Translation-modulation invariant Banach spaces of ultradistributions

We introduce and study a new class of translation-modulation invariant Banach spaces of ultradistributions. These spaces show stability under Fourier transform and tensor products; furthermore, they have a natural Banach convolution module structure over a certain associated Beurling algebra, as well as a Banach multiplication module structure over an associated Wiener-Beurling algebra. We also investigate a new class of modulation spaces, the Banach spaces of ultradistributions $\mathcal{M}^F$ on $\mathbb{R}^{d}$, associated to translation-modulation invariant Banach spaces of ultradistributions $F$ on $\mathbb{R}^{2d}$.Comment: 19 page

Expanding the Toolkit for Metabolic Engineering

The essence of metabolic engineering is the modification of microbes for the overproduction of useful compounds. These cellular factories are increasingly recognized as an environmentally-friendly and cost-effective way to convert inexpensive and renewable feedstocks into products, compared to traditional chemical synthesis from petrochemicals. The products span the spectrum of specialty, fine or bulk chemicals, with uses such as pharmaceuticals, nutraceuticals, flavors and fragrances, agrochemicals, biofuels and building blocks for other compounds. However, the process of metabolic engineering can be long and expensive, primarily due to technological hurdles, our incomplete understanding of biology, as well as redundancies and limitations built into the natural program of living cells. Combinatorial or directed evolution approaches can enable us to make progress even without a full understanding of the cell, and can also lead to the discovery of new knowledge. This thesis is focused on addressing the technological bottlenecks in the directed evolution cycle, specifically de novo DNA assembly to generate strain libraries and small molecule product screens and selections

Advances and Novel Approaches in Discrete Optimization

Discrete optimization is an important area of Applied Mathematics with a broad spectrum of applications in many fields. This book results from a Special Issue in the journal Mathematics entitled ‘Advances and Novel Approaches in Discrete Optimization’. It contains 17 articles covering a broad spectrum of subjects which have been selected from 43 submitted papers after a thorough refereeing process. Among other topics, it includes seven articles dealing with scheduling problems, e.g., online scheduling, batching, dual and inverse scheduling problems, or uncertain scheduling problems. Other subjects are graphs and applications, evacuation planning, the max-cut problem, capacitated lot-sizing, and packing algorithms

49th Annual Midwest Estate, Tax & Business Planning Institute

Meeting proceedings of a seminar by the same name, held June 9-10, 2022

Improving the quality of tissue-cultured plants by fixing the problems related to an inadequate water balance, hyperhydricity

In vitro tissue culture is a technique for accelerating plant propagation and supplying high- quality starting material which has a positive impact on product commercialization. Several obstacles may occur during the culture process, one of which is hyperhydricity. Hyperhydric shoots are characterized by extensive accumulation of water in the apoplast, the continuum of cell walls and intercellular air spaces which is almost completely flooded. The occurrence of hyperhydricity is a major problem in the micropropagation industry, since it reduces the quality and multiplication rate of microplants. Although numerous studies have been put forward to explain hyperhydricity, the underlying mechanism and causative factors of hyperhydricity are still debated. Understanding the underlying mechanisms and factors involved in the control of plant growth in vitro can greatly improve the quality of micropropagated plants. The research presented in this thesis succeeded in elucidating aspects of the mechanism, causality factors and methods to prevent hyperhydricity in in vitro grown Arabidopsis thaliana and Limonium sinuatum. Our study found that hypolignification of cell walls was an important causative factor in the development of hyperhydricity. The specific interaction of the plantlets, medium components and microenvironments were found to affect lignin biosynthesis, to lead to irregular stomatal features, abnormal anatomy of mesophyll cells and large intercellular spaces, to affect the water retention capacity and the transpiration rate. Exogenously applied calcium in combination with a specific lignin biosynthesis precursor, p-coumaric acid, and a stomatal opener (ALA) as supplements to the medium proved capable of reducing the occurrence or delaying the onset of hyperhydricity by stimulating cell wall lignin biosynthesis and modifying the pectin content of the leaves

