Interval Representation Research Articles

Interval graph representation with given interval and intersection lengths

We consider the problem of finding interval graph representations that additionally respect given interval lengths and/or pairwise intersection lengths, which are represented as weight functions on the vertices and edges, respectively. Pe'er and Shamir (1997 [25]) proved that the problem is NP-complete if only the former are given. For the case when both are given, Fulkerson and Gross (1965 [8]) gave an O(n2) time algorithm; we improve this to O(n+m) time and supplement it with a logspace algorithm. For the case when only the latter are given, we give both an O(nm) time algorithm and a logspace algorithm. In all these bounds, n is the number of vertices and m is the number of edges in the input graph.Complementing their hardness result, Pe'er and Shamir give a polynomial-time algorithm for the case that the input graph has a unique interval ordering of its maximal cliques. For such graphs, their algorithm computes an interval representation (if it exists) that respects a given set of distance inequalities between the interval endpoints. We observe that deciding if such a representation exists is NL-complete.

Music, clicks, and their imaginations favor differently the event-based timing component for rhythmic movements.

The involvement or noninvolvement of a clock-like neural process, an effector-independent representation of the time intervals to produce, is described as the essential difference between event-based and emergent timing. In a previous work (Bravi et al. in Exp Brain Res 232:1663-1675, 2014a. doi: 10.1007/s00221-014-3845-9 ), we studied repetitive isochronous wrist's flexion-extensions (IWFEs), performed while minimizing visual and tactile information, to clarify whether non-temporal and temporal characteristics of paced auditory stimuli affect the precision and accuracy of the rhythmic motor performance. Here, with the inclusion of new recordings, we expand the examination of the dataset described in our previous study to investigate whether simple and complex paced auditory stimuli (clicks and music) and their imaginations influence in a different way the timing mechanisms for repetitive IWFEs. Sets of IWFEs were analyzed by the windowed (lag one) autocorrelation-wγ(1), a statistical method recently introduced for the distinction between event-based and emergent timing. Our findings provide evidence that paced auditory information and its imagination favor the engagement of a clock-like neural process, and specifically that music, unlike clicks, lacks the power to elicit event-based timing, not counteracting the natural shift of wγ(1) toward positive values as frequency of movements increase.

Assessment of the different sources of uncertainty in a SWAT model of the River Senne (Belgium)

Although rainfall input uncertainties are widely identified as being a key factor in hydrological models, the rainfall uncertainty is typically not included in the parameter identification and model output uncertainty analysis of complex distributed models such as SWAT and in maritime climate zones. This paper presents a methodology to assess the uncertainty of semi-distributed hydrological models by including, in addition to a list of model parameters, additional unknown factors in the calibration algorithm to account for the rainfall uncertainty (using multiplication factors for each separately identified rainfall event) and for the heteroscedastic nature of the errors of the stream flow. We used the Differential Evolution Adaptive Metropolis algorithm (DREAM(zs)) to infer the parameter posterior distributions and the output uncertainties of a SWAT model of the River Senne (Belgium). Explicitly considering heteroscedasticity and rainfall uncertainty leads to more realistic parameter values, better representation of water balance components and prediction uncertainty intervals.

On the non-unit count of interval graphs

We introduce the non-unit count of an interval graph as the minimum number of intervals in an interval representation whose lengths deviate from one. We characterize a variant of the non-unit count (where all interval lengths are required to be at least one) and graphs with non-unit count 1.

Distortion of time interval reproduction in an epileptic patient with a focal lesion in the right anterior insular/inferior frontal cortices

This case report on an epileptic patient suffering from a focal lesion at the junction of the right anterior insular cortex (AIC) and the adjacent inferior frontal cortex (IFC) provides the first evidence that damage to this brain region impairs temporal performance in a visual time reproduction task in which participants had to reproduce the presentation duration (3, 5 and 7s) of emotionally-neutral and -negative pictures. Strikingly, as compared to a group of healthy subjects, the AIC/IFC case considerably overestimated reproduction times despite normal variability. The effect was obtained in all duration and emotion conditions. Such a distortion in time reproduction was not observed in four other epileptic patients without insular or inferior frontal damage. Importantly, the absolute extent of temporal over-reproduction increased in proportion to the magnitude of the target durations, which concurs with the scalar property of interval timing, and points to an impairment of time-specific rather than of non temporal (such as motor) mechanisms. Our data suggest that the disability in temporal reproduction of the AIC/IFC case would result from a distorted memory representation of the encoded duration, occurring during the process of storage and/or of recovery from memory and leading to a deviation of the temporal judgment during the reproduction task. These findings support the recent proposal that the anterior insular/inferior frontal cortices would be involved in time interval representation.

