Equilibration through local information exchange in networks

We study the equilibrium states of energy functions involving a large set of real variables, defined on the links of sparsely connected networks, and interacting at the network nodes, using the cavity and replica methods. When applied to the representative problem of network resource allocation, an efficient distributed algorithm is devised, with simulations showing full agreement with theory. Scaling properties with the network connectivity and the resource availability are found.Comment: v1: 7 pages, 1 figure, v2: 4 pages, 2 figures, simplified analysis and more organized results, v3: minor change

Toeplitz Inverse Covariance-Based Clustering of Multivariate Time Series Data

Subsequence clustering of multivariate time series is a useful tool for discovering repeated patterns in temporal data. Once these patterns have been discovered, seemingly complicated datasets can be interpreted as a temporal sequence of only a small number of states, or clusters. For example, raw sensor data from a fitness-tracking application can be expressed as a timeline of a select few actions (i.e., walking, sitting, running). However, discovering these patterns is challenging because it requires simultaneous segmentation and clustering of the time series. Furthermore, interpreting the resulting clusters is difficult, especially when the data is high-dimensional. Here we propose a new method of model-based clustering, which we call Toeplitz Inverse Covariance-based Clustering (TICC). Each cluster in the TICC method is defined by a correlation network, or Markov random field (MRF), characterizing the interdependencies between different observations in a typical subsequence of that cluster. Based on this graphical representation, TICC simultaneously segments and clusters the time series data. We solve the TICC problem through alternating minimization, using a variation of the expectation maximization (EM) algorithm. We derive closed-form solutions to efficiently solve the two resulting subproblems in a scalable way, through dynamic programming and the alternating direction method of multipliers (ADMM), respectively. We validate our approach by comparing TICC to several state-of-the-art baselines in a series of synthetic experiments, and we then demonstrate on an automobile sensor dataset how TICC can be used to learn interpretable clusters in real-world scenarios.Comment: This revised version fixes two small typos in the published versio

Network Inference via the Time-Varying Graphical Lasso

Many important problems can be modeled as a system of interconnected entities, where each entity is recording time-dependent observations or measurements. In order to spot trends, detect anomalies, and interpret the temporal dynamics of such data, it is essential to understand the relationships between the different entities and how these relationships evolve over time. In this paper, we introduce the time-varying graphical lasso (TVGL), a method of inferring time-varying networks from raw time series data. We cast the problem in terms of estimating a sparse time-varying inverse covariance matrix, which reveals a dynamic network of interdependencies between the entities. Since dynamic network inference is a computationally expensive task, we derive a scalable message-passing algorithm based on the Alternating Direction Method of Multipliers (ADMM) to solve this problem in an efficient way. We also discuss several extensions, including a streaming algorithm to update the model and incorporate new observations in real time. Finally, we evaluate our TVGL algorithm on both real and synthetic datasets, obtaining interpretable results and outperforming state-of-the-art baselines in terms of both accuracy and scalability

Dynamic Gaussian graphical models for modelling genomic networks

After sequencing the entire DNA for various organisms, the challenge has become understanding the functional interrelatedness of the genome. Only by understanding the pathways for various complex diseases can we begin to make sense of any type of treatment. Unfortu- nately, decyphering the genomic network structure is an enormous task. Even with a small number of genes the number of possible networks is very large. This problem becomes even more difficult, when we consider dynamical networks. We consider the problem of estimating a sparse dy- namic Gaussian graphical model with L1 penalized maximum likelihood of structured precision matrix. The structure can consist of specific time dynamics, known presence or absence of links in the graphical model or equality constraints on the parameters. The model is defined on the basis of partial correlations, which results in a specific class precision matrices. A priori L1 penalized maximum likelihood estimation in this class is extremely difficult, because of the above mentioned constraints, the computational complexity of the L1 constraint on the side of the usual positive-definite constraint. The implementation is non-trivial, but we show that the computation can be done effectively by taking advan- tage of an efficient maximum determinant algorithm developed in convex optimization

Likelihood Geometry

We study the critical points of monomial functions over an algebraic subset of the probability simplex. The number of critical points on the Zariski closure is a topological invariant of that embedded projective variety, known as its maximum likelihood degree. We present an introduction to this theory and its statistical motivations. Many favorite objects from combinatorial algebraic geometry are featured: toric varieties, A-discriminants, hyperplane arrangements, Grassmannians, and determinantal varieties. Several new results are included, especially on the likelihood correspondence and its bidegree. These notes were written for the second author's lectures at the CIME-CIRM summer course on Combinatorial Algebraic Geometry at Levico Terme in June 2013.Comment: 45 pages; minor changes and addition

