Moral Status and Agent-Centred Options

If we were required to sacrifice our own interests whenever doing so was best overall, or prohibited from doing so unless it was optimal, then we would be mere sites for the realisation of value. Our interests, not ourselves, would wholly determine what we ought to do. We are not mere sites for the realisation of value — instead we, ourselves, matter unconditionally. So we have options to act suboptimally. These options have limits, grounded in the very same considerations. Though not merely such sites, you and I are also sites for the realisation of value, and our interests (and ourselves) must therefore sometimes determine what others ought to do, in particular requiring them to bear reasonable costs for our sake. Likewise, just as my moral status grounds a requirement that others show me appropriate respect, so must I do to myself

Gaps in Taylor series of algebraic functions

Let $f$ be a rational function on an algebraic curve over the complex numbers. For a point $p$ and local parameter $x$ we can consider the Taylor series for $f$ in the variable $x$. In this paper we give an upper bound on the frequency with which the terms in the Taylor series have $0$ as their coefficient

Sharp Bounds on Davenport-Schinzel Sequences of Every Order

One of the longest-standing open problems in computational geometry is to bound the lower envelope of $n$ univariate functions, each pair of which crosses at most $s$ times, for some fixed $s$. This problem is known to be equivalent to bounding the length of an order-$s$ Davenport-Schinzel sequence, namely a sequence over an $n$-letter alphabet that avoids alternating subsequences of the form $a \cdots b \cdots a \cdots b \cdots$ with length $s+2$. These sequences were introduced by Davenport and Schinzel in 1965 to model a certain problem in differential equations and have since been applied to bounding the running times of geometric algorithms, data structures, and the combinatorial complexity of geometric arrangements. Let $\lambda_s(n)$ be the maximum length of an order-$s$ DS sequence over $n$ letters. What is $\lambda_s$ asymptotically? This question has been answered satisfactorily (by Hart and Sharir, Agarwal, Sharir, and Shor, Klazar, and Nivasch) when $s$ is even or $s\le 3$. However, since the work of Agarwal, Sharir, and Shor in the mid-1980s there has been a persistent gap in our understanding of the odd orders. In this work we effectively close the problem by establishing sharp bounds on Davenport-Schinzel sequences of every order $s$. Our results reveal that, contrary to one's intuition, $\lambda_s(n)$ behaves essentially like $\lambda_{s-1}(n)$ when $s$ is odd. This refutes conjectures due to Alon et al. (2008) and Nivasch (2010).Comment: A 10-page extended abstract will appear in the Proceedings of the Symposium on Computational Geometry, 201

Localized Immunotherapy Delivery Using Injectable in situ Forming Chitosan Hydrogel

Cytokine-based cancer immunotherapies stimulate a host’s immune system to fight cancer. In particular, interleukin-12 (IL-12), a potent pro-inflammatory cytokine, has demonstrated the ability to eliminate tumors in a number of preclinical models. Toxicities associated with the systemic delivery of IL-12 have precluded its use in the clinic. We are developing a novel chitosan-based hydrogel to maintain high local concentrations of cytokines, such as IL-12, in the tumor while minimizing its systemic dissemination. This hydrogel was found to form spontaneously within ten seconds of mixing two proprietary components. To increase the usefulness of the hydrogel, an efficient mixing and delivery system is needed. We designed and evaluated a device capable of mixing two solutions from two syringes during injection. A total of eight prototypes were created using three-dimensional printers; six were printed on an Object30; one was printed on a MakerBot; another was printed on an uPrint SE Plus. Three tests were used to determine the effectiveness of the device. The first test was a dimensional test to check for fitting of the syringes and needle. After passing this test, the fluid dynamics were tested using distilled water. If the device pasted the previous tests, the third test determined the mixing ability of the device using the novel hydrogel. After success in all three tests, the sterility of the device became the main goal. Hydrogel formation was achieved but a better material for the device is still under investigation

An evolutionary advantage for extravagant honesty

A game-theoretic model of handicap signalling over a pair of signalling channels is introduced in order to determine when one channel has an evolutionary advantage over the other. The stability conditions for honest handicap signalling are presented for a single channel and are shown to conform with the results of prior handicap signalling models. Evolutionary simulations are then used to show that, for a two-channel system in which honest signalling is possible on both channels, the channel featuring larger advertisements at equilibrium is favoured by evolution. This result helps to address a significant tension in the handicap principle literature. While the original theory was motivated by the prevalence of extravagant natural signalling, contemporary models have demonstrated that it is the cost associated with deception that stabilises honesty, and that the honest signals exhibited at equilibrium need not be extravagant at all. The current model suggests that while extravagant and wasteful signals are not required to ensure a signalling system's evolutionary stability, extravagant signalling systems may enjoy an advantage in terms of evolutionary attainability