Ivan Shishov, the First Attempts of Melody Analysis in the Soviet Union

Describes the life and works of the Russian composer Ivan Shishov (1888-1947) and examines his article “On the Analysis Of Melodic Structure” (1927). The author argues that Shishov’s method was based on the numerical representation of melodic intervals and questing for the numerical and graphical elements of symmetry, which manifests in the interval structure of a melody.

Variable timing of synaptic transmission in cerebellar unipolar brush cells

The cerebellum ensures the smooth execution of movements, a task that requires accurate neural signaling on multiple time scales. Computational models of cerebellar timing mechanisms have suggested that temporal information in cerebellum-dependent behavioral tasks is in part computed locally in the cerebellar cortex. These models rely on the local generation of delayed signals spanning hundreds of milliseconds, yet the underlying neural mechanism remains elusive. Here we show that a granular layer interneuron, called the unipolar brush cell, is well suited to represent time intervals in a robust way in the cerebellar cortex. Unipolar brush cells exhibited delayed increases in excitatory synaptic input in response to presynaptic stimulation in mouse cerebellar slices. Depending on the frequency of stimulation, delays extended from zero up to hundreds of milliseconds. Such controllable protraction of delayed currents was the result of an unusual mode of synaptic integration, which was well described by a model of steady-state AMPA receptor activation. This functionality extends the capabilities of the cerebellum for adaptive control of behavior by facilitating appropriate output in a broad temporal window.

Study on Knowledge Representation of Temporal Conceptual Graph in the Context

In the semantic analysis and the pragmatic analysis, the knowledge representation of the context is a very important domain. For the representation of the context, traditional conceptual graph is very complex. Some problems of more nodes, conceptual graph multilayer nested, difficulties in connecting and matching of often appear. Especially when the statement includes the temporal, modal and negation, these defects are even more prominent. Aiming at the shortcomings, the knowledge representation of temporal conceptual graph is presented. First of all, the time interval and the temporal interval representation method of English tenses are defined. On this basis, it focuses on the simple matching rule and the structure of the temporal conceptual graph. Finally, the performance of traditional conceptual graph and temporal conceptual graph are compared through an essay. The results indicate that the temporal conceptual graph is propitious to the semantic analysis and the pragmatic analysis.

Aggregation functions for typical hesitant fuzzy elements and the action of automorphisms

This work studies the aggregation operators on the set of all possible membership degrees of typical hesitant fuzzy sets, which we refer to as H, as well as the action of H-automorphisms which are defined over the set of all finite non-empty subsets of the unitary interval. In order to do so, the partial order ⩽H, based on α-normalization, is introduced, leading to a comparison based on selecting the greatest membership degrees of the related fuzzy sets. Additionally, the idea of interval representation is extended to the context of typical hesitant aggregation functions named as the H-representation. As main contribution, we consider the class of finite hesitant triangular norms, studying their properties and analyzing the H-conjugate functions over such operators.

The role of posterior parietal cortices on prismatic adaptation effects on the representation of time intervals

Previous studies provided evidence of an ascending left-to-right spatial representation of time durations by using a technique affecting high levels of spatial cognition, i.e. prismatic adaptation (PA). Indeed, PA that induced a leftward aftereffect distorted time representation toward an underestimation, while PA that induced a rightward aftereffect distorted time representation toward an overestimation. The present study advances previous findings on the effects of PA on time by investigating the neural basis subtending these effects. We focused on the posterior parietal cortex (PPC) since it is involved in the PA procedure and also in the formulation of the spatial representation of time. We conducted two experiments where right-handed healthy adults were submitted to a time task, before and after PA, that could induce a leftward or rightward aftereffect. Repetitive TMS (rTMS) was used to inhibit the left or right PPC before PA administration. In a first experiment the time task consisted of reproducing an half duration (time bisection task) by pressing a key and the participants responded and adapted to prisms with their right hand. In a second experiment the time task consisted of reproducing a whole duration (time reproduction task) by pressing a key and the participants responded and adapted to prisms with their left hand.We found an abolition of the effects of PA on time when rTMS was delivered on the left and not on the right PPC, regardless of the task and moreover, when the participants responded and adapted with the right hand and also with the left hand. This result suggests a direct involvement of the left PPC in the interactive process, between spatial modulations induced by PA and the spatial representation of time, that does not depend on motor processes. This study provides useful results for future investigations on the neural mechanisms subtending the effects of PA on spatial representations.

