Congruent families and invariant tensors

Classical results of Chentsov and Campbell state that -- up to constant multiples -- the only $2$-tensor field of a statistical model which is invariant under congruent Markov morphisms is the Fisher metric and the only invariant $3$-tensor field is the Amari-Chentsov tensor. We generalize this result for arbitrary degree $n$, showing that any family of $n$-tensors which is invariant under congruent Markov morphisms is algebraically generated by the canonical tensor fields defined in an earlier paper

Quantifying structure in networks

We investigate exponential families of random graph distributions as a framework for systematic quantification of structure in networks. In this paper we restrict ourselves to undirected unlabeled graphs. For these graphs, the counts of subgraphs with no more than k links are a sufficient statistics for the exponential families of graphs with interactions between at most k links. In this framework we investigate the dependencies between several observables commonly used to quantify structure in networks, such as the degree distribution, cluster and assortativity coefficients.Comment: 17 pages, 3 figure

Complexity Measures from Interaction Structures

We evaluate new complexity measures on the symbolic dynamics of coupled tent maps and cellular automata. These measures quantify complexity in terms of $k$-th order statistical dependencies that cannot be reduced to interactions between $k-1$ units. We demonstrate that these measures are able to identify complex dynamical regimes.Comment: 11 pages, figures improved, minor changes to the tex

Treatment technologies of fresh market wastewater

Fresh Market Wastewater (FMWW) is rich with high amounts of suspended solids, organic and inorganic compounds, nutrients, gases and some elements which come from fish entrails and seafood preparation sales, meat cutting, poultry slaughtering, fruits and vegetables sales. The excess of these parameters are harmful to the aquatic life since the FMWW is usually discharged into the drainage systems without any treatment or partial treatment. The FMWW technologies are developed due to some technical factors influencing the designation and construction. There are several projects of fresh market treatment technologies used on site area in small scale which could be replicated to other fresh market, and some case study have been tested in laboratory batch experiments. All the projects exhibited an efficiency to reduce critical parameters in FMWW and give positive impacts to the locals and responsible parties

Compressibility and probabilistic proofs

We consider several examples of probabilistic existence proofs using compressibility arguments, including some results that involve Lov\'asz local lemma.Comment: Invited talk for CiE 2017 (full version

Geometry of Policy Improvement

We investigate the geometry of optimal memoryless time independent decision making in relation to the amount of information that the acting agent has about the state of the system. We show that the expected long term reward, discounted or per time step, is maximized by policies that randomize among at most $k$ actions whenever at most $k$ world states are consistent with the agent's observation. Moreover, we show that the expected reward per time step can be studied in terms of the expected discounted reward. Our main tool is a geometric version of the policy improvement lemma, which identifies a polyhedral cone of policy changes in which the state value function increases for all states.Comment: 8 page

Mitochondrial Calcium Deregulation in the Mechanism of Beta-Amyloid and Tau Pathology

Aggregation and deposition of β-amyloid and/or tau protein are the key neuropathological features in neurodegenerative disorders such as Alzheimer’s disease (AD) and other tauopathies including frontotemporal dementia (FTD). The interaction between oxidative stress, mitochondrial dysfunction and the impairment of calcium ions (Ca2+) homeostasis induced by misfolded tau and β-amyloid plays an important role in the progressive neuronal loss occurring in specific areas of the brain. In addition to the control of bioenergetics and ROS production, mitochondria are fine regulators of the cytosolic Ca2+ homeostasis that induce vital signalling mechanisms in excitable cells such as neurons. Impairment in the mitochondrial Ca2+ uptake through the mitochondrial Ca2+ uniporter (MCU) or release through the Na+/Ca2+ exchanger may lead to mitochondrial Ca2+ overload and opening of the permeability transition pore inducing neuronal death. Recent evidence suggests an important role for these mechanisms as the underlying causes for neuronal death in β-amyloid and tau pathology. The present review will focus on the mechanisms that lead to cytosolic and especially mitochondrial Ca2+ disturbances occurring in AD and tau-induced FTD, and propose possible therapeutic interventions for these disorders

Geometry of Information Integration

Information geometry is used to quantify the amount of information integration within multiple terminals of a causal dynamical system. Integrated information quantifies how much information is lost when a system is split into parts and information transmission between the parts is removed. Multiple measures have been proposed as a measure of integrated information. Here, we analyze four of the previously proposed measures and elucidate their relations from a viewpoint of information geometry. Two of them use dually flat manifolds and the other two use curved manifolds to define a split model. We show that there are hierarchical structures among the measures. We provide explicit expressions of these measures

Pregnancy Related Sequential Changes of the Foetal Fluids And Foetal Positioning in Sahel Goats

A study on pregnancy related, and sequential, changes in the Sahel goat foetal fluid and foetal disposition at various stages of pregnancy wasundertaken to provide basic data in these aspects of gestation in goats. Twenty five pregnant Sahel goats of known pregnancy stages, and managed under controlled conditions were used for this study. Thirtythree foetuses were obtained from these pregnancies of which 18 (54.5%) were females and 15 (45.5%) were males; 17 (68%) had single foetus,8(32%) twin foetuses. Transuterine migration was 23.53% in single and 37.5% in twin pregnancies. The foetal fluid changes showed that the volume of the amniotic fluid increased from day 28 (21.0 ± 0.33 ml)of gestation to day 112 (500 ± 15.81 ml) and then dropped onwards up to day 140 (220 ± 10.80 ml). Conversely, the allantoic fluid (25.5 ± 2.00 ml at 28d to 735.0 ± 17.08 ml at 140d) continued to increase in volume throughout pregnancy. The volume, colour, consistency and pH changed with increase in gestation period. The specific gravity of the amnioticfluid increased with advancing pregnancy. The results of this study suggest that urine enters first into amniotic cavity and then into the allantoic cavityby 112d pregnancy in goats. The present study also provided a guide to be used in assessing the volume and consistencies of foetal fluids in goats and the intrauterine positioning of foetuses as a measure to monitor and manage pregnant Sahel does.KEY WORDS: fluids, foetal, position, Sahel goat,sequential

Knockouts, Robustness and Cell Cycles

The response to a knockout of a node is a characteristic feature of a networked dynamical system. Knockout resilience in the dynamics of the remaining nodes is a sign of robustness. Here we study the effect of knockouts for binary state sequences and their implementations in terms of Boolean threshold networks. Beside random sequences with biologically plausible constraints, we analyze the cell cycle sequence of the species Saccharomyces cerevisiae and the Boolean networks implementing it. Comparing with an appropriate null model we do not find evidence that the yeast wildtype network is optimized for high knockout resilience. Our notion of knockout resilience weakly correlates with the size of the basin of attraction, which has also been considered a measure of robustness.Comment: 11 pages, 3 figures, 3 table