Scenario Cluster Lagrangian Decomposition in two stage stochastic mixed 0-1 optimization

In this paper we introduce four scenario Cluster based Lagrangian Decomposition (CLD) procedures for obtaining strong lower bounds to the (optimal) solution value of two-stage stochastic mixed 0-1 problems. At each iteration of the Lagrangian based procedures, the traditional aim consists of obtaining the solution value of the corresponding Lagrangian dual via solving scenario submodels once the nonanticipativity constraints have been dualized. Instead of considering a splitting variable representation over the set of scenarios, we propose to decompose the model into a set of scenario clusters. We compare the computational performance of the four Lagrange multiplier updating procedures, namely the Subgradient Method, the Volume Algorithm, the Progressive Hedging Algorithm and the Dynamic Constrained Cutting Plane scheme for different numbers of scenario clusters and different dimensions of the original problem. Our computational experience shows that the CLD bound and its computational effort depend on the number of scenario clusters to consider. In any case, our results show that the CLD procedures outperform the traditional LD scheme for single scenarios both in the quality of the bounds and computational effort. All the procedures have been implemented in a C++ experimental code. A broad computational experience is reported on a test of randomly generated instances by using the MIP solvers COIN-OR and CPLEX for the auxiliary mixed 0-1 cluster submodels, this last solver within the open source engine COIN-OR. We also give computational evidence of the model tightening effect that the preprocessing techniques, cut generation and appending and parallel computing tools have in stochastic integer optimization. Finally, we have observed that the plain use of both solvers does not provide the optimal solution of the instances included in the testbed with which we have experimented but for two toy instances in affordable elapsed time. On the other hand the proposed procedures provide strong lower bounds (or the same solution value) in a considerably shorter elapsed time for the quasi-optimal solution obtained by other means for the original stochastic problem.

Generating cluster submodels from a multistage stochastic mixed integer optimization model using break stage

We present a scheme to generate clusters submodels with stage ordering from a (symmetric or a nonsymmetric one) multistage stochastic mixed integer optimization model using break stage. We consider a stochastic model in compact representation and MPS format with a known scenario tree. The cluster submodels are built by storing first the 0-1 the variables, stage by stage, and then the continuous ones, also stage by stage. A C++ experimental code has been implemented for reordering the stochastic model as well as the cluster decomposition after the relaxation of the non-anticipativiy constraints until the so-called breakstage. The computational experience shows better performance of the stage ordering in terms of elapsed time in a randomly generated testbed of multistage stochastic mixed integer problems.

Cytokine pathway disruption in a mouse model of schizophrenia induced by Munc18-1a overexpression in the brain

Background: An accumulating body of evidence points to the significance of neuroinflammation and immunogenetics in schizophrenia, and an imbalance of cytokines in the central nervous system (CNS) has been suggested to be associated with the disorder. Munc18-overexpressing mice (Munc18-OE) have provided a model for the study of the alterations that may underlie the symptoms of subjects with schizophrenia. The aim of the present study was to elucidate the involvement of neuroinflammation and cytokine imbalance in this model. Methods: Cytokines were evaluated in the cortex and the striatum of Munc18-OE and wild-type (WT) mice by enzyme-linked immunosorbent assay (ELISA). Protein levels of specific microglia and macrophage, astrocytic and neuroinflammation markers were quantified by western blot in the cortex and the striatum of Munc18-OE and WT mice. Results: Each cytokine evaluated (Interferon-gamma (IFN-gamma), Tumor Necrosis Factor-alpha (TNF-alpha), Interleukin-2 (IL-2) and CCL2 chemokine) was present at higher levels in the striatum of Munc18-OE mice than WT. Cortical TNF-alpha and IL-2 levels were significantly lower in Munc18-OE mice than WT mice. The microglia and macrophage marker CD11b was lower in the cortexes of Munc18-OE mice than WT, but no differences were observed in the striatum. Glial Fibrillary Acidic Protein (GFAP) and Nuclear Factor-kappaB (NF-kappa B)p65 levels were not different between the groups. Interleukin-1beta (IL-1 beta) and IL-6 levels were beneath detection limits. Conclusions: The disrupted levels of cytokines detected in the brain of Munc18-OE mice was found to be similar to clinical reports and endorses study of this type for analysis of this aspect of the disorder. The lower CD11b expression in the cortex but not in the striatum of the Munc18-OE mice may reflect differences in physiological activity. The cytokine expression pattern observed in Munc18-OE mice is similar to a previously published model of schizophrenia caused by maternal immune activation. Together, these data suggest a possible role for an immune imbalance in this disorder.