An Antimicrobial Prescription Surveillance System that Learns from Experience

Inappropriate prescribing of antimicrobials is a major clinical and health concern, as well as a financial burden, in hospitals worldwide. In this paper, we describe a deployed automated antimicrobial prescription surveillance system that has been assisting hospital pharmacists in identifying and reporting inappropriate antimicrobial prescriptions. One of the key characteristics of this system is its ability to learn new rules for detecting inappropriate prescriptions based on previous false alerts. The supervised learning algorithm combines instancebased learning and rule induction techniques. It exploits temporal abstraction to extract a meaningful time interval representation from raw clinical data, and applies nearest neighbor classification with a distance function on both temporal and non-temporal parameters. The learning capability is valuable both in configuring the system for initial deployment and improving its long term use. We give an overview of the application, point to lessons learned so far and provide insight into the machine learning capability.

Optimizing the representation of intervals

A representation of intervals is proposed that, instead of both endpoints, uses the lower endpoint and the width of the interval. This proposed representation is more efficient since both endpoints have many corresponding bits that are equal. Consequently, the width of the interval can be represented with a smaller number of bits than an endpoint, resulting in a better utilization of the number of bits available. Considering the case in which the total number of bits is the same as for the traditional representation (say, two double-precision floating-point numbers) we determine the number of bits of the lower endpoint and of the width so that the rounding error is minimized. The use of this combination of bits would result in a variable representation, which is difficult to implement. Alternatively, it is possible to use a fixed partition that gives good results for a variety of applications.The proposed representation is evaluated for several computations. Using a total number of 128 bits to represent the interval we conclude that it produces intervals that are substantially narrower than those obtained with the traditional representation.Alternative implementations of the calculation of the width are proposed. The interval widths produced are shown to be very similar, so that the choice of the alternative can be made by considerations such as area and delay.

Some continuity notions for interval functions and representation

The formalization of correctness and optimality concepts, which are desirable requirements for interval (and other self-validated methods) libraries, is related to topological aspects of real numbers and Moore arithmetics, characterizing some families of interval functions. The main motivation is that real continuous functions are largely used in many fields of human activity, and a characterization of their interval representation in terms of interval topologies leads to the knowledge of how interval algorithms are suitable to represent those functions. In this paper, we characterize and relate some classes of interval functions with respect to three natures of an interval (as a set, as an information, as a number). These natures establish different ways to classify intervals, and hence different notions of continuity. Here we relate the notion of interval representations with those classes of functions.

Interval-valued fuzzy coimplications and related dual interval-valued conjugate functions

The aim of this paper is to introduce the dual notion of interval conjugate implications, the interval coimplications, as interval representations of corresponding conjugate fuzzy coimplications. Using the canonical representation, this paper considers both the correctness and the optimality criteria, in order to provide interpretation for fuzzy coimplications as the non-truth degree of conditional rule in expert systems and study the action of interval automorphisms on such interval fuzzy connectives. It is proved that interval automorphisms acting on N-dual interval coimplications preserve the main properties of interval implications discussed in the literature including the duality principle. Lastly, the action of interval automorphisms on interval classes of border, model and S-coimplications are considered, summarized in commutative diagrams.

Numerical quantity affects time estimation in the suprasecond range

Of stimuli differing in the magnitude of their numerical information, the one with the larger numerosity is perceived to last longer than that with the smaller numerosity. This numerosity–time interaction is proposed to be due to a shared neural representation for numerical magnitude and time intervals in the parietal cortex. Neuroimaging studies of temporal processing suggest that subsecond and suprasecond intervals could be mediated by distinct neural substrates. However, whether the numerosity–time interaction occurs independently of the time intervals used in the tasks remains unknown. Here we show that numerical information interacts with time estimation in the suprasecond range in females, but not in males. Our results suggest that the numerical magnitude and suprasecond intervals have shared representations in the human brain, but the associative strength between these dimensions might be different between males and females.

