Representation and aggregation of crisp and fuzzy ordered structures: applications to social choice

The present memory is structured as follows: after the Introduction, in the Chapter 2 of preliminaries, we will pay attention to the three areas which sustain the development of this thesis. These are, binary relations, Social Choice and Fuzzy sets. Chapter 3 is devoted to the study of fuzzy Arrovian models. First, it is introduced the concept of a fuzzy preference. Next, we define fuzzy aggregation rules and all of the restrictions of common sense, which are inspired by the restrictions that come from the classic Arrovian model. Next, different models are defined in the fuzzy setting. Their definitions depend on the particular nuances and features of a preference (choosing a transitivity type and a connectedness type) and the restrictions on an aggregation function (choosing an independence of irrelevant alternatives property,an unanimity property, etc). Different possibility and impossibility theorems have been proved depending on the set of definition and restrictions. In Chapter 4 it is studied the problem of the decomposition of fuzzy binary relations. There, it is defined clearly the problem of setting suitable decomposition rules. That is, we analyze how to obtain a strict preference and an indifference from the weak preference in a fuzzy approach. In this chapter, the existence and the uniqueness of certain kind of decomposition rules associated to fuzzy unions are characterized. In Chapter 5, the decomposition rules studied in Chapter 4 are used to achieve a new impossibility result. It is important to point out that in the proof of the main result in this chapter it is introduced a new technique. In this proof, fuzzy preferences are framed through an auxiliary tuple of five crisp binary relations, that we name a pseudofuzzy preference. An aggregation model à la Arrow of pseudofuzzy preferences is also studied,but the main result is about the aggregation of fuzzy preferences that come from decompositions.Chapters 3, 4 and 5 constitute the main body of this memory. Then a section of conclusions is included. It contains suggestions for further studies, open problems and several final comments. Finally, an Appendix has been added in order to give an account of the work done within these three years, that can not be included in the body of the present memory.

The Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: measurement of the BAO and growth rate of structure of the emission line galaxy sample from the anisotropic power spectrum between redshift 0.6 and 1.1

We analyse the large-scale clustering in Fourier space of emission line galaxies (ELG) from the Data Release 16 of the Sloan Digital Sky Survey IV extended Baryon Oscillation Spectroscopic Survey. The ELG sample contains 173,736 galaxies covering 1,170 square degrees in the redshift range 0.6 < z < 1.1. We perform a BAO measurement from the post-reconstruction power spectrum monopole, and study redshift space distortions (RSD) in the first three even multipoles. Photometric variations yield fluctuations of both the angular and radial survey selection functions. Those are directly inferred from data, imposing integral constraints which we model consistently. The full data set has only a weak preference for a BAO feature (1.4σ). At the effective redshift zeff = 0.845 we measure $D_{\rm V}(z_{\rm eff})/r_{\rm drag} = 18.33_{-0.62}^{+0.57}$, with DV the volume-averaged distance and rdrag the comoving sound horizon at the drag epoch. In combination with the RSD measurement, at zeff = 0.85 we find $f\sigma _8(z_{\rm eff}) = 0.289_{-0.096}^{+0.085}$, with f the growth rate of structure and σ8 the normalisation of the linear power spectrum, $D_{\rm H}(z_{\rm eff})/r_{\rm drag} = 20.0_{-2.2}^{+2.4}$ and DM(zeff)/rdrag = 19.17 ± 0.99 with DH and DM the Hubble and comoving angular distances, respectively. These results are in agreement with those obtained in configuration space, thus allowing a consensus measurement of fσ8(zeff) = 0.315 ± 0.095, $D_{\rm H}(z_{\rm eff})/r_{\rm drag} = 19.6_{-2.1}^{+2.2}$ and DM(zeff)/rdrag = 19.5 ± 1.0. This measurement is consistent with a flat ΛCDM model with Planck parameters.

The relationship between a combinatorial processing rule and a continuous mate preference function in an insect