Algebraic Stream Processing

We identify and analyse the typically higher-order approaches to stream processing in the literature. From this analysis we motivate an alternative approach to the specification of SPSs as STs based on an essentially first-order equational representation. This technique is called Cartesian form specification. More specifically, while STs are properly second-order objects we show that using Cartesian forms, the second-order models needed to formalise STs are so weak that we may use and develop well-understood first-order methods from computability theory and mathematical logic to reason about their properties. Indeed, we show that by specifying STs equationally in Cartesian form as primitive recursive functions we have the basis of a new, general purpose and mathematically sound theory of stream processing that emphasises the formal specification and formal verification of STs. The main topics that we address in the development of this theory are as follows. We present a theoretically well-founded general purpose stream processing language ASTRAL (Algebraic Stream TRAnsformer Language) that supports the use of modular specification techniques for full second-order STs. We show how ASTRAL specifications can be given a Cartesian form semantics using the language PREQ that is an equational characterisation of the primitive recursive functions. In more detail, we show that by compiling ASTRAL specifications into an equivalent Cartesian form in PREQ we can use first-order equational logic with induction as a logical calculus to reason about STs. In particular, using this calculus we identify a syntactic class of correctness statements for which the verification of ASTRAL programmes is decidable relative to this calculus. We define an effective algorithm based on term re-writing techniques to implement this calculus and hence to automatically verify a very broad class of STs including conventional hardware devices. Finally, we analyse the properties of this abstract algorithm as a proof assistant and discuss various techniques that have been adopted to develop software tools based on this algorithm

Poincaré's philosophy of mathematics

The primary concern of this thesis is to investigate the explicit philosophy of mathematics in the work of Henri Poincare. In particular, I argue that there is a well-founded doctrine which grounds both Poincare's negative thesis, which is based on constructivist sentiments, and his positive thesis, via which he retains a classical conception of the mathematical continuum. The doctrine which does so is one which is founded on the Kantian theory of synthetic a priori intuition. I begin, therefore, by outlining Kant's theory of the synthetic a priori, especially as it applies to mathematics. Then, in the main body of the thesis, I explain how the various central aspects of Poincare's philosophy of mathematics - e.g. his theory of induction; his theory of the continuum; his views on impredicativiti his theory of meaning - must, in general, be seen as an adaptation of Kant's position. My conclusion is that not only is there a well-founded philosophical core to Poincare's philosophy, but also that such a core provides a viable alternative in contemporary debates in the philosophy of mathematics. That is, Poincare's theory, which is secured by his doctrine of a priori intuitions, and which describes a position in between the two extremes of an "anti-realist" strict constructivism and a "realist" axiomatic set theory, may indeed be true

Cryptocurrencies and beyond: using design science research to demonstrate diverse applications of blockchains

This thesis investigates blockchain technology and whether its mutually cooperative topology and commons-based peer production practices have implications for society because, instead of the traditional top-down, centralised model of governance, blockchains represent an alternative way of collaborating. Much of the literature anticipates the vast potential of the permanent and publicly auditable nature of the propagated values of blockchains. Indeed, writers have supposed that the smart contract capabilities of the technology may prove revolutionary for areas beyond that of the economic domain targeted by the cryptocurrency Bitcoin, which is the first successful use-case of a blockchain. However, few advanced use cases beyond that economic realm have materialised; this research demonstrates such usecases. This thesis asks four research questions. The first asks whether blockchains can help reduce energy consumption. The second asks whether blockchains can help digitise the informal sector. The third asks whether blockchains can help counter fake news. The final question asks whether blockchains can help address criticisms of humanitarian aid. Those topics are four amongst many urgent problems currently facing humankind, and therefore, the overarching research question of this thesis becomes whether blockchains can help humanity. This work advances the supposed potential of blockchains proposed by current literature by using design science research to create software artefacts that propose solutions for incentivising energy efficiency, fighting financial fraud, providing digital provenance and adding trust to humanitarian aid reporting. By demonstrating blockchain-based software solutions in those four topic areas, this thesis concludes that blockchains can help humanity. However, if they are to help society address some of its problems, blockchains have significant technological and organisational barriers to overcome. Furthermore, the idea that blockchains can help humanity is a form of techno-determinism and this research concludes that it is impossible to solve every issue by diversifying technical operations; humankind must also change political, economic, and cultural goals, too. Nevertheless, this thesis has implications for regulators, despite the barriers and false solutionism offered by technology because, rather than the trusted lawmakers and experts that nations used to look up to as oracles of truth, now it may be possible to look to blockchains, instead