Epitope mapping of antibodies to alpha-synuclein in LRRK2 mutation carriers, idiopathic Parkinson disease patients, and healthy controls

Alpha-synuclein (Snca) plays a major role in Parkinson disease (PD). Circulating anti-Snca antibodies has been described in PD patients and healthy controls, but they have been poorly characterized. This study was designed to assess the prevalence of anti-Snca reactivity in human subjects carrying the LRRK2 mutation, idiopathic PD (iPD) patients, and healthy controls and to map the epitopes of the anti-Snca antibodies. Antibodies to Snca were detected by ELISA and immunoblotting using purified recombinant Snca in plasma from individuals carrying LRRK2 mutations (104), iPD patients (59), and healthy controls (83). Epitopes of antibodies were mapped using recombinant protein constructs comprising different regions of Snca. Clear positive anti-Snca reactivity showed no correlation with age, sex, years of evolution, or the disability scores for PD patients and anti-Snca reactivity was not prevalent in human patients with other neurological or autoimmune diseases. Thirteen of the positive individuals were carriers of LRRK2 mutations either non-manifesting (8 out 49 screened) or manifesting (5 positive out 55), three positive (out of 59) were iPD patients, and five positive (out of 83) were healthy controls. Epitope mapping showed that antibodies against the N-terminal (a.a. 1-60) or C-terminal (a.a. 109-140) regions of Snca predominate in LRRK2 mutation carriers and iPD patients, being N122 a critical amino acid for recognition by the anti-C-terminal directed antibodies. Anti-Snca circulating antibodies seem to cluster within families carrying the LRRK2 mutation indicating possible genetic or common environmental factors in the generation of anti-Snca antibodies. These results suggest that case-controls' studies are insufficient and further studies in family cohorts of patients and healthy controls should be undertaken, to progress in the understanding of the possible relationship of anti-Snca antibodies and PD patholog

Altered expression of Alzheimer's disease-related genes in the cerebellum of autistic patients: a model for disrupted brain connectome and therapy

Autism and Alzheimer's disease (AD) are, respectively, neurodevelopmental and degenerative diseases with an increasing epidemiological burden. The AD-associated amyloid-beta precursor protein-alpha has been shown to be elevated in severe autism, leading to the 'anabolic hypothesis' of its etiology. Here we performed a focused microarray analysis of genes belonging to NOTCH and WNT signaling cascades, as well as genes related to AD and apoptosis pathways in cerebellar samples from autistic individuals, to provide further evidence for pathological relevance of these cascades for autism. By using the limma package from R and false discovery rate, we demonstrated that 31% (116 out of 374) of the genes belonging to these pathways displayed significant changes in expression (corrected P-values <0.05), with mitochondria- related genes being the most downregulated. We also found upregulation of GRIN1, the channel-forming subunit of NMDA glutamate receptors, and MAP3K1, known activator of the JNK and ERK pathways with anti-apoptotic effect. Expression of PSEN2 (presinilin 2) and APBB1 (or F65) were significantly lower when compared with control samples. Based on these results, we propose a model of NMDA glutamate receptor-mediated ERK activation of alpha-secretase activity and mitochondrial adaptation to apoptosis that may explain the early brain overgrowth and disruption of synaptic plasticity and connectome in autism. Finally, systems pharmacology analyses of the model that integrates all these genes together (NOWADA) highlighted magnesium (Mg2+) and rapamycin as most efficient drugs to target this network model in silico. Their potential therapeutic application, in the context of autism, is therefore discussed.