A glimpse into the differential topology and geometry of optimal transport

This note exposes the differential topology and geometry underlying some of the basic phenomena of optimal transportation. It surveys basic questions concerning Monge maps and Kantorovich measures: existence and regularity of the former, uniqueness of the latter, and estimates for the dimension of its support, as well as the associated linear programming duality. It shows the answers to these questions concern the differential geometry and topology of the chosen transportation cost. It also establishes new connections --- some heuristic and others rigorous --- based on the properties of the cross-difference of this cost, and its Taylor expansion at the diagonal.Comment: 27 page

NIH Workshop 2018: Towards Minimally-invasive or Non-invasive Approaches to Assess Tissue Oxygenation Pre- and Post-Transfusion

Because blood transfusion is one of the most common therapeutic interventions in hospitalized patients, much recent research has focused on improving the storage quality in vitro of donor red blood cells (RBCs) that are then used for transfusion. However, there is a significant need for enhancing our understanding of the efficacy of the transfused RBCs in vivo. To this end, the NIH sponsored a one-and-a-half-day workshop that brought together experts in multiple disciplines relevant to tissue oxygenation (e.g., transfusion medicine, critical care medicine, cardiology, neurology, neonatology and pediatrics, bioengineering, biochemistry, and imaging). These individuals presented their latest findings, discussed key challenges, and aimed to construct recommendations for facilitating development of new technologies and/or biomarker panels to assess tissue oxygenation in a minimally-invasive to non-invasive fashion, before and after RBC transfusion. The workshop was structured into four sessions: (1) Global Perspective; (2) Organ Systems; (3) Neonatology; and (4) Emerging Technologies. The first day provided an overview of current approaches in the clinical setting, both from a global perspective, including the use of metabolomics for studying RBCs and tissue perfusion, and from a more focused perspective, including tissue oxygenation assessments in neonates and in specific adult organ systems. The second day focused on emerging technologies, which could be applied pre- and post-RBC transfusion, to assess tissue oxygenation in minimally-invasive or non-invasive ways. Each day concluded with an open-microphone discussion among the speakers and workshop participants. The workshop presentations and ensuing interdisciplinary discussions highlighted the potential of technologies to combine global “omics” signatures with additional measures (e.g., thenar eminence measurements or various imaging methods) to predict which patients could potentially benefit from a RBC transfusion and whether the ensuing RBC transfusion was effective. The discussions highlighted the need for collaborations across the various disciplines represented at the meeting to leverage existing technologies and to develop novel approaches for assessing RBC transfusion efficacy in various clinical settings. Although the Workshop took place in April, 2018, the concepts described and the ensuing discussions were, perhaps, even more relevant in April, 2020, at the time of writing this manuscript, during the explosive growth of the COVID-19 pandemic in the United States. Thus, issues relating to maintaining and improving tissue oxygenation and perfusion are especially pertinent because of the extensive pulmonary damage resulting from SARS-CoV-2 infection [1], compromises in perfusion caused by thrombotic-embolic phenomena [2], and damage to circulating RBCs, potentially compromising their oxygen-carrying capacity [3]. The severe end organ effects of SARS-CoV-2 infection mandate even more urgency for improving our understanding of tissue perfusion and oxygenation, improve methods for measuring and monitoring them, and develop novel ways of enhancing them

NIH Workshop 2018: Towards Minimally Invasive or Noninvasive Approaches to Assess Tissue Oxygenation Pre- and Post-transfusion

Because blood transfusion is one of the most common therapeutic interventions in hospitalized patients, much recent research has focused on improving the storage quality in vitro of donor red blood cells (RBCs) that are then used for transfusion. However, there is a significant need for enhancing our understanding of the efficacy of the transfused RBCs in vivo. To this end, the NIH sponsored a one-and-a-half-day workshop that brought together experts in multiple disciplines relevant to tissue oxygenation (eg, transfusion medicine, critical care medicine, cardiology, neurology, neonatology and pediatrics, bioengineering, biochemistry, and imaging). These individuals presented their latest findings, discussed key challenges, and aimed to identify opportunities for facilitating development of new technologies and/or biomarker panels to assess tissue oxygenation in a minimally-invasive to non-invasive fashion, before and after RBC transfusion