Mate choice involves processing signals that can reach high levels of complexity and feature multiple components, even in small animals with tiny brains. This raises the question of whether and how such organisms deal with this complexity. One solution involves combinatorial processing, whereby different signal elements are processed as single units. Combinatorial processing has been described in several mammals and birds, and recently in a vibrationally signalling insect, Enchenopa treehoppers. Here, we ask about the relationship between combinatorial rules and mate preferences for continuously varying signal features. Enchenopa male advertisement signals are composed of two elements: a ‘whine’ followed by a set of pulses. The dominant frequency of the whine and element combination both matter to females. We presented synthetic signals varying in element order (natural [whine-pulses], reverse [pulses-whine]) and in frequency to Enchenopa females and recorded their responses. The reverse combination resulted in a decrease in attractiveness of the signals, and also slightly changed the shape of the preference for frequency. We found that females could be classified into three ‘types’: females with both a strong preference and a strong combinatorial rule, females with both a weak preference and weak rule, and females with a strong preference but a weak rule. Our results suggest that in Enchenopa signal processing, the mate preference for a continuous signal feature ‘takes precedence’ over, but also interacts with, the combinatorial rule. The relationship between the preference and the rule could evolve to take different forms according to selection on mate choice decisions. We suggest that exploring the relationship between such preferences and rules in species with more complex signals will bring insight into the evolution of the multi-component communication systems.

Transient brightenings in the quiet Sun detected by ALMA at 3 mm

Aims. We investigate transient brightenings, that is, weak, small-scale episodes of energy release, in the quiet solar chromosphere; these episodes can provide insights into the heating mechanism of the outer layers of the solar atmosphere. Methods. Using Atacama Large Millimeter/submillimeter Array (ALMA) observations, we performed the first systematic survey for quiet Sun transient brightenings at 3 mm. Our dataset included images of six 87″ × 87″ fields of view of the quiet Sun obtained with angular resolution of a few arcsec at a cadence of 2 s. The transient brightenings were detected as weak enhancements above the average intensity after we removed the effect of the p-mode oscillations. A similar analysis, over the same fields of view, was performed for simultaneous 304 and 1600 Å data obtained with the Atmospheric Imaging Assembly. Results. We detected 184 3 mm transient brightening events with brightness temperatures from 70 K to more than 500 K above backgrounds of ∼7200 − 7450 K. All events showed light curves with a gradual rise and fall, strongly suggesting a thermal origin. Their mean duration and maximum area were 51.1 s and 12.3 Mm2, respectively, with a weak preference of appearing at network boundaries rather than in cell interiors. Both parameters exhibited power-law behavior with indices of 2.35 and 2.71, respectively. Only a small fraction of ALMA events had either 304 or 1600 Å counterparts but the properties of these events were not significantly different from those of the general population except that they lacked their low-end energy values. The total thermal energies of the ALMA transient brightenings were between 1.5 × 1024 and 9.9 × 1025 erg and their frequency distribution versus energy was a power law with an index of 1.67 ± 0.05. We found that the power per unit area provided by the ALMA events could account for only 1% of the chromospheric radiative losses (10% of the coronal ones). Conclusions. We were able to detect, for the first time, a significant number of weak 3 mm quiet Sun transient brightenings. However, their energy budget falls short of meeting the requirements for the heating of the upper layers of the solar atmosphere and this conclusion does not change even if we use the least restrictive criteria possible for the detection of transient brightenings.

An Analysis Framework for Metric Voting based on LP Duality

Distortion-based analysis has established itself as a fruitful framework for comparing voting mechanisms. m voters and n candidates are jointly embedded in an (unknown) metric space, and the voters submit rankings of candidates by non-decreasing distance from themselves. Based on the submitted rankings, the social choice rule chooses a winning candidate; the quality of the winner is the sum of the (unknown) distances to the voters. The rule's choice will in general be suboptimal, and the worst-case ratio between the cost of its chosen candidate and the optimal candidate is called the rule's distortion. It was shown in prior work that every deterministic rule has distortion at least 3, while the Copeland rule and related rules guarantee distortion at most 5; a very recent result gave a rule with distortion 2 + √5 ≈ 4.236.We provide a framework based on LP-duality and flow interpretations of the dual which provides a simpler and more unified way for proving upper bounds on the distortion of social choice rules. We illustrate the utility of this approach with three examples. First, we show that the Ranked Pairs and Schulze rules have distortion Θ(√n). Second, we give a fairly simple proof of a strong generalization of the upper bound of 5 on the distortion of Copeland, to social choice rules with short paths from the winning candidate to the optimal candidate in generalized weak preference graphs. A special case of this result recovers the recent 2 + √5 guarantee. Finally, our framework naturally suggests a combinatorial rule that is a strong candidate for achieving distortion 3, which had also been proposed in recent work. We prove that the distortion bound of 3 would follow from any of three combinatorial conjectures we formulate.

