, there is a need for end to end security management, which will ensure the security and privacy of the network and will save the data inside networks from malicious users. As the network devices are growing, so the level of threats is also increasing for these devices. The proposed research is an endeavor toward the detection of data packets attack by using the rough set theory for a secure end to end communication. The experimental work was performed by the RSES tool. The accuracy of the K-NN was 88% for the total objects of 8459. For cross validation purposes, the decision rules and decomposition tree algorithms were used. The DR algorithm showed accuracy of 59.1%, while the DT showed accuracy of 61.5%. The experimental results of the proposed study show that the research is capable of detecting data packets attack. (shrink)

We work in the context of ω-stable theories. We obtain a natural, algebraic equivalent of ENI-NDOP and discuss recent joint proofs with Shelah that if an ω-stable theory has either ENI-DOP or is ENI-NDOP and is ENI-deep, then the set of models of T with universe ω is Borel complete.

We study tree-like decompositions of models of a theory and a related complexity measure called partition width. We prove a dichotomy concerning partition width and definable pairing functions: either the partition width of models is bounded, or the theory admits definable pairing functions. Our proof rests on structure results concerning indiscernible sequences and finitely satisfiable types for theories without definable pairing functions. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

We argue that C. Darwin and more recently W. Hennig worked at times under the simplifying assumption of an eternal biosphere. So motivated, we explicitly consider the consequences which follow mathematically from this assumption, and the infinite graphs it leads to. This assumption admits certain clusters of organisms which have some ideal theoretical properties of species, shining some light onto the species problem. We prove a dualization of a law of T.A. Knight and C. Darwin, and sketch a decomposition (...) result involving the internodons of D. Kornet, J. Metz and H. Schellinx. A further goal of this paper is to respond to B. Sturmfels’ question, “Can biology lead to new theorems?”. (shrink)

This paper argues for a particular semantic decomposition of morphological definiteness. I propose that the meaning of ‘the’ comprises two distinct compositional operations. The first builds a set of witnesses that satisfy the restricting noun phrase. The second tests this set for uniqueness. The motivation for decomposing the denotation of the definite determiner in this way comes from split-scope intervention effects. The two components—the selection of witnesses on the one hand and the counting of witnesses on the other—may take (...) effect at different points in the composition of a constituent, and this has non-trivial semantic consequences when other operators inside the DP take action in between them. In particular, I analyze well-known examples of mutually recursive definite descriptions like ‘the rabbit in the hat’ as examples of definites whose referent-introducing and referent-testing components are interleaved rather than nested. I further demonstrate that this picture leads to a new theory of relative superlative descriptions like ‘the kid who climbed the highest tree’, which explains the previously mysterious role of the definite determiner in licensing such readings. (shrink)

This paper proposes a synthetic presentation of the proof construction paradigm, which underlies most of the research and development in the so-called “logic programming” area. Two essential aspects of this paradigm are discussed here: true non-determinism and partial information. A new formulation of Focussing, the basic property used to deal with non-determinism in proof construction, is presented. This formulation is then used to introduce a general constraint-based technique capable of dealing with partial information in proof construction. One of the baselines (...) of the paper is to avoid to rely on syntax to describe the key mechanisms of the paradigm. In fact, the bipolar decomposition of formulas captures their main structure, which can then be directly mapped into a sequent system that uses only atoms. This system thus completely “dissolves” the syntax of the formulas and retains only their behavioural content as far as proof construction is concerned. One step further is taken with the so-called “abstract” proofs, which dissolves in a similar way the specific tree-like syntax of the proofs themselves and retains only what is relevant to proof construction. (shrink)

Peter Fitzpatrick’s writings prove once and for all that it is possible for a law professor to write in beautiful English. His work also proves once and for all that the dominating tradition of Anglo-American legal philosophy and of law teaching has been barking up the wrong tree: namely, that the philosopher and professional law teachers can understand justice as nested in empty forms, better known as rules, doctrines, principles, policies, and other standards. The more rigorous our analysis or (...) decomposition of the forms, we have believed, the more closely do we access the identity of laws. Justice has been assumed to be a matter of intellectually accessing such analysed forms. Fitzpatrick’s articles and books embody an implicit critique of the analytic view of law and of justice. My entry point into this critique is his preoccupation with Jacques Derrida’s theory of laws as universals and with Derrida’s theory of justice as an inaccessible immediacy or presence in context-specific or concrete experienced events. Each event is experienced in an official’s decision. Such a decision represents what Derrida, Fitzpatrick, and Hegel call ‘individuality’. -/- Derrida’s theory of law presents a conundrum. Derrida misses the possibility that law may exist by virtue of its content rather than its form. Derrida misses this possibility because, heavily influenced by Kant (in Derrida’s theory of law), Derrida associates law with universals. This is so because Kant (and Derrida) are preoccupied with the identity of what counts as a law (lois) rather than with a law’s legitimacy. A universal cannot exist unless it is legitimate, and it is legitimate, I claim, by virtue of its content. In his association of law with universals, Derrida presupposes that legal knowledge exists with reference to a territorial-like boundary. The forms are represented or signified by signs (signifiers) within a boundary of the ultimate form (the state, the nation, or humanity). This ultimate form as a universal, like the discrete rules or forms, lacks socially contingent content. A boundary separates knowable universals from the unknowable world on the exteriority of the boundary. The unknowable world is constituted by concrete events experienced in context-specific circumstances. In his legal theory Derrida hones in upon the decision as the experienced event. In a decision, one is present or immediate with the event. Derrida considers such immediacy as justice. The immediacy, however, can only be represented as a sign (sometimes called a signifier). The sign, in turn, represents an empty signified or form, according to Derrida. Because the immediacy remains a representation rather than a presentation of the experienced event, laws as universals cannot be just. The rupture between the inaccessible immediacy of a decision on the one hand and the represented empty forms on the other is critical to Derrida’s theory of law. -/- I claim that this rupture permeates Derrida’s writings about law because Derrida possesses a territorial-like sense of legal knowledge. I shall argue to this effect as follows. In the first section I shall explain the importance of Fitzpatrick’s exposure of the vacuity of the foundation of the system or structure of universals. In the second section I shall flesh out two elements of Derrida’s legal theory: law as form and the ipseity or concrete event that the form excludes from law. This takes me to the third section, where I shall elaborate how Derrida’s legal theory presupposes knowledge as territorial. I shall argue in the final section that this very sense of territorial knowledge prevents justice from accessing law and law from accessing justice. I conclude with the hint of a very different sense of law, one that draws from experiential knowledge in contradistinction to territorial knowledge. (shrink)

