scholarly journals Scoring interval forecasts: Equal-tailed, shortest, and modal interval

Bernoulli ◽  
2021 ◽  
Vol 27 (3) ◽  
Author(s):  
Jonas R. Brehmer ◽  
Tilmann Gneiting
Keyword(s):  
Modal Interval

scholarly journals Reasoning with Time Intervals: A Logical and Computational Perspective

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Guido Sciavicco
Keyword(s):  
Temporal Reasoning ◽  
Point Of View ◽  
Time Intervals ◽  
First Order ◽  
Modal Interval ◽  
The Family ◽  
First Results ◽  
Comprehensive Survey ◽  
Classical Point

The role of time in artificial intelligence is extremely important. Interval-based temporal reasoning can be seen as a generalization of the classical point-based one, and the first results in this field date back to Hamblin (1972) and Benhtem (1991) from the philosophical point of view, to Allen (1983) from the algebraic and first-order one, and to Halpern and Shoham (1991) from the modal logic one. Without purporting to provide a comprehensive survey of the field, we take the reader to a journey through the main developments in modal and first-order interval temporal reasoning over the past ten years and outline some landmark results on expressiveness and (un)decidability of the satisfiability problem for the family of modal interval logics.

scholarly journals On the indirect elicitability of the mode and modal interval

2019 ◽  
Vol 72 (5) ◽  
pp. 1095-1108 ◽  
Author(s):  
Krisztina Dearborn ◽  
Rafael Frongillo
Keyword(s):  
Modal Interval

The effect of behavioural arousal on the activity of hypothalamic neurons in unanaesthetized, freely moving rats and rabbits

1982 ◽  
Vol 214 (1195) ◽  
pp. 263-272 ◽  
Keyword(s):  
Neuronal Activity ◽  
Cortical Neurons ◽  
Hypothalamic Neurons ◽  
Extracellular Recordings ◽  
Modal Interval ◽  
Individual Mode ◽  
Consistent Manner ◽  
Freely Moving ◽  
The Relationship ◽  
The Continuum

Experiments were carried out to investigate the relationship between levels of arousal and the temporal discharge pattern of hypothalamic neurons in unanaesthetized, unrestrained rats and rabbits. Extracellular recordings were taken from 22 hypothalamic neurons in animals that had been implanted previously with platinum microwire electrodes. Separate records of neuronal activity were taken from each neuron when the animal was at two extremes of arousal, sleep and alarm, and compared with an intermediate state of arousal, awake and relaxed. The extremes of arousal were defined by simple behavioural criteria, shown to coincide with specific patterns of electrocorticographic activity. Interval distributions were constructed from these records of neuronal activity. The modal interval, but not the frequency of discharge of these neurons, changed in a consistent manner with the level of arousal for all the neurons recorded. The modal interval was always short (9.59 ±1.2 ms (mean ± s.e.), n = 17) during sleep and longer when the animal was alarmed (57.15 ± 7.59 ms, n = 13). When the animals were awake and relaxed the modal interval was between those of sleep and alarm (27.5 ± 2.79 ms, n = 19). Scatter about an individual mode was greater in sleep than during alarm. It is suggested that the continuum of arousal from sleep to alarm is reflected by a continuously shifting modal interval for each hypothalamic neuron. This is essentially similar to reports on the effect of arousal on cortical neurons.

scholarly journals A Generalization of Trapezoidal Fuzzy Numbers Based on Modal Interval Theory

Symmetry ◽  
2017 ◽  
Vol 9 (10) ◽  
pp. 198 ◽  
Author(s):  
Lambert Jorba ◽  
Romà Adillon
Keyword(s):  
Fuzzy Numbers ◽  
Trapezoidal Fuzzy Numbers ◽  
Modal Interval

The effects of changing levels of arousal on the spontaneous activity of cortical neurones II. Relaxation and alarm

1976 ◽  
Vol 194 (1115) ◽  
pp. 239-251 ◽  
Keyword(s):  
Spontaneous Activity ◽  
Temporal Pattern ◽  
Discharge Rate ◽  
Geometric Standard Deviation ◽  
Sudden Increase ◽  
Lateral Cortex ◽  
Infrared Telescope ◽  
Modal Interval ◽  
Log Normal ◽  
Two Parameters

In a previous paper it has been shown that interval distributions derived from the activity of single cortical neurones can be described by log-normal curves. A cell’s temporal pattern of discharge can therefore be defined by the values of two parameters – a modal interval, and a geometric standard deviation (g. s. d.). It has also been shown that the values of both parameters change when an animal falls asleep. The modal interval becomes shorter, and the g. s. d. usually becomes larger. This paper deals with the effects of changes in arousal of animals which are awake; and, in particular, with the effects of the transition from relaxation to alarm. Single unit recordings have been made from neurones in the post-lateral and supra-sylvian gyri of unrestrained cats. In order to eliminate the direct effects of eye-movements, the experiments were carried out in complete darkness, and the animal was observed through an infrared telescope. Alarm was produced by the hiss of compressed air. An animal was said to be alarmed when he stood up abruptly and turned towards the source of the noise. Alarm produced a marked fall in the discharge frequency of those cells in post-lateral cortex which initially showed a low ( < 2 action potentials per second) rate of spontaneous activity. The discharge rate of the remaining neurones (whether in suprasylvian or post-lateral cortex) was unaffected by the sudden increase in arousal. But the temporal pattern of discharge of every cell was altered. The modal interval became longer when the animal was alarmed, and the g. s. d. usually became smaller. Such changes could have been predicted from a knowledge of the neural concomitants of the transition from sleep to wakefulness. These results suggest that the activity of all cortical neurones is affected by the level of arousal of the animal, and that this modulation takes the form of a continuum of possible modal intervals, and possible g.s.ds.

scholarly journals Marks: A New Interval Tool for Uncertainty, Vagueness and Indiscernibility

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2116
Author(s):  
Miguel A. Sainz ◽  
Remei Calm ◽  
Lambert Jorba ◽  
Ivan Contreras ◽  
Josep Vehi
Keyword(s):  
Dynamical Systems ◽  
Measurement Errors ◽  
Practical Application ◽  
Modal Interval ◽  
The Difference ◽  
Systems Simulation ◽  
And Control ◽  
Physical Quantities ◽  
Successive Calculation

The system of marks created by Dr. Ernest Gardenyes and Dr. Lambert Jorba was first published as a doctoral thesis in 2003 and then as a chapter in the book Modal Interval Analysis in 2014. Marks are presented as a tool to deal with uncertainties in physical quantities from measurements or calculations. When working with iterative processes, the slow convergence or the high number of simulation steps means that measurement errors and successive calculation errors can lead to a lack of significance in the results. In the system of marks, the validity of any computation results is explicit in their calculation. Thus, the mark acts as a safeguard, warning of such situations. Despite the obvious contribution that marks can make in the simulation, identification, and control of dynamical systems, some improvements are necessary for their practical application. This paper aims to present these improvements. In particular, a new, more efficient characterization of the difference operator and a new implementation of the marks library is presented. Examples in dynamical systems simulation, fault detection and control are also included to exemplify the practical use of the marks.

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