A Neural Circuit Arbitrates between Persistence and Withdrawal in Hungry Drosophila

In pursuit of food, hungry animals mobilize significant energy resources and overcome exhaustion and fear. How need and motivation control the decision to continue or change behavior is not understood. Using a single fly treadmill, we show that hungry flies persistently track a food odor and increase their effort over repeated trials in the absence of reward suggesting that need dominates negative experience. We further show that odor tracking is regulated by two mushroom body output neurons (MBONs) connecting the MB to the lateral horn. These MBONs, together with dopaminergic neurons and Dop1R2 signaling, control behavioral persistence. Conversely, an octopaminergic neuron, VPM4, which directly innervates one of the MBONs, acts as a brake on odor tracking by connecting feeding and olfaction. Together, our data suggest a function for the MB in internal state-dependent expression of behavior that can be suppressed by external inputs conveying a competing behavioral drive

A critical role for astrocytes in hypercapnic vasodilation in brain

Cerebral blood flow (CBF) is controlled by arterial blood pressure, arterial CO2, arterial O2, and brain activity and is largely constant in the awake state. Although small changes in arterial CO2 are particularly potent to change CBF (1 mmHg variation in arterial CO2 changes CBF by 3-4%), the coupling mechanism is incompletely understood. We tested the hypothesis that astrocytic prostaglandin E2 (PgE2) plays a key role for cerebrovascular CO2 reactivity and that preserved synthesis of glutathione is essential for the full development of this response. We combined two-photon imaging microscopy in brain slices with in vivo work in rats and C57Bl/6J mice to examine the hemodynamic responses to CO2 and somatosensory stimulation before and after inhibition of astrocytic glutathione and PgE2 synthesis. We demonstrate that hypercapnia (increased CO2) evokes an increase in astrocyte [Ca2+]i and stimulates COX-1 activity. The enzyme downstream of COX-1 that synthesizes PgE2 (microsomal prostaglandin E synthase-1) depends critically for its vasodilator activity on the level of glutathione in the brain. We show that when glutathione levels are reduced, astrocyte calcium-evoked release of PgE2 is decreased and vasodilation triggered by astrocyte [Ca2+]i in vitro and by hypercapnia in vivo is inhibited. Astrocyte synthetic pathways, dependent on glutathione, are involved in cerebrovascular reactivity to CO2. Reductions in glutathione levels in ageing, stroke or schizophrenia could lead to dysfunctional regulation of CBF and subsequent neuronal damage

Whole blood long-chain n-3 fatty acids as a measure of fish oil compliance in children with acute lymphoblastic leukemia: a pilot study

Long-chain n-3 fatty acids (n-3 LCPUFA) may prevent chemotherapy-induced hyperlipidemia in children with acute lymphoblastic leukemia (ALL). However, compliance could be a problem and intake-biomarker correlations may be affected by bodyweight and blood transfusions. We assessed whole blood n-3 LCPUFA three times during the first 83 days of treatment in six 1-17-year-old children with ALL, who received 2.4-4.9 g/d n-3 LCPUFA depending on bodyweight. Mean compliance was 73%, which resulted in a 2.5-fold increase in blood n-3 LCPUFA irrespective of blood transfusions. The correlation between relative blood content of n-3 LCPUFA and intake in g/d across the study period was strong (r=0.76, p=0.001). When n-3 LCPUFA was expressed in absolute concentrations and intake per kg bodyweight the correlation decreased (r=0.39, p=0.164) and was driven by baseline values. Thus, relative content of n-3 LCPUFA in blood reflects fish oil compliance in children with ALL despite blood transfusions and differences in bodyweight

DHA effects in brain development and function

Docosahexaenoic acid (DHA) is a structural constituent of membranes specifically in the central nervous system. Its accumulation in the fetal brain takes place mainly during the last trimester of pregnancy and continues at very high rates up to the end of the second year of life. Since the endogenous formation of DHA seems to be relatively low, DHA intake may contribute to optimal conditions for brain development. We performed a narrative review on research on the associations between DHA levels and brain development and function throughout the lifespan. Data from cell and animal studies justify the indication of DHA in relation to brain function for neuronal cell growth and differentiation as well as in relation to neuronal signaling. Most data from human studies concern the contribution of DHA to optimal visual acuity development. Accumulating data indicate that DHA may have effects on the brain in infancy, and recent studies indicate that the effect of DHA may depend on gender and genotype of genes involved in the endogenous synthesis of DHA. While DHA levels may affect early development, potential effects are also increasingly recognized during childhood and adult life, suggesting a role of DHA in cognitive decline and in relation to major psychiatric disorders