Poly(m-Phenylenediamine) Nanospheres and Nanorods: Selective Synthesis and Their Application for Multiplex Nucleic Acid Detection

In this paper, we demonstrate for the first time that poly(m-phenylenediamine) (PMPD) nanospheres and nanorods can be selectively synthesized via chemical oxidation polymerization of m-phenylenediamine (MPD) monomers using ammonium persulfate (APS) as an oxidant at room temperature. It suggests that the pH value plays a critical role in controlling the the morphology of the nanostructures and fast polymerization rate favors the anisotropic growth of PMPD under homogeneous nucleation condition. We further demonstrate that such PMPD nanostructures can be used as an effective fluorescent sensing platform for multiplex nucleic acid detection. A detection limit as low as 50 pM and a high selectivity down to single-base mismatch could be achieved. The fluorescence quenching is attributed to photoinduced electron transfer from nitrogen atom in PMPD to excited fluorophore. Most importantly, the successful use of this sensing platform in human blood serum system is also demonstrated

Facile formation of highly mobile supported lipid bilayers on surface-quaternized pH-responsive polymer brushes

Poly(2-dimethylamino)ethyl methacrylate) (PDMA) brushes are grown from planar substrates via surface atom transfer radical polymerization (ATRP). Quaternization of these brushes is conducted using 1-iodooctadecane in n-hexane, which is a non-solvent for PDMA. Ellipsometry, AFM, and water contact angle measurements show that surface-confined quaternization occurs under these conditions, producing pH-responsive brushes that have a hydrophobic upper surface. Systematic variation of the 1-iodooctadecane concentration and reaction time enables the mean degree of surface quaternization to be optimized. Relatively low degrees of surface quaternization (ca. 10 mol % as judged by XPS) produce brushes that enable the formation of supported lipid bilayers, with the hydrophobic pendent octadecyl groups promoting in situ rupture of lipid vesicles. Control experiments confirm that quaternized PDMA brushes prepared in a good brush solvent (THF) produce non-pH-responsive brushes, presumably because the pendent octadecyl groups form micelle-like physical cross-links throughout the brush layer. Supported lipid bilayers (SLBs) can also be formed on the non-quaternized PDMA precursor brushes, but such structures proved to be unstable to small changes in pH. Thus, surface quaternization of PDMA brushes using 1-iodooctadecane in n-hexane provides the best protocol for the formation of robust SLBs. Fluorescence recovery after photobleaching (FRAP) studies of such SLBs indicate diffusion coefficients (2.8 ± 0.3 μm s–1) and mobile fractions (98 ± 2%) that are comparable to the literature data reported for SLBs prepared directly on planar glass substrates

Use of vegetation to increase building energy efficiency: application to a real case study

The research here presented deals with the relationship between vegetation and architecture, and how its presence can influence a building project and performance. In the last years, many ways of integrating green in building envelopes have already been experimented, for their potential of reducing thermal loads; the research investigates a specific solution, the vertical forest, which integrates trees and small bushes in specific permanent planters on balconies of high-rise buildings. The main scope is to understand if trees, treated as shadings, can really affect positively the building energy consumptions. Moreover, other aspects, such as trees mechanical stability, construction issues and maintenance are deepened. Through a particular case study, energy consumptions are analysed using dynamic simulations tools, developed with Grasshopper™ and EnergyPlus™ software, in which trees are considered as special external shadings, characterized by a variable permeability to solar radiation during the year. Results demonstrate that trees can contribute to reduce energy loads, depending on species and orientation, especially in association with traditional shading systems. Eventually, some guidelines on technological and construction aspects, as well as on trees species selection, are given, in order to assure the optimal vegetation life and to maximize its benefits on the building

Weak-type inequalities for conjugate first-order Riesz-Laguerre Transforms

In this paper we introduce a conjugate class of Riesz transforms in the context of Laguerre polynomials. We prove their weak-type (1,1) and L^p boundedness with respect to the Laguerre measure. A similar result is known in the Hermite context