Computing Equilibria of Semi-algebraic Economies Using Triangular Decomposition and Real Solution Classification

In this paper, we are concerned with the problem of determining the existence of multiple equilibria in economic models. We propose a general and complete approach for identifying multiplicities of equilibria in semi-algebraic economies, which may be expressed as semi-algebraic systems. The approach is based on triangular decomposition and real solution classification, two powerful tools of algebraic computation. Its effectiveness is illustrated by two examples of application.Comment: 24 pages, 5 figure

Closed-Loop Brain-Computer Interfaces for Memory Restoration Using Deep Brain Stimulation

The past two decades have witnessed the rapid growth of therapeutic brain-computer interfaces (BCI) targeting a diversity of brain dysfunctions. Among many neurosurgical procedures, deep brain stimulation (DBS) with neuromodulation technique has emerged as a fruitful treatment for neurodegenerative disorders such as epilepsy, Parkinson\u27s disease, post-traumatic amnesia, and Alzheimer\u27s disease, as well as neuropsychiatric disorders such as depression, obsessive-compulsive disorder, and schizophrenia. In parallel to the open-loop neuromodulation strategies for neuromotor disorders, recent investigations have demonstrated the superior performance of closed-loop neuromodulation systems for memory-relevant disorders due to the more sophisticated underlying brain circuitry during cognitive processes. Our efforts are focused on discovering unique neurophysiological patterns associated with episodic memories then applying control theoretical principles to achieve closed-loop neuromodulation of such memory-relevant oscillatory activity, especially, theta and gamma oscillations. First, we use a unique dataset with intracranial electrodes inserted simultaneously into the hippocampus and seven cortical regions across 40 human subjects to test for the presence of a pattern that the phase of hippocampal theta oscillation modulates gamma oscillations in the cortex, termed cross-regional phase-amplitude coupling (xPAC), representing a key neurophysiological mechanism that promotes the temporal organization of interregional oscillatory activities, which has not previously been observed in human subjects. We then establish that the magnitude of xPAC predicts memory encoding success along with other properties of xPAC. We find that strong functional xPAC occurs principally between the hippocampus and other mesial temporal structures, namely entorhinal and parahippocampal cortices, and that xPAC is overall stronger for posterior hippocampal connections. Next, we focus on hippocampal gamma power as a `biomarker\u27 and use a novel dataset in which open-loop DBS was applied to the posterior cingulate cortex (PCC) during the encoding of episodic memories. We evaluate the feasibility of modulating hippocampal power by a precise control of stimulation via a linear quadratic integral (LQI) controller based on autoregressive with exogenous input (ARX) modeling for in-vivo use. In the simulation framework, we demonstrate proposed BCI system achieves effective control of hippocampal gamma power in 15 out of 17 human subjects and we show our DBS pattern is physiologically safe with realistic time scales. Last, we further develop the PCC-applied binary-noise (BN) DBS paradigm targeting the neuromodulation of both hippocampal theta and gamma oscillatory power in 12 human subjects. We utilize a novel nonlinear autoregressive with exogenous input neural network (NARXNN) as the plant paired with a proportional–integral–derivative (PID) controller (NARXNN-PID) for delivering a precise stimulation pattern to achieve desired oscillatory power level. Compared to a benchmark consisted of a linear state-space model (LSSM) with a PID controller, we not only demonstrate that the superior performance of our NARXNN plant model but also show the greater capacity of NARXNN-PID architecture in controlling both hippocampal theta and gamma power. We outline further experimentation to test our BCI system and compare our findings to emerging closed-loop neuromodulation strategies

Three-dimensional ZnO hierarchical nanostructures: Solution phase synthesis and applications

Zinc oxide (ZnO) nanostructures have been studied extensively in the past 20 years due to their novel electronic, photonic, mechanical and electrochemical properties. Recently, more attention has been paid to assemble nanoscale building blocks into three-dimensional (3D) complex hierarchical structures, which not only inherit the excellent properties of the single building blocks but also provide potential applications in the bottom-up fabrication of functional devices. This review article focuses on 3D ZnO hierarchical nanostructures, and summarizes major advances in the solution phase synthesis, applications in environment, and electrical/electrochemical devices. We present the principles and growth mechanisms of ZnO nanostructures via different solution methods, with an emphasis on rational control of the morphology and assembly. We then discuss the applications of 3D ZnO hierarchical nanostructures in photocatalysis, field emission, electrochemical sensor, and lithium ion batteries. Throughout the discussion, the relationship between the device performance and the microstructures of 3D ZnO hierarchical nanostructures will be highlighted. This review concludes with a personal perspective on the current challenges and future research

Disruption of Nrf2 Enhances the Upregulation of Nuclear Factor-kappaB Activity, Tumor Necrosis Factor-α, and Matrix Metalloproteinase-9 after Spinal Cord Injury in Mice

Matrix metalloproteinase-9 (MMP-9) plays an important role in the acute periods of spinal cord injury (SCI), and its expression is related to the inflammation which could cause the disruption of the blood-spinal barrier (BBB). Nuclear factor erythroid 2-related factor 2 (Nrf2) is a key transcription factor that plays a crucial role in cytoprotection against inflammation. The present study investigated the role of Nrf2 in upregulating of nuclear factor kappa B (NF-κB) activity, tumor necrosis factor-α (TNF-α), and MMP-9 after SCI. Wild-type Nrf2 (+/+) and Nrf2-deficient (Nrf (−/−)) mice were subjected to an SCI model induced by the application of vascular clips (force of 10 g) to the dura after a three-level T8-T10 laminectomy. We detected the wet/dry weight ratio of impaired spinal cord tissue, the activation of NF-κB, the mRNA and protein levels of TNF-α and MMP-9, and the enzyme activity of MMP-9. Nrf2 (−/−) mice were demonstrated to have more spinal cord edema, NF-κB activation, TNF-α production, and MMP-9 expression after SCI compared with the wild-type controls. The results suggest that Nrf2 may play an important role in limiting the upregulation of NF-κB activity, TNF-α, and MMP-9 in spinal cord after SCI