Lagrangian Numerical Methods for Ocean Biogeochemical Simulations

We propose two closely--related Lagrangian numerical methods for the simulation of physical processes involving advection, reaction and diffusion. The methods are intended to be used in settings where the flow is nearly incompressible and the P\'eclet numbers are so high that resolving all the scales of motion is unfeasible. This is commonplace in ocean flows. Our methods consist in augmenting the method of characteristics, which is suitable for advection--reaction problems, with couplings among nearby particles, producing fluxes that mimic diffusion, or unresolved small-scale transport. The methods conserve mass, obey the maximum principle, and allow to tune the strength of the diffusive terms down to zero, while avoiding unwanted numerical dissipation effects

Efficient approximation of functions of some large matrices by partial fraction expansions

Some important applicative problems require the evaluation of functions $\Psi$ of large and sparse and/or \emph{localized} matrices $A$. Popular and interesting techniques for computing $\Psi(A)$ and $\Psi(A)\mathbf{v}$, where $\mathbf{v}$ is a vector, are based on partial fraction expansions. However, some of these techniques require solving several linear systems whose matrices differ from $A$ by a complex multiple of the identity matrix $I$ for computing $\Psi(A)\mathbf{v}$ or require inverting sequences of matrices with the same characteristics for computing $\Psi(A)$. Here we study the use and the convergence of a recent technique for generating sequences of incomplete factorizations of matrices in order to face with both these issues. The solution of the sequences of linear systems and approximate matrix inversions above can be computed efficiently provided that $A^{-1}$ shows certain decay properties. These strategies have good parallel potentialities. Our claims are confirmed by numerical tests

Computing the matrix Mittag-Leffler function with applications to fractional calculus

The computation of the Mittag-Leffler (ML) function with matrix arguments, and some applications in fractional calculus, are discussed. In general the evaluation of a scalar function in matrix arguments may require the computation of derivatives of possible high order depending on the matrix spectrum. Regarding the ML function, the numerical computation of its derivatives of arbitrary order is a completely unexplored topic; in this paper we address this issue and three different methods are tailored and investigated. The methods are combined together with an original derivatives balancing technique in order to devise an algorithm capable of providing high accuracy. The conditioning of the evaluation of matrix ML functions is also studied. The numerical experiments presented in the paper show that the proposed algorithm provides high accuracy, very often close to the machine precision

Variation in dopamine D2 and serotonin 5-HT2A receptor genes is associated with working memory processing and response to treatment with antipsychotics

Dopamine D2 and serotonin 5-HT2A receptors contribute to modulate prefrontal cortical physiology and response to treatment with antipsychotics in schizophrenia. Similarly, functional variation in the genes encoding these receptors is also associated with these phenotypes. In particular, the DRD2 rs1076560 T allele predicts a lower ratio of expression of D2 short/long isoforms, suboptimal working memory processing, and better response to antipsychotic treatment compared with the G allele. Furthermore, the HTR2A T allele is associated with lower 5-HT2A expression, impaired working memory processing, and poorer response to antipsychotics compared with the C allele. Here, we investigated in healthy subjects whether these functional polymorphisms have a combined effect on prefrontal cortical physiology and related cognitive behavior linked to schizophrenia as well as on response to treatment with secondgeneration antipsychotics in patients with schizophrenia. In a total sample of 620 healthy subjects, we found that subjects with the rs1076560 T and rs6314 T alleles have greater fMRI prefrontal activity during working memory. Similar results were obtained within the attentional domain. Also, the concomitant presence of the rs1076560 T/rs6314 T alleles also predicted lower behavioral accuracy during working memory. Moreover, we found that rs1076560 T carrier/rs6314 CC individuals had better responses to antipsychotic treatment in two independent samples of patients with schizophrenia (n¼63 and n¼54, respectively), consistent with the previously reported separate effects of these genotypes. These results indicate that DRD2 and HTR2A genetic variants together modulate physiological prefrontal efficiency during working memory and also modulate the response to antipsychotics. Therefore, these results suggest that further exploration is needed to better understand the clinical consequences of these genotype–phenotype relationships