Decomposition and Arrow-Like Aggregation of Fuzzy Preferences

We analyze the concept of a fuzzy preference on a set of alternatives, and how it can be decomposed in a triplet of new fuzzy binary relations that represent strict preference, weak preference and indifference. In this setting, we analyze the problem of aggregation of individual fuzzy preferences in a society into a global one that represents the whole society and accomplishes a shortlist of common-sense properties in the spirit of the Arrovian model for crisp preferences. We introduce a new technique that allows us to control a fuzzy preference by means of five crisp binary relations. This leads to an Arrovian impossibility theorem in this particular fuzzy setting.

On cognitive preferences and the plausibility of rule-based models

It is conventional wisdom in machine learning and data mining that logical models such as rule sets are more interpretable than other models, and that among such rule-based models, simpler models are more interpretable than more complex ones. In this position paper, we question this latter assumption by focusing on one particular aspect of interpretability, namely the plausibility of models. Roughly speaking, we equate the plausibility of a model with the likeliness that a user accepts it as an explanation for a prediction. In particular, we argue that—all other things being equal—longer explanations may be more convincing than shorter ones, and that the predominant bias for shorter models, which is typically necessary for learning powerful discriminative models, may not be suitable when it comes to user acceptance of the learned models. To that end, we first recapitulate evidence for and against this postulate, and then report the results of an evaluation in a crowdsourcing study based on about 3000 judgments. The results do not reveal a strong preference for simple rules, whereas we can observe a weak preference for longer rules in some domains. We then relate these results to well-known cognitive biases such as the conjunction fallacy, the representative heuristic, or the recognition heuristic, and investigate their relation to rule length and plausibility.

Nested plant LTR retrotransposons target specific regions of other elements, while all LTR retrotransposons often target palindromes and nucleosome-occupied regions: in silico study

Background Nesting is common in LTR retrotransposons, especially in large genomes containing a high number of elements. Results We analyzed 12 plant genomes and obtained 1491 pairs of nested and original (pre-existing) LTR retrotransposons. We systematically analyzed mutual nesting of individual LTR retrotransposons and found that certain families, more often belonging to the Ty3/gypsy than Ty1/copia superfamilies, showed a higher nesting frequency as well as a higher preference for older copies of the same family (“autoinsertions”). Nested LTR retrotransposons were preferentially located in the 3’UTR of other LTR retrotransposons, while coding and regulatory regions (LTRs) are not commonly targeted. Insertions displayed a weak preference for palindromes and were associated with a strong positional pattern of higher predicted nucleosome occupancy. Deviation from randomness in target site choice was also found in 13,983 non-nested plant LTR retrotransposons. Conclusions We reveal that nesting of LTR retrotransposons is not random. Integration is correlated with sequence composition, secondary structure and the chromatin environment. Insertion into retrotransposon positions with a low negative impact on family fitness supports the concept of the genome being viewed as an ecosystem of various elements.

Stable Matching with Uncertain Linear Preferences

We consider the two-sided stable matching setting in which there may be uncertainty about the agents’ preferences due to limited information or communication. We consider three models of uncertainty: (1) lottery model—for each agent, there is a probability distribution over linear preferences, (2) compact indifference model—for each agent, a weak preference order is specified and each linear order compatible with the weak order is equally likely and (3) joint probability model—there is a lottery over preference profiles. For each of the models, we study the computational complexity of computing the stability probability of a given matching as well as finding a matching with the highest probability of being stable. We also examine more restricted problems such as deciding whether a certainly stable matching exists. We find a rich complexity landscape for these problems, indicating that the form uncertainty takes is significant.

From ridge tops to ravines: landscape drivers of chimpanzee ranging patterns

Recent improvements in tracking technologies have resulted in a growing number of fine-scale animal movement studies in a variety of fields from wildlife management to animal cognition. Most studies assume that an animal’s “optimal” foraging route is linear, ignoring the role the energy landscape can play in influencing movement efficiency. Our objective was to investigate whether landscape features that affect movement costs; topographic variation, and super and substrate, influence the movement of chimpanzees (Pan troglodytes) in a rugged, montane environment. We tested for route re-use and preferential use of human-made trails and ridge tops using 14 months of focal follow data from 14 individuals and maps of established chimpanzee trails. Chimpanzees travelled on human-made trails significantly more than expected and showed weak preference for use of ridge tops for travel. Line density analysis demonstrated route re-use in chimpanzees and uncovered a network of high-use routes across their range. To our knowledge, this is the first study to empirically demonstrate route re-use and preferential use of human-made trails for travel by chimpanzees. We discuss the energetic and cognitive benefits of trail use and the implications for chimpanzee sociality. By applying the latest GIS analytical techniques to fine-scale movement data, this study demonstrates the importance of incorporating landscape features in predictive animal movement models.