Impossibility of independence amplification in Kolmogorov complexity theory

The paper studies randomness extraction from sources with bounded independence and the issue of independence amplification of sources, using the framework of Kolmogorov complexity. The dependency of strings $x$ and $y$ is ${\rm dep}(x,y) = \max\{C(x) - C(x \mid y), C(y) - C(y\mid x)\}$, where $C(\cdot)$ denotes the Kolmogorov complexity. It is shown that there exists a computable Kolmogorov extractor $f$ such that, for any two $n$-bit strings with complexity $s(n)$ and dependency $\alpha(n)$, it outputs a string of length $s(n)$ with complexity $s(n)- \alpha(n)$ conditioned by any one of the input strings. It is proven that the above are the optimal parameters a Kolmogorov extractor can achieve. It is shown that independence amplification cannot be effectively realized. Specifically, if (after excluding a trivial case) there exist computable functions $f_1$ and $f_2$ such that ${\rm dep}(f_1(x,y), f_2(x,y)) \leq \beta(n)$ for all $n$-bit strings $x$ and $y$ with ${\rm dep}(x,y) \leq \alpha(n)$, then $\beta(n) \geq \alpha(n) - O(\log n)$

Cell-Type-Specific Recruitment of Amygdala Interneurons to Hippocampal Theta Rhythm and Noxious Stimuli In Vivo

Neuronal synchrony in the basolateral amygdala (BLA) is critical for emotional behavior. Coordinated theta-frequency oscillations between the BLA and the hippocampus and precisely timed integration of salient sensory stimuli in the BLA are involved in fear conditioning. We characterized GABAergic interneuron types of the BLA and determined their contribution to shaping these network activities. Using in vivo recordings in rats combined with the anatomical identification of neurons, we found that the firing of BLA interneurons associated with network activities was cell type specific. The firing of calbindin-positive interneurons targeting dendrites was precisely theta-modulated, but other cell types were heterogeneously modulated, including parvalbumin-positive basket cells. Salient sensory stimuli selectively triggered axo-axonic cells firing and inhibited firing of a disctinct projecting interneuron type. Thus, GABA is released onto BLA principal neurons in a time-, domain-, and sensory-specific manner. These specific synaptic actions likely cooperate to promote amygdalo-hippocampal synchrony involved in emotional memory formation

Computable randomness is about more than probabilities

We introduce a notion of computable randomness for infinite sequences that generalises the classical version in two important ways. First, our definition of computable randomness is associated with imprecise probability models, in the sense that we consider lower expectations (or sets of probabilities) instead of classical 'precise' probabilities. Secondly, instead of binary sequences, we consider sequences whose elements take values in some finite sample space. Interestingly, we find that every sequence is computably random with respect to at least one lower expectation, and that lower expectations that are more informative have fewer computably random sequences. This leads to the intriguing question whether every sequence is computably random with respect to a unique most informative lower expectation. We study this question in some detail and provide a partial answer

Algorithmic statistics: forty years later

Algorithmic statistics has two different (and almost orthogonal) motivations. From the philosophical point of view, it tries to formalize how the statistics works and why some statistical models are better than others. After this notion of a "good model" is introduced, a natural question arises: it is possible that for some piece of data there is no good model? If yes, how often these bad ("non-stochastic") data appear "in real life"? Another, more technical motivation comes from algorithmic information theory. In this theory a notion of complexity of a finite object (=amount of information in this object) is introduced; it assigns to every object some number, called its algorithmic complexity (or Kolmogorov complexity). Algorithmic statistic provides a more fine-grained classification: for each finite object some curve is defined that characterizes its behavior. It turns out that several different definitions give (approximately) the same curve. In this survey we try to provide an exposition of the main results in the field (including full proofs for the most important ones), as well as some historical comments. We assume that the reader is familiar with the main notions of algorithmic information (Kolmogorov complexity) theory.Comment: Missing proofs adde