Prefronto-striatal physiology is associated with schizotypy and is modulated by a functional variant of DRD2

Peer reviewe

DRD2 genotype predicts prefrontal activity during working memory after stimulation of D2 receptors with bromocriptine

Rationale: Pharmacological stimulation of D2 receptors modulates prefrontal neural activity associated with working memory (WM) processing. The T allele of a functional single-nucleotide polymorphism (SNP) within DRD2 (rs1076560 G > T) predicts reduced relative expression of the D2S receptor isoform and less efficient neural cortical responses during WM tasks. Objective: We used functional MRI to test the hypothesis that DRD2 rs1076560 genotype interacts with pharmacological stimulation of D2 receptors with bromocriptine on prefrontal responses during different loads of a spatial WM task (N-Back). Methods: Fifty-three healthy subjects (38 GG and 15 GT) underwent two 3-T functional MRI scans while performing the 1-, 2- and 3-Back versions of the N-Back WM task. Before the imaging sessions, either bromocriptine or placebo was administered to all subjects in a counterbalanced order. A factorial repeated-measures ANOVA within SPM8 (p < 0.05, family-wise error corrected) was used. Results: On bromocriptine, GG subjects had reduced prefrontal activity at 3-Back together with a significant decrement in performance, compared with placebo. On the other hand, GT subjects had lower activity for the same level of performance at 1-Back but a trend for reduced behavioral performance in the face of unchanged activity at 2-Back. Conclusions: These results indicate that bromocriptine stimulation modulates prefrontal activity in terms of disengagement or of efficiency depending on DRD2 genotype and working memory load

Variation in dopamine D2 and serotonin 5-HT2A receptor genes is associated with working memory processing and response to treatment with antipsychotics

Dopamine D2 and serotonin 5-HT2A receptors contribute to modulate prefrontal cortical physiology and response to treatment with antipsychotics in schizophrenia. Similarly, functional variation in the genes encoding these receptors is also associated with these phenotypes. In particular, the DRD2 rs1076560 T allele predicts a lower ratio of expression of D2 short/long isoforms, suboptimal working memory processing, and better response to antipsychotic treatment compared with the G allele. Furthermore, the HTR2A T allele is associated with lower 5-HT2A expression, impaired working memory processing, and poorer response to antipsychotics compared with the C allele. Here, we investigated in healthy subjects whether these functional polymorphisms have a combined effect on prefrontal cortical physiology and related cognitive behavior linked to schizophrenia as well as on response to treatment with secondgeneration antipsychotics in patients with schizophrenia. In a total sample of 620 healthy subjects, we found that subjects with the rs1076560 T and rs6314 T alleles have greater fMRI prefrontal activity during working memory. Similar results were obtained within the attentional domain. Also, the concomitant presence of the rs1076560 T/rs6314 T alleles also predicted lower behavioral accuracy during working memory. Moreover, we found that rs1076560 T carrier/rs6314 CC individuals had better responses to antipsychotic treatment in two independent samples of patients with schizophrenia (n¼63 and n¼54, respectively), consistent with the previously reported separate effects of these genotypes. These results indicate that DRD2 and HTR2A genetic variants together modulate physiological prefrontal efficiency during working memory and also modulate the response to antipsychotics. Therefore, these results suggest that further exploration is needed to better understand the clinical consequences of these genotype–phenotype relationships

A matrix approach for partial differential equations with Riesz space fractional derivatives

Fractional partial differential equations are emerging in many scientific fields and their numerical solution is becoming a fundamental topic. In this paper we consider the Riesz fractional derivative operator and its discretization by fractional centered differences. The resulting matrix is studied, with an interesting result on a connection between the decay behavior of its entries and the short memory principle from fractional calculus. The Shift-and-Invert method is then applied to approximate the solution of the partial differential equation as the action of the matrix exponential on a suitable vector which mimics the given initial conditions. The numerical results confirm the good approximation quality and encourage the use of the proposed approach