Parallel indexing technique for spatio-temporal data

The requirements for efficient access and management of massive multi-dimensional spatio-temporal data in geographical information system and its applications are well recognized and researched. The most popular spatio-temporal access method is the R-Tree and its variants. However, it is difficult to use them for parallel access to multi-dimensional spatio-temporal data because R-Trees, and variants thereof, are in hierarchical structures which have severe overlapping problems in high dimensional space. We extended a two-dimensional interval space representation of intervals to a multi-dimensional parallel space, and present a set of formulae to transform spatio-temporal queries into parallel interval set operations. This transformation reduces problems of multi-dimensional object relationships to simpler two-dimensional spatial intersection problems. Experimental results show that the new parallel approach presented in this paper has superior range query performance than R*-trees for handling multi-dimensional spatio-temporal data and multi-dimensional interval data. When the number of CPU cores is larger than that of the space dimensions, the insertion performance of this new approach is also superior to R*-trees. The proposed approach provides a potential parallel indexing solution for fast data retrieval of massive four-dimensional or higher dimensional spatio-temporal data.

A hybrid genetic algorithm–fuzzy c-means approach for incomplete data clustering based on nearest-neighbor intervals

Incomplete data are often encountered in data sets used in clustering problems, and inappropriate treatment of incomplete data can significantly degrade the clustering performance. In view of the uncertainty of missing attributes, we put forward an interval representation of missing attributes based on nearest-neighbor information, named nearest-neighbor interval, and a hybrid approach utilizing genetic algorithm and fuzzy c-means is presented for incomplete data clustering. The overall algorithm is within the genetic algorithm framework, which searches for appropriate imputations of missing attributes in corresponding nearest-neighbor intervals to recover the incomplete data set, and hybridizes fuzzy c-means to perform clustering analysis and provide fitness metric for genetic optimization simultaneously. Several experimental results on a set of real-life data sets are presented to demonstrate the better clustering performance of our hybrid approach over the compared methods.

APPLICATION OF INTERVAL ANALYSIS ON ERROR ANALYSIS OF REFLECTION-ONLY MATERIAL CHARACTERIZATION METHODS

When performing electromagnetic material characteriza- tion, an error analysis should be performed to determine the sensitivity of the extracted permittivity and permeability. Traditional error anal- ysis methods such as the error propagation method and Monte Carlo simulations can pose di-culties when analyzing free space material characterization methods. This paper thus shows how interval analy- sis can be implemented to perform error analysis on free space material characterization methods and provide an alternate means to perform error analysis. Background is presented on interval representations and interval functions, and a procedure for performing error analysis with interval analysis is presented. An error analysis is performed on the free space implementation of the layer-shift method with interval analysis and the subsequent standard deviations computed with inter- val analysis are compared to standard deviations computed through Monte Carlo simulation.

Cartesian displays of many interval estimates

We consider the problem of constructing static graphical representations of a large number of interval estimates. Because of clutter, traditional graphical summaries are visually ineffective for representing more then a few intervals. The Cartesian displays introduced in this article overcome the limitations stemming from visual clutter and can represent effectively very many intervals. The construction of a Cartesian display for symmetric intervals is first presented in the context of a multiple comparisons application. Generalizations involving the representation of asymmetric intervals are then introduced and used to summarize aspects of the posterior distributions of numerous parameter contrasts in two hierarchical Bayes models.

Interval representations, Łukasiewicz implicators and Smets–Magrez axioms

The Smets–Magrez axiomatic is usually used to define the class of fuzzy continuous implications which are both S and R-implications (Łukasiewicz implications). Another approach is the construction of such class starting from a basic implication and applying automorphisms. Literature has shown that there is a harmony between those approaches, however in this paper we show that the extension of the Łukasiewicz implication defined on [0,1] for interval values cannot be applied in a direct way.We show that the harmony between the Smets–Magrez axiomatic approach and the one that comes from the generation by automorphisms is not preserved when such extension is done. One of the main consequences lies on the fact that the automorphism approach induces the loss of R-implications from the resulting class of implicators. More precisely, we show that the interval version of such approaches produce two disjunct classes of implicators, meaning that, unlike the usual case, the choice of the respective approach is an important step.