Graphene-Based Nanomaterials for Neuroengineering: Recent Advances and Future Prospective

Graphene unique physicochemical properties made it prominent among other allotropic forms of carbon, in many areas of research and technological applications. Interestingly, in recent years, many studies exploited the use of graphene family nanomaterials (GNMs) for biomedical applications such as drug delivery, diagnostics, bioimaging, and tissue engineering research. GNMs are successfully used for the design of scaffolds for controlled induction of cell differentiation and tissue regeneration. Critically, it is important to identify the more appropriate nano/bio material interface sustaining cells differentiation and tissue regeneration enhancement. Specifically, this review is focussed on graphene-based scaffolds that endow physiochemical and biological properties suitable for a specific tissue, the nervous system, that links tightly morphological and electrical properties. Different strategies are reviewed to exploit GNMs for neuronal engineering and regeneration, material toxicity, and biocompatibility. Specifically, the potentiality for neuronal stem cells differentiation and subsequent neuronal network growth as well as the impact of electrical stimulation through GNM on cells is presented. The use of field effect transistor (FET) based on graphene for neuronal regeneration is described. This review concludes the important aspects to be controlled to make graphene a promising candidate for further advanced application in neuronal tissue engineering and biomedical use

Isoperimetric Inequalities in Simplicial Complexes

In graph theory there are intimate connections between the expansion properties of a graph and the spectrum of its Laplacian. In this paper we define a notion of combinatorial expansion for simplicial complexes of general dimension, and prove that similar connections exist between the combinatorial expansion of a complex, and the spectrum of the high dimensional Laplacian defined by Eckmann. In particular, we present a Cheeger-type inequality, and a high-dimensional Expander Mixing Lemma. As a corollary, using the work of Pach, we obtain a connection between spectral properties of complexes and Gromov's notion of geometric overlap. Using the work of Gunder and Wagner, we give an estimate for the combinatorial expansion and geometric overlap of random Linial-Meshulam complexes

Diquat Derivatives: Highly Active, Two-Dimensional Nonlinear Optical Chromophores with Potential Redox Switchability

In this article, we present a detailed study of structure−activity relationships in diquaternized 2,2′-bipyridyl (diquat) derivatives. Sixteen new chromophores have been synthesized, with variations in the amino electron donor substituents, π-conjugated bridge, and alkyl diquaternizing unit. Our aim is to combine very large, two-dimensional (2D) quadratic nonlinear optical (NLO) responses with reversible redox chemistry. The chromophores have been characterized as their PF_6^− salts by using various techniques including electronic absorption spectroscopy and cyclic voltammetry. Their visible absorption spectra are dominated by intense π → π^* intramolecular charge-transfer (ICT) bands, and all show two reversible diquat-based reductions. First hyperpolarizabilities β have been measured by using hyper-Rayleigh scattering with an 800 nm laser, and Stark spectroscopy of the ICT bands affords estimated static first hyperpolarizabilities β_0. The directly and indirectly derived β values are large and increase with the extent of π-conjugation and electron donor strength. Extending the quaternizing alkyl linkage always increases the ICT energy and decreases the E_(1/2) values for diquat reduction, but a compensating increase in the ICT intensity prevents significant decreases in Stark-based β_0 responses. Nine single-crystal X-ray structures have also been obtained. Time-dependent density functional theory clarifies the molecular electronic/optical properties, and finite field calculations agree with polarized HRS data in that the NLO responses of the disubstituted species are dominated by ‘off-diagonal’ β_(zyy) components. The most significant findings of these studies are: (i) β_0 values as much as 6 times that of the chromophore in the technologically important material (E)-4′-(dimethylamino)-N-methyl-4-stilbazolium tosylate; (ii) reversible electrochemistry that offers potential for redox-switching of optical properties over multiple states; (iii) strongly 2D NLO responses that may be exploited for novel practical applications; (iv) a new polar material, suitable for bulk NLO behavior

On Eigenvalues of Random Complexes

We consider higher-dimensional generalizations of the normalized Laplacian and the adjacency matrix of graphs and study their eigenvalues for the Linial-Meshulam model $X^k(n,p)$ of random $k$-dimensional simplicial complexes on $n$ vertices. We show that for $p=\Omega(\log n/n)$, the eigenvalues of these matrices are a.a.s. concentrated around two values. The main tool, which goes back to the work of Garland, are arguments that relate the eigenvalues of these matrices to those of graphs that arise as links of $(k-2)$-dimensional faces. Garland's result concerns the Laplacian; we develop an analogous result for the adjacency matrix. The same arguments apply to other models of random complexes which allow for dependencies between the choices of $k$-dimensional simplices. In the second part of the paper, we apply this to the question of possible higher-dimensional analogues of the discrete Cheeger inequality, which in the classical case of graphs relates the eigenvalues of a graph and its edge expansion. It is very natural to ask whether this generalizes to higher dimensions and, in particular, whether the higher-dimensional Laplacian spectra capture the notion of coboundary expansion - a generalization of edge expansion that arose in recent work of Linial and Meshulam and of Gromov. We show that this most straightforward version of a higher-dimensional discrete Cheeger inequality fails, in quite a strong way: For every $k\geq 2$ and $n\in \mathbb{N}$, there is a $k$-dimensional complex $Y^k_n$ on $n$ vertices that has strong spectral expansion properties (all nontrivial eigenvalues of the normalised $k$-dimensional Laplacian lie in the interval $[1-O(1/\sqrt{n}),1+O(1/\sqrt{n})]$) but whose coboundary expansion is bounded from above by $O(\log n/n)$ and so tends to zero as $n\rightarrow \infty$; moreover, $Y^k_n$ can be taken to have vanishing integer homology in dimension less than $k$.Comment: Extended full version of an extended abstract that appeared at SoCG 2012, to appear in Israel Journal of Mathematic

