Boolean derivatives and computation of cellular automata

The derivatives of a Boolean function are defined up to any order. The Taylor and MacLaurin expansions of a Boolean function are thus obtained. The last corresponds to the ring sum expansion (RSE) of a Boolean function, and is a more compact form than the usual canonical disjunctive form. For totalistic functions the RSE allows the saving of a large number of Boolean operations. The algorithm has natural applications to the simulations of cellular automata using the multi site coding technique. Several already published algorithms are analized, and expressions with fewer terms are generally found.Comment: 15 page

A roadmap to integrate astrocytes into Systems Neuroscience.

Systems neuroscience is still mainly a neuronal field, despite the plethora of evidence supporting the fact that astrocytes modulate local neural circuits, networks, and complex behaviors. In this article, we sought to identify which types of studies are necessary to establish whether astrocytes, beyond their well-documented homeostatic and metabolic functions, perform computations implementing mathematical algorithms that sub-serve coding and higher-brain functions. First, we reviewed Systems-like studies that include astrocytes in order to identify computational operations that these cells may perform, using Ca2+ transients as their encoding language. The analysis suggests that astrocytes may carry out canonical computations in a time scale of subseconds to seconds in sensory processing, neuromodulation, brain state, memory formation, fear, and complex homeostatic reflexes. Next, we propose a list of actions to gain insight into the outstanding question of which variables are encoded by such computations. The application of statistical analyses based on machine learning, such as dimensionality reduction and decoding in the context of complex behaviors, combined with connectomics of astrocyte-neuronal circuits, is, in our view, fundamental undertakings. We also discuss technical and analytical approaches to study neuronal and astrocytic populations simultaneously, and the inclusion of astrocytes in advanced modeling of neural circuits, as well as in theories currently under exploration such as predictive coding and energy-efficient coding. Clarifying the relationship between astrocytic Ca2+ and brain coding may represent a leap forward toward novel approaches in the study of astrocytes in health and disease

RAS and beyond: The many faces of the neurofibromatosis type 1 protein

Neurofibromatosis type 1 is a rare neurogenetic syndrome, characterized by pigmentary abnormalities, learning and social deficits, and a predisposition for benign and malignant tumor formation caused by germline mutations in the NF1 gene. With the cloning of the NF1 gene and the recognition that the encoded protein, neurofibromin, largely functions as a negative regulator of RAS activity, attention has mainly focused on RAS and canonical RAS effector pathway signaling relevant to disease pathogenesis and treatment. However, as neurofibromin is a large cytoplasmic protein the RAS regulatory domain of which occupies only 10% of its entire coding sequence, both canonical and non-canonical RAS pathway modulation, as well as the existence of potential non-RAS functions, are becoming apparent. In this Special article, we discuss our current understanding of neurofibromin function

Partial Information Decomposition as a Unified Approach to the Specification of Neural Goal Functions

In many neural systems anatomical motifs are present repeatedly, but despite their structural similarity they can serve very different tasks. A prime example for such a motif is the canonical microcircuit of six-layered neo-cortex, which is repeated across cortical areas, and is involved in a number of different tasks (e.g.sensory, cognitive, or motor tasks). This observation has spawned interest in finding a common underlying principle, a 'goal function', of information processing implemented in this structure. By definition such a goal function, if universal, cannot be cast in processing-domain specific language (e.g. 'edge filtering', 'working memory'). Thus, to formulate such a principle, we have to use a domain-independent framework. Information theory offers such a framework. However, while the classical framework of information theory focuses on the relation between one input and one output (Shannon's mutual information), we argue that neural information processing crucially depends on the combination of \textit{multiple} inputs to create the output of a processor. To account for this, we use a very recent extension of Shannon Information theory, called partial information decomposition (PID). PID allows to quantify the information that several inputs provide individually (unique information), redundantly (shared information) or only jointly (synergistic information) about the output. First, we review the framework of PID. Then we apply it to reevaluate and analyze several earlier proposals of information theoretic neural goal functions (predictive coding, infomax, coherent infomax, efficient coding). We find that PID allows to compare these goal functions in a common framework, and also provides a versatile approach to design new goal functions from first principles. Building on this, we design and analyze a novel goal function, called 'coding with synergy'. [...]Comment: 21 pages, 4 figures, appendi

Partial information decomposition as a unified approach to the specification of neural goal functions

In many neural systems anatomical motifs are present repeatedly, but despite their structural similarity they can serve very different tasks. A prime example for such a motif is the canonical microcircuit of six-layered neo-cortex, which is repeated across cortical areas, and is involved in a number of different tasks (e.g. sensory, cognitive, or motor tasks). This observation has spawned interest in finding a common underlying principle, a ‘goal function’, of information processing implemented in this structure. By definition such a goal function, if universal, cannot be cast in processing-domain specific language (e.g. ‘edge filtering’, ‘working memory’). Thus, to formulate such a principle, we have to use a domain-independent framework. Information theory offers such a framework. However, while the classical framework of information theory focuses on the relation between one input and one output (Shannon’s mutual information), we argue that neural information processing crucially depends on the combination of multiple inputs to create the output of a processor. To account for this, we use a very recent extension of Shannon Information theory, called partial information decomposition (PID). PID allows to quantify the information that several inputs provide individually (unique information), redundantly (shared information) or only jointly (synergistic information) about the output. First, we review the framework of PID. Then we apply it to reevaluate and analyze several earlier proposals of information theoretic neural goal functions (predictive coding, infomax and coherent infomax, efficient coding). We find that PID allows to compare these goal functions in a common framework, and also provides a versatile approach to design new goal functions from first principles. Building on this, we design and analyze a novel goal function, called ‘coding with synergy’, which builds on combining external input and prior knowledge in a synergistic manner. We suggest that this novel goal function may be highly useful in neural information processing

