Conditional Hardness of Earth Mover Distance

The Earth Mover Distance (EMD) between two sets of points A, B subseteq R^d with |A| = |B| is the minimum total Euclidean distance of any perfect matching between A and B. One of its generalizations is asymmetric EMD, which is the minimum total Euclidean distance of any matching of size |A| between sets of points A,B subseteq R^d with |A| <= |B|. The problems of computing EMD and asymmetric EMD are well-studied and have many applications in computer science, some of which also ask for the EMD-optimal matching itself. Unfortunately, all known algorithms require at least quadratic time to compute EMD exactly. Approximation algorithms with nearly linear time complexity in n are known (even for finding approximately optimal matchings), but suffer from exponential dependence on the dimension. In this paper we show that significant improvements in exact and approximate algorithms for EMD would contradict conjectures in fine-grained complexity. In particular, we prove the following results: - Under the Orthogonal Vectors Conjecture, there is some c>0 such that EMD in Omega(c^{log^* n}) dimensions cannot be computed in truly subquadratic time. - Under the Hitting Set Conjecture, for every delta>0, no truly subquadratic time algorithm can find a (1 + 1/n^delta)-approximate EMD matching in omega(log n) dimensions. - Under the Hitting Set Conjecture, for every eta = 1/omega(log n), no truly subquadratic time algorithm can find a (1 + eta)-approximate asymmetric EMD matching in omega(log n) dimensions

An associative network with spatially organized connectivity

We investigate the properties of an autoassociative network of threshold-linear units whose synaptic connectivity is spatially structured and asymmetric. Since the methods of equilibrium statistical mechanics cannot be applied to such a network due to the lack of a Hamiltonian, we approach the problem through a signal-to-noise analysis, that we adapt to spatially organized networks. The conditions are analyzed for the appearance of stable, spatially non-uniform profiles of activity with large overlaps with one of the stored patterns. It is also shown, with simulations and analytic results, that the storage capacity does not decrease much when the connectivity of the network becomes short range. In addition, the method used here enables us to calculate exactly the storage capacity of a randomly connected network with arbitrary degree of dilution.Comment: 27 pages, 6 figures; Accepted for publication in JSTA

A model for generating synthetic dendrites of cortical neurons

One of the main challenges in neuroscience is to define the detailed structural design of the nervous system. This challenge is one of the first steps towards understanding how neural circuits contribute to the functional organization of the nervous system. In the cerebral cortex pyramidal neurons are key elements in brain function as they represent the most abundant cortical neuronal type and the main source of cortical excitatory synapses. Therefore, many researchers are interested in the analysis of the microanatomy of pyramidal cells since it constitutes an excellent tool for better understanding cortical processing of information. Computational models of neuronal networks based on real cortical circuits have become useful tools for studying certain aspects of the functional organization of the neocortex. Neuronal morphologies (morphological models) represent key features in these functional models. For these purposes, synthetic or virtual dendritic trees can be generated through a morphological model of a given neuronal type based on real morphometric parameters obtained from intracellularly-filled single neurons. This paper presents a new method to construct virtual dendrites by means of sampling a branching model that represents the dendritic morphology. This method has been contrasted using complete basal dendrites from 374 layer II/III pyramidal neurons of the mouse neocortex

Site fidelity and movement patterns of short-finned pilot whales within the Canary Islands : evidence for resident and transient populations

Funding: co-funded by the Canary Government (Consejería de Política Territorial, Sostenibilidad y Seguridad), the Spanish Government (Fundación Biodiversidad and Ministerio de Medio Ambiente, Medio Rural y Marino), Fundación La Caixa, and by a number of international projects funded by EU programmes MACETUS (FEDER/INTERREG III-B MAC/4.2/M10), EMECETUS (FEDER/INTERREG III-B56105/MAC/4.2/M10), LIFE (LIFE03NAT0062), INDEMARES LIFE+ (LIFE07/NAT/E/00732).1. The geographic location and oceanographic, physical, and chemical water properties make the Canary Islands one of the planet's biodiversity hotspots. The short‐finned pilot whale (Globicephala macrorhynchus) is one of the archipelago's most commonly encountered species and is potentially vulnerable to a range of anthropogenic pressures, including habitat degradation, acoustic pollution, fishing, whale‐watching operations, and shipping. Assessment of impact has not been possible because of a lack of even basic information about occurrence and distribution. 2. Spatial and temporal distributions, ranging behaviour, and residence patterns of short‐finned pilot whales were explored for the first time using survey and photo‐identification data collected in the Canary Islands between 1999 and 2012. In total, 1,081 pilot whale sightings were recorded during 70,620 km of search effort over 1,782 survey days. 3. Pilot whales were detected year round and distributed non‐uniformly within the archipelago, with greater densities concentrated in patchy areas mainly on the leeward side of the main islands. In total, 1,320 well‐marked individuals were identified, which exhibited a large degree of variability in site fidelity. 4. Different but not isolated subpopulations of pilot whales that share ranges and maintain social interactions were apparently present in the Canary Islands. Strong evidence of an island‐associated subpopulation was found, with a group of 50 ‘core resident’ individuals associated particularly with Tenerife. There were also ‘transient’ individuals or temporary migrants, which, probably driven by inter‐ and intra‐specific competition, may travel long distances whilst using the archipelago as part of a larger range. 5. These findings fill a major gap in the knowledge of this species’ occurrence, distribution, movements, and site fidelity in the archipelago and provide much needed data to allow the initiation of informed conservation assessments and management actions.PostprintPeer reviewe