On the succinctness of query rewriting over shallow ontologies

We investigate the succinctness problem for conjunctive query rewritings over OWL2QL ontologies of depth 1 and 2 by means of hypergraph programs computing Boolean functions. Both positive and negative results are obtained. We show that, over ontologies of depth 1, conjunctive queries have polynomial-size nonrecursive datalog rewritings; tree-shaped queries have polynomial positive existential rewritings; however, in the worst case, positive existential rewritings can be superpolynomial. Over ontologies of depth 2, positive existential and nonrecursive datalog rewritings of conjunctive queries can suffer an exponential blowup, while first-order rewritings can be superpolynomial unless NP �is included in P/poly. We also analyse rewritings of tree-shaped queries over arbitrary ontologies and note that query entailment for such queries is fixed-parameter tractable

The biogeochemistry of carbon across a gradient of streams and rivers within the Congo Basin

Author Posting. © American Geophysical Union, 2014. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research: Biogeosciences 119 (2014): 687–702, doi:10.1002/2013JG002442.Dissolved organic carbon (DOC) and inorganic carbon (DIC, pCO2), lignin biomarkers, and theoptical properties of dissolved organic matter (DOM) were measured in a gradient of streams and rivers within the Congo Basin, with the aim of examining how vegetation cover and hydrology influences the composition and concentration of fluvial carbon (C). Three sampling campaigns (February 2010, November 2010, and August 2011) spanning 56 sites are compared by subbasin watershed land cover type (savannah, tropical forest, and swamp) and hydrologic regime (high, intermediate, and low). Land cover properties predominately controlled the amount and quality of DOC, chromophoric DOM (CDOM) and lignin phenol concentrations (∑8) exported in streams and rivers throughout the Congo Basin. Higher DIC concentrations and changing DOM composition (lower molecular weight, less aromatic C) during periods of low hydrologic flow indicated shifting rapid overland supply pathways in wet conditions to deeper groundwater inputs during drier periods. Lower DOC concentrations in forest and swamp subbasins were apparent with increasing catchment area, indicating enhanced DOC loss with extended water residence time. Surface water pCO2 in savannah and tropical forest catchments ranged between 2,600 and 11,922 µatm, with swamp regions exhibiting extremely high pCO2 (10,598–15,802 µatm), highlighting their potential as significant pathways for water-air efflux. Our data suggest that the quantity and quality of DOM exported to streams and rivers are largely driven by terrestrial ecosystem structure and that anthropogenic land use or climate change may impact fluvial C composition and reactivity, with ramifications for regional C budgets and future climate scenarios.This work was supported by the National Science Foundation as part of the ETBC Collaborative Research: Controls on the Flux, Age, and Composition of Terrestrial Organic Carbon Exported by Rivers to the Ocean (0851101 and 0851015).2014-10-3

Propositional update operators based on formula/literal dependence

International audienceWe present and study a general family of belief update operators in a propositional setting. Its operators are based on formula/literal dependence, which is more fine-grained than the notion of formula/variable dependence that was proposed in the literature: formula/variable dependence is a particular case of formula/literal dependence. Our update operators are defined according to the "forget-then-conjoin" scheme: updating a belief base by an input formula consists in first forgetting in the base every literal on which the input formula has a negative influence, and then conjoining the resulting base with the input formula. The operators of our family differ by the underlying notion of formula/literal dependence, which may be defined syntactically or semantically, and which may or may not exploit further information like known persistent literals and pre-set dependencies. We argue that this allows to handle the frame problem and the ramification problem in a more appropriate way. We evaluate the update operators of our family w.r.t. two important dimensions: the logical dimension, by checking the status of the Katsuno-Mendelzon postulates for update, and the computational dimension, by identifying the complexity of a number of decision problems (including model checking, consistency and inference), both in the general case and in some restricted cases, as well as by studying compactability issues. It follows that several operators of our family are interesting alternatives to previous belief update operators