EXPANSION: A Webserver to Explore the Functional Consequences of Protein-Coding Alternative Splice Variants in Cancer Genomics

EXPANSION (https://expansion.bioinfolab.sns.it/) is an integrated web-server to explore the functional consequences of protein-coding alternative splice (AS) variants. We combined information from Differentially Expressed (DE) protein-coding transcripts from cancer genomics, together with domain architecture, protein interaction network, and gene enrichment analysis to provide an easy-to-interpret view of the effects of protein-coding splice variants. We retrieved all the protein-coding Ensembl transcripts and mapped Interpro domains and Post-translational modifications (PTMs) on canonical sequences to identify functionally relevant splicing events. We also retrieved isoform-specific protein-protein interactions (PPIs) and binding regions from IntAct to uncover isoform-specific functions via gene-sets over-representation analysis. Through EXPANSION, users can analyse pre-calculated or user-inputted DE transcript datasets, to easily gain functional insights on any protein spliceform of interest

Non-Canonical Splicing and Its Implications in Brain Physiology and Cancer

The advance of experimental and computational techniques has allowed us to highlight the existence of numerous different mechanisms of RNA maturation, which have been so far unknown. Besides canonical splicing, consisting of the removal of introns from pre-mRNA molecules, non-canonical splicing events may occur to further increase the regulatory and coding potential of the human genome. Among these, splicing of microexons, recursive splicing and biogenesis of circular and chimeric RNAs through back-splicing and trans-splicing processes, respectively, all contribute to expanding the repertoire of RNA transcripts with newly acquired regulatory functions. Interestingly, these non-canonical splicing events seem to occur more frequently in the central nervous system, affecting neuronal development and differentiation programs with important implications on brain physiology. Coherently, dysregulation of non-canonical RNA processing events is associated with brain disorders, including brain tumours. Herein, we summarize the current knowledge on molecular and regulatory mechanisms underlying canonical and non-canonical splicing events with particular emphasis on cis-acting elements and trans-acting factors that all together orchestrate splicing catalysis reactions and decisions. Lastly, we review the impact of non-canonical splicing on brain physiology and pathology and how unconventional splicing mechanisms may be targeted or exploited for novel therapeutic strategies in cancer

Conservation and global distribution of non-canonical antigens in enterotoxigenic Escherichia coli

BACKGROUND: Enterotoxigenic Escherichia coli (ETEC) cause significant diarrheal morbidity and mortality in children of resource-limited regions, warranting development of effective vaccine strategies. Genetic diversity of the ETEC pathovar has impeded development of broadly protective vaccines centered on the classical canonical antigens, the colonization factors and heat-labile toxin. Two non-canonical ETEC antigens, the EtpA adhesin, and the EatA mucinase are immunogenic in humans and protective in animal models. To foster rational vaccine design that complements existing strategies, we examined the distribution and molecular conservation of these antigens in a diverse population of ETEC isolates. METHODS: Geographically diverse ETEC isolates (n = 1159) were interrogated by PCR, immunoblotting, and/or whole genome sequencing (n = 46) to examine antigen conservation. The most divergent proteins were purified and their core functions assessed in vitro. RESULTS: EatA and EtpA or their coding sequences were present in 57.0% and 51.5% of the ETEC isolates overall, respectively; and were globally dispersed without significant regional differences in antigen distribution. These antigens also exhibited \u3e93% amino acid sequence identity with even the most divergent proteins retaining the core adhesin and mucinase activity assigned to the prototype molecules. CONCLUSIONS: EtpA and EatA are well-conserved molecules in the ETEC pathovar, suggesting that they serve important roles in virulence and that they could be exploited for rational vaccine design

Generalizing the Sampling Property of the Q-function for Error Rate Analysis of Cooperative Communication in Fading Channels

This paper extends some approximation methods that are used to identify closed form Bit Error Rate (BER) expressions which are frequently utilized in investigation and comparison of performance for wireless communication systems in the literature. By using this group of approximation methods, some expectation integrals, which are complicated to analyze and have high computational complexity to evaluate through Monte Carlo simulations, are computed. For these integrals, by using the sampling property of the integrand functions of one or more arguments, reliable BER expressions revealing the diversity and coding gains are derived. Although the methods we present are valid for a larger class of integration problems, in this work we show the step by step derivation of the BER expressions for a canonical cooperative communication scenario in addition to a network coded system starting from basic building blocks. The derived expressions agree with the simulation results for a very wide range of signal-to-noise ratio (SNR) values.Comment: 5 pages, 5 figures, Submitted to IEEE International Symposium on Information Theory, ISIT 2013, Istanbul, Turke