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Tissue engineering is an active field and one of its aims is to produce tissues to repair the human body. The Advanced Regenerative Medicine Initiative (ARMI) currently seeks to help increase the manufacturability of tissue engineering products (TEMPs). One of the critical components of large-scale manufacturing is the sensing of information for quality control and critical feedback of tissue growth patterns. Modern sensors that provide information about physical qualities of tissues, however, are invasive or destructive. The goal of this project is to develop noninvasive methodologies to measure the mechanical properties of TEMPs. Our approach is to utilize acoustic waves to induce nano-scale level vibrations in the enginineered tissues in which corresponding displacements are measured in full-field with quantitative optical techniques. In our work, a digital holographic system images the tissue’s vibration at significant modes and provides the displacement patterns of the tissue at various points along the sinusoidal excitation curve. These data are applied to a neural network to compare the experimental vibrational modes to the ones obtained by FEA simulation to estimate the physical properties of the tissue. This methodology has the promise of yielding critical control parameters that would allow technicians to noninvasively and consistently determine when samples are ready to be packaged or if their growth deviates from expected time frames or if there are defects in the tissue. It is expected that this approach will streamline several components of the quality control and production process. 

The Frobenius-Perron theory of an endofunctor of a k \Bbbk -linear category (recently introduced in Chen et al. [Algebra Number Theory 13 (2019), pp. 2005–2055]) provides new invariants for abelian and triangulated categories. Here we study Frobenius-Perron type invariants for derived categories of commutative and noncommutative projective schemes. In particular, we calculate the Frobenius-Perron dimension for domestic and tubular weighted projective lines, define Frobenius-Perron generalizations of Calabi-Yau and Kodaira dimensions, and provide examples. We apply this theory to the derived categories associated to certain Artin-Schelter regular and finite-dimensional algebras. 

One of the critical components of large-scale manufacturing of bioengineered tissues is the sensing of information for quality control and critical feedback of tissue growth. Modern sensors that measure mechanical qualities of tissues, however, are invasive and destructive. The goal of this project is to develop noninvasive methodologies to measure the mechanical properties of tissue engineering products. Our approach is to utilize acoustic waves to induce nanoscale level vibrations in the engineered tissues in which corresponding displacements are measured in full-field with quantitative optical techniques. A digital holographic system images the tissue’s vibration at significant modes and provides the displacement patterns of the tissue. These data are used to train a supervised learning classifier with a goal of using the comparisons between the experimental vibrational modes and the ones obtained by finite element simulation to estimate the physical properties of the tissue. This methodology has the promise of mechanical properties that would allow technicians to noninvasively determine when samples are ready to be packaged, if their growth deviates from expected time frames, or if there are defects in the tissue. It is expected that this approach will streamline several components of the quality control and production process. 

Recent advances in the blockchain research have been made in two important directions. One is refined resilience analysis utilizing game theory to study the consequences of selfish behavior of users (miners), and the other is the extension from a linear (chain) structure to a non-linear (graphical) structure for performance improvements, such as IOTA and Graphcoin. The first question that comes to mind is what improvements that a blockchain system would see by leveraging these new advances. In this paper, we consider three major properties for a blockchain system: α-partial verification, scalability, and finality-duration. We establish a formal framework and prove that no blockchain system can achieve ?-partial verification for any fixed constant ?, high scalability, and low finality-duration simultaneously. We observe that classical blockchain systems like Bitcoin achieves full verification (α=1) and low finality-duration, Ethereum 2.0 Sharding achieves low finality-duration and high scalability. We are interested in whether it is possible to partially satisfy the three properties. 

Copper sulphide (CuxS, x=1 to 2) is a metal chalcogenide semiconductor that exhibits useful optical and electrical properties due to the presence of copper vacancies. This makes CuxS thin films useful for a number of applications including infrared absorbing coatings, solar cells, thin-film electronics, and as a precursor for CZTS (Copper Zinc Tin Sulphide) thin films. Post-deposition sintering of CuxS nanoparticle films is a key process that affects the film properties and hence determines its operational characteristics in the above applications. Intense pulse light (IPL) sintering uses visible broad-spectrum xenon light to rapidly sinter nanoparticle films over large-areas, and is compatible with methods such as roll-to-roll deposition for large-area deposition of colloidal nanoparticle films and patterns. This paper experimentally examines the effect of IPL parameters on sintering of CuxS thin films. As-deposited and sintered films are compared in terms of their crystal structure, as well as optical and electrical properties, as a function of the IPL parameters.