Symmetric LDPC codes and local testing

Coding theoretic and complexity theoretic considerations naturally lead to the question of generating symmetric, sparse, redundant linear systems. This paper provides new way of constructions with better parameters and new lower bounds. Low Density Parity Check (LDPC) codes are linear codes defined by short constraints (a property essential for local testing of a code). Some of the best (theoretically and practically) used codes are LDPC. Symmetric codes are those in which all coordinates “look the same”, namely there is some transitive group acting on the coordinates which preserves the code. Some of the most commonly used locally testable codes (especially in PCPs and other proof systems), including all “low-degree” codes, are symmetric. Requiring that a symmetric binary code of length n has large (linear or near-linear) distance seems to suggest a “conflict” between 1/rate and density (constraint length). In known constructions, if one is constant then the other is almost worst possible- n/poly(log n). Our main positive result simultaneously achieves symmetric low density, constant rate codes generated by a single constraint. We present an explicit construction of a symmetric and transitiv

Early health system responses to the COVID-19 pandemic in Mediterranean countries: A tale of successes and challenges

This paper conducts a comparative review of the (curative) health systems’ response taken by Cyprus, Greece, Israel, Italy, Malta, Portugal, and Spain during the first six months of the COVID-19 pandemic. Prior to the COVID-19 pandemic, these Mediterranean countries shared similarities in terms of health system resources, which were low compared to the EU/OECD average. We distill key policy insights regarding the governance tools adopted to manage the pandemic, the means to secure sufficient physical infrastructure and workforce capacity and some financing and coverage aspects. We performed a qualitative analysis of the evidence reported to the ‘Health System Response Monitor’ platform of the European Observatory by country experts. We found that governance in the early stages of the pandemic was undertaken centrally in all the Mediterranean countries, even in Italy and Spain where regional authorities usually have autonomy over health matters. Stretched public resources prompted countries to deploy “flexible” intensive care unit capacity and health workforce resources as agile solutions. The private sector was also utilized to expand resources and health workforce capacity, through special public-private partnerships. Countries ensured universal coverage for COVID-19-related services, even for groups not usually entitled to free publicly financed health care, such as undocumented migrants. We conclude that flexibility, speed and adaptive management in health policy responses were key to responding to immediate needs during the COVID-19 pandemic. Financial barriers to accessing care as well as potentially higher mortality rates were avoided in most of the countries during the first wave. Yet it is still early to assess to what extent countries were able to maintain essential services without undermining equitable access to high quality care. © 202

Early health system responses to the COVID-19 pandemic in Mediterranean countries: A tale of successes and challenges

This paper conducts a comparative review of the (curative) health systems’ response taken by Cyprus, Greece, Israel, Italy, Malta, Portugal, and Spain during the first six months of the COVID-19 pandemic. Prior to the COVID-19 pandemic, these Mediterranean countries shared similarities in terms of health system resources, which were low compared to the EU/OECD average. We distill key policy insights regarding the governance tools adopted to manage the pandemic, the means to secure sufficient physical infrastructure and workforce capacity and some financing and coverage aspects. We performed a qualitative analysis of the evidence reported to the ‘Health System Response Monitor’ platform of the European Observatory by country experts. We found that governance in the early stages of the pandemic was undertaken centrally in all the Mediterranean countries, even in Italy and Spain where regional authorities usually have autonomy over health matters. Stretched public resources prompted countries to deploy “flexible” intensive care unit capacity and health workforce resources as agile solutions. The private sector was also utilized to expand resources and health workforce capacity, through special public-private partnerships. Countries ensured universal coverage for COVID-19-related services, even for groups not usually entitled to free publicly financed health care, such as undocumented migrants. We conclude that flexibility, speed and adaptive management in health policy responses were key to responding to immediate needs during the COVID-19 pandemic. Financial barriers to accessing care as well as potentially higher mortality rates were avoided in most of the countries during the first wave. Yet it is still early to assess to what extent countries were able to maintain essential services without undermining equitable access to high quality care