Integrated information increases with fitness in the evolution of animats

One of the hallmarks of biological organisms is their ability to integrate disparate information sources to optimize their behavior in complex environments. How this capability can be quantified and related to the functional complexity of an organism remains a challenging problem, in particular since organismal functional complexity is not well-defined. We present here several candidate measures that quantify information and integration, and study their dependence on fitness as an artificial agent ("animat") evolves over thousands of generations to solve a navigation task in a simple, simulated environment. We compare the ability of these measures to predict high fitness with more conventional information-theoretic processing measures. As the animat adapts by increasing its "fit" to the world, information integration and processing increase commensurately along the evolutionary line of descent. We suggest that the correlation of fitness with information integration and with processing measures implies that high fitness requires both information processing as well as integration, but that information integration may be a better measure when the task requires memory. A correlation of measures of information integration (but also information processing) and fitness strongly suggests that these measures reflect the functional complexity of the animat, and that such measures can be used to quantify functional complexity even in the absence of fitness data.Comment: 27 pages, 8 figures, one supplementary figure. Three supplementary video files available on request. Version commensurate with published text in PLoS Comput. Bio

Decomposing Neural Synchrony: Toward an Explanation for Near-Zero Phase-Lag in Cortical Oscillatory Networks

Background: Synchronized oscillation in cortical networks has been suggested as a mechanism for diverse functions ranging from perceptual binding to memory formation to sensorimotor integration. Concomitant with synchronization is the occurrence of near-zero phase-lag often observed between network components. Recent theories have considered the importance of this phenomenon in establishing an effective communication framework among neuronal ensembles. Methodology/Principal Findings: Two factors, among possibly others, can be hypothesized to contribute to the near-zero phase-lag relationship: (1) positively correlated common input with no significant relative time delay and (2) bidirectional interaction. Thus far, no empirical test of these hypotheses has been possible for lack of means to tease apart the specific causes underlying the observed synchrony. In this work simulation examples were first used to illustrate the ideas. A quantitative method that decomposes the statistical interdependence between two cortical areas into a feed-forward, a feed-back and a common-input component was then introduced and applied to test the hypotheses on multichannel local field potential recordings from two behaving monkeys. Conclusion/Significance: The near-zero phase-lag phenomenon is important in the study of large-scale oscillatory networks. A rigorous mathematical theorem is used for the first time to empirically examine the factors that contribute to this phenomenon. Given the critical role that oscillatory activity is likely to play in the regulation of biological processes at al

Qualia: The Geometry of Integrated Information

According to the integrated information theory, the quantity of consciousness is the amount of integrated information generated by a complex of elements, and the quality of experience is specified by the informational relationships it generates. This paper outlines a framework for characterizing the informational relationships generated by such systems. Qualia space (Q) is a space having an axis for each possible state (activity pattern) of a complex. Within Q, each submechanism specifies a point corresponding to a repertoire of system states. Arrows between repertoires in Q define informational relationships. Together, these arrows specify a quale—a shape that completely and univocally characterizes the quality of a conscious experience. Φ— the height of this shape—is the quantity of consciousness associated with the experience. Entanglement measures how irreducible informational relationships are to their component relationships, specifying concepts and modes. Several corollaries follow from these premises. The quale is determined by both the mechanism and state of the system. Thus, two different systems having identical activity patterns may generate different qualia. Conversely, the same quale may be generated by two systems that differ in both activity and connectivity. Both active and inactive elements specify a quale, but elements that are inactivated do not. Also, the activation of an element affects experience by changing the shape of the quale. The subdivision of experience into modalities and submodalities corresponds to subshapes in Q. In principle, different aspects of experience may be classified as different shapes in Q, and the similarity between experiences reduces to similarities between shapes. Finally, specific qualities, such as the “redness” of red, while generated by a local mechanism, cannot be reduced to it, but require considering the entire quale. Ultimately, the present framework may offer a principled way for translating qualitative properties of experience into mathematics