We generalise the concept of clique width to structures of arbitrary signature and cardinality. We present characterisations of clique width in terms of decompositions of a structure and via interpretations in trees. Several model-theoretic properties of clique width are investigated including VC-dimension and preservation of finite clique width under elementary extensions and compactness.

We show that under the proper forcing axiom the class of all Aronszajn lines behave like [Formula: see text]-scattered orders under the embeddability relation. In particular, we are able to show that the class of better-quasi-order labeled fragmented Aronszajn lines is itself a better-quasi-order. Moreover, we show that every better-quasi-order labeled Aronszajn line can be expressed as a finite sum of labeled types which are algebraically indecomposable. By encoding lines with finite labeled trees, we are also able to deduce a (...) decomposition result, that for every Aronszajn line [Formula: see text] there is an integer [Formula: see text] such that for any finite coloring of [Formula: see text] there is subset [Formula: see text] of [Formula: see text] isomorphic to [Formula: see text] which uses no more than [Formula: see text] colors. (shrink)

This paper studies internal (or intra-)mathematical explanations, namely those proofs of mathematical theorems that seem to explain the theorem they prove. The goal of the paper is a rigorous analysis of these explanations. This will be done in two steps. First, we will show how to move from informal proofs of mathematical theorems to a formal presentation that involves proof trees, together with a decomposition of their elements; secondly we will show that those mathematical proofs that are regarded as (...) having explanatory power all display an increase of conceptual complexity from the assumptions to the conclusion. (shrink)

The main results in the paper are the following. Theorem A. Suppose that T is superstable and M ⊂ N are distinct models of T eq . Then there is a c ϵ N⧹M such that t is regular. For M ⊂ N two models we say that M ⊂ na N if for all a ϵ M and θ such that θ ≠ θ , there is a b ∈ θ ⧹ acl . Theorem B Suppose that T is (...) superstable , M ⊂ na N are models of T eq , and p is a regular type non-orthogonal to t . Then there is a c ϵ N such that t is regular and non-orthogonal to p. Furthermore, there is a formula θ ∈ t such that a ∈ θ and t ⊥ ̷ p ⇒ t is regular. We used these results to obtain ‘good’ tree decompositions of models in superstable theories with NDOP. See Definition 5.1 for the undefined terms. Theorem C Suppose that T is superstable with NDOP and M ⊨ T eq . Then every ⊂ na - decomposition inside M extends to a ⊂ na -decomposition of M. Furthermore, if 〈N η , a η : η ∈ I〉 is any ⊂ na -decomposition of M, then M is minimal over ∪N η and for all η ∈ I. M is dominated by ∪N η over N η . Using some stable group theory we show that when Th is superstable with NDOP and 〈 N η : η ∈ I 〉 is a tree decomposition of M, then M is constructible over ∪ n η with respect to a very strong isolation relation. (shrink)

Impaired neurodevelopmental outcome, in particular cognitive impairment, after neonatal hypoxic-ischemic encephalopathy is a major concern for parents, clinicians, and society. This study aims to investigate the potential benefits of using advanced quantitative electroencephalography analysis for early prediction of cognitive outcomes, assessed here at 2 years of age. EEG data were recorded within the first week after birth from a cohort of twenty infants with neonatal hypoxic-ischemic encephalopathy. A proposed regression framework was based on two different sets of features, namely graph-theoretical (...) features derived from the weighted phase-lag index and entropies metrics represented by sample entropy, permutation entropy, and spectral entropy. Both sets of features were calculated within the noise-assisted multivariate empirical mode decomposition domain. Correlation analysis showed a significant association in the delta band between the proposed features, graph attributes and entropy features from the neonatal EEG data and the cognitive development at age two years. These features were used to train and test the tree ensemble regression models. The highest prediction performance was reached to 14.27 root mean square error, 12.07 mean absolute error, and 0.45 R-squared using the entropy features with a boosted tree regression model. Thus, the results demonstrate that the proposed qEEG features show the state of brain function at an early stage; hence, they could serve as predictive biomarkers of later cognitive impairment, which could facilitate identifying those who might benefit from early targeted intervention. (shrink)

We present a canonical form for definable subsets of algebraically closed valued fields by means of decompositions into sets of a simple form, and do the same for definable subsets of real closed valued fields. Both cases involve discs, forming "Swiss cheeses" in the algebraically closed case, and cuts in the real closed case. As a step in the development, we give a proof for the fact that in "most" valued fields F, if f(x),g(x) ∈ F[ x] and v is (...) the valuation map, then the set {x : v(f(x)) ≤ v(g(x))} is a Boolean combination of discs; in fact, it is a finite union of Swiss cheeses. The development also depends on the introduction of "valued trees", which we define formally. (shrink)