Oscillation of linear ordinary differential equations: on a theorem by A. Grigoriev

We give a simplified proof and an improvement of a recent theorem by A. Grigoriev, placing an upper bound for the number of roots of linear combinations of solutions to systems of linear equations with polynomial or rational coefficients.Comment: 16 page

Gated communities: Definitions, causes and consequences

Gated communities became an 'object of study' in the 1990s as social scientists observed their growth in several cities; they are now a feature of the urban landscape in most cities around the world. The expansion of gated communities has led to prolific research, examining different aspects of this type of residential development and providing evidence from case studies worldwide. This paper reviews how gated communities are conceptualised according to the literature and identifies the main factors influencing their development. It also considers spatial, economic, political and social consequences of the development of gated communities. These elements should be taken into account by planners and policymakers to minimise their negative impacts and maximise the positive consequences of a residential option that is likely to be part of the urban landscape for a long time

Graded associative conformal algebras of finite type

In this paper, we consider graded associative conformal algebras. The class of these objects includes pseudo-algebras over non-cocommutative Hopf algebras of regular functions on some linear algebraic groups. In particular, an associative conformal algebra which is graded by a finite group $\Gamma$ is a pseudo-algebra over the coordinate Hopf algebra of a linear algebraic group $G$ such that the identity component $G^0$ is the affine line and $G/G^0\simeq \Gamma$. A classification of simple and semisimple graded associative conformal algebras of finite type is obtained

Sources contributing to the average extracellular concentration of dopamine in the nucleus accumbens

Mesolimbic dopamine neurons fire in both tonic and phasic modes resulting in detectable extracellular levels of dopamine in the nucleus accumbens (NAc). In the past, different techniques have targeted dopamine levels in the NAc to establish a basal concentration. In this study, we used in vivo fast scan cyclic voltammetry (FSCV) in the NAc of awake, freely moving rats. The experiments were primarily designed to capture changes in dopamine caused by phasic firing - that is, the measurement of dopamine 'transients'. These FSCV measurements revealed for the first time that spontaneous dopamine transients constitute a major component of extracellular dopamine levels in the NAc. A series of experiments were designed to probe regulation of extracellular dopamine. Lidocaine was infused into the ventral tegmental area, the site of dopamine cell bodies, to arrest neuronal firing. While there was virtually no instantaneous change in dopamine concentration, longer sampling revealed a decrease in dopamine transients and a time-averaged decrease in the extracellular level. Dopamine transporter inhibition using intravenous GBR12909 injections increased extracellular dopamine levels changing both frequency and size of dopamine transients in the NAc. To further unmask the mechanics governing extracellular dopamine levels we used intravenous injection of the vesicular monoamine transporter (VMAT2) inhibitor, tetrabenazine, to deplete dopamine storage and increase cytoplasmic dopamine in the nerve terminals. Tetrabenazine almost abolished phasic dopamine release but increased extracellular dopamine to ~500 nM, presumably by inducing reverse transport by dopamine transporter (DAT). Taken together, data presented here show that average extracellular dopamine in the NAc is low (20-30 nM) and largely arises from phasic dopamine transients

Genetic inhibition of neurotransmission reveals role of glutamatergic input to dopamine neurons in high-effort behavior

Midbrain dopamine neurons are crucial for many behavioral and cognitive functions. As the major excitatory input, glutamatergic afferents are important for control of the activity and plasticity of dopamine neurons. However, the role of glutamatergic input as a whole onto dopamine neurons remains unclear. Here we developed a mouse line in which glutamatergic inputs onto dopamine neurons are specifically impaired, and utilized this genetic model to directly test the role of glutamatergic inputs in dopamine-related functions. We found that while motor coordination and reward learning were largely unchanged, these animals showed prominent deficits in effort-related behavioral tasks. These results provide genetic evidence that glutamatergic transmission onto dopaminergic neurons underlies incentive motivation, a willingness to exert high levels of effort to obtain reinforcers, and have important implications for understanding the normal function of the midbrain dopamine system.Fil: Hutchison, M. A.. National Institutes of Health; Estados UnidosFil: Gu, X.. National Institutes of Health; Estados UnidosFil: Adrover, Martín Federico. National Institutes of Health; Estados Unidos. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Investigaciones en Ingeniería Genética y Biología Molecular "Dr. Héctor N. Torres"; ArgentinaFil: Lee, M. R.. National Institutes of Health; Estados UnidosFil: Hnasko, T. S.. University of California at San Diego; Estados UnidosFil: Alvarez, V. A.. National Institutes of Health; Estados UnidosFil: Lu, W.. National Institutes of Health; Estados Unido

Dynamic Integration of Reward and Stimulus Information in Perceptual Decision-Making

In perceptual decision-making, ideal decision-makers should bias their choices toward alternatives associated with larger rewards, and the extent of the bias should decrease as stimulus sensitivity increases. When responses must be made at different times after stimulus onset, stimulus sensitivity grows with time from zero to a final asymptotic level. Are decision makers able to produce responses that are more biased if they are made soon after stimulus onset, but less biased if they are made after more evidence has been accumulated? If so, how close to optimal can they come in doing this, and how might their performance be achieved mechanistically? We report an experiment in which the payoff for each alternative is indicated before stimulus onset. Processing time is controlled by a “go” cue occurring at different times post stimulus onset, requiring a response within msec. Reward bias does start high when processing time is short and decreases as sensitivity increases, leveling off at a non-zero value. However, the degree of bias is sub-optimal for shorter processing times. We present a mechanistic account of participants' performance within the framework of the leaky competing accumulator model [1], in which accumulators for each alternative accumulate noisy information subject to leakage and mutual inhibition. The leveling off of accuracy is attributed to mutual inhibition between the accumulators, allowing the accumulator that gathers the most evidence early in a trial to suppress the alternative. Three ways reward might affect decision making in this framework are considered. One of the three, in which reward affects the starting point of the evidence accumulation process, is consistent with the qualitative pattern of the observed reward bias effect, while the other two are not. Incorporating this assumption into the leaky competing accumulator model, we are able to provide close quantitative fits to individual participant data

High Accordance in Prognosis Prediction of Colorectal Cancer across Independent Datasets by Multi-Gene Module Expression Profiles

A considerable portion of patients with colorectal cancer have a high risk of disease recurrence after surgery. These patients can be identified by analyzing the expression profiles of signature genes in tumors. But there is no consensus on which genes should be used and the performance of specific set of signature genes varies greatly with different datasets, impeding their implementation in the routine clinical application. Instead of using individual genes, here we identified functional multi-gene modules with significant expression changes between recurrent and recurrence-free tumors, used them as the signatures for predicting colorectal cancer recurrence in multiple datasets that were collected independently and profiled on different microarray platforms. The multi-gene modules we identified have a significant enrichment of known genes and biological processes relevant to cancer development, including genes from the chemokine pathway. Most strikingly, they recruited a significant enrichment of somatic mutations found in colorectal cancer. These results confirmed the functional relevance of these modules for colorectal cancer development. Further, these functional modules from different datasets overlapped significantly. Finally, we demonstrated that, leveraging above information of these modules, our module based classifier avoided arbitrary fitting the classifier function and screening the signatures using the training data, and achieved more consistency in prognosis prediction across three independent datasets, which holds even using very small training sets of tumors