Task-Specific Codes for Face Recognition: How they Shape the Neural Representation of Features for Detection and Individuation

The variety of ways in which faces are categorized makes face recognition challenging for both synthetic and biological vision systems. Here we focus on two face processing tasks, detection and individuation, and explore whether differences in task demands lead to differences both in the features most effective for automatic recognition and in the featural codes recruited by neural processing.Our study appeals to a computational framework characterizing the features representing object categories as sets of overlapping image fragments. Within this framework, we assess the extent to which task-relevant information differs across image fragments. Based on objective differences we find among task-specific representations, we test the sensitivity of the human visual system to these different face descriptions independently of one another. Both behavior and functional magnetic resonance imaging reveal effects elicited by objective task-specific levels of information. Behaviorally, recognition performance with image fragments improves with increasing task-specific information carried by different face fragments. Neurally, this sensitivity to the two tasks manifests as differential localization of neural responses across the ventral visual pathway. Fragments diagnostic for detection evoke larger neural responses than non-diagnostic ones in the right posterior fusiform gyrus and bilaterally in the inferior occipital gyrus. In contrast, fragments diagnostic for individuation evoke larger responses than non-diagnostic ones in the anterior inferior temporal gyrus. Finally, for individuation only, pattern analysis reveals sensitivity to task-specific information within the right "fusiform face area".OUR RESULTS DEMONSTRATE: 1) information diagnostic for face detection and individuation is roughly separable; 2) the human visual system is independently sensitive to both types of information; 3) neural responses differ according to the type of task-relevant information considered. More generally, these findings provide evidence for the computational utility and the neural validity of fragment-based visual representation and recognition

Visually Driven Activation in Macaque Areas V2 and V3 without Input from the Primary Visual Cortex

Creating focal lesions in primary visual cortex (V1) provides an opportunity to study the role of extra-geniculo-striate pathways for activating extrastriate visual cortex. Previous studies have shown that more than 95% of neurons in macaque area V2 and V3 stop firing after reversibly cooling V1 [1], [2], [3]. However, no studies on long term recovery in areas V2, V3 following permanent V1 lesions have been reported in the macaque. Here we use macaque fMRI to study area V2, V3 activity patterns from 1 to 22 months after lesioning area V1. We find that visually driven BOLD responses persist inside the V1-lesion projection zones (LPZ) of areas V2 and V3, but are reduced in strength by ∼70%, on average, compared to pre-lesion levels. Monitoring the LPZ activity over time starting one month following the V1 lesion did not reveal systematic changes in BOLD signal amplitude. Surprisingly, the retinotopic organization inside the LPZ of areas V2, V3 remained similar to that of the non-lesioned hemisphere, suggesting that LPZ activation in V2, V3 is not the result of input arising from nearby (non-lesioned) V1 cortex. Electrophysiology recordings of multi-unit activity corroborated the BOLD observations: visually driven multi-unit responses could be elicited inside the V2 LPZ, even when the visual stimulus was entirely contained within the scotoma induced by the V1 lesion. Restricting the stimulus to the intact visual hemi-field produced no significant BOLD modulation inside the V2, V3 LPZs. We conclude that the observed activity patterns are largely mediated by parallel, V1-bypassing, subcortical pathways that can activate areas V2 and V3 in the absence of V1 input. Such pathways may contribute to the behavioral phenomenon of blindsight

Mapping Human Whole-Brain Structural Networks with Diffusion MRI

Understanding the large-scale structural network formed by neurons is a major challenge in system neuroscience. A detailed connectivity map covering the entire brain would therefore be of great value. Based on diffusion MRI, we propose an efficient methodology to generate large, comprehensive and individual white matter connectional datasets of the living or dead, human or animal brain. This non-invasive tool enables us to study the basic and potentially complex network properties of the entire brain. For two human subjects we find that their individual brain networks have an exponential node degree distribution and that their global organization is in the form of a small world