Let F be a field, G = (V,E) be an undirected graph on n vertices, and let S(F,G) be the set of all symmetric n × n matrices whose nonzero off-diagonal entries occur in exactly the positions corresponding to the edges of G. Let mr(F,G)be the minimum rank over all matrices in S(F,G). We give a field independent proof of a well-known result that for a tree the sum of its path cover number and minimal rank is equal to the number of vertices in the tree. The rank-spread of a vertex v of G is the difference between the minimal ranks of G and G - v, the graph obtained by deleting v and all its incident edges from G. The rank-spread of an edge is defined similarly. We derive a formula that expresses the minimal rank of a tree as the difference of sums of rank-spreads, the first being the sum of the rank-spreads of all the vertices and the second the sum of the rank-spreads of all the edges. We show that this is a special case of a more general inequality for all graphs. In proving the above results we explore how rank-spreads change as graphs are vertex-summed.

The purpose of this thesis was to test the hypothesis that multiple-listing of equity options leads to lower bid-ask spreads because of increased competition. This competition can come in two forms, actual or potential, both of which are theorized to have the same effect on spreads. A model of the determinants of the bid-ask spread was formulated. Separate tests were conducted on 1985 and on 1992 CBOE data. The first test arose from the fact that in 1985, only a certain number of options were multiple-listed, or eligible to be multiple-listed. Spreads for multiple-listed options were conjectured to be below spreads for single-listed options across low levels of volume, and equal to single-listed option spreads at higher levels of volume. The evidence for this was mixed based on several regressions with different functional forms. The second test arose from the fact that in 1992, because of an SEC rule change, all options were eligible to be multiple-listed but still only a few were. Spreads for multiple-listed options were conjectured to be equal to spreads for single-listed options because the single-listed options had the potential to become multiple-listed. Again, the evidence for this was mixed. It appears that the actual and potential competitive effects from multiple-listing had yet to come to fruition as of 1992. Further testing revealed that, on an option-by-option basis, spreads generally rose from 1985 to 1992. / Master of Arts

The use of practically non-repeating spreading codes to generate sequence-based spread spectrum waveforms is a strong method to improve transmission security, by limiting an observers opportunity to cross-correlate snapshots of the signal into a coherent gain. Such time-varying codes, particularly when used to define multi-bit resolution arbitrary-phase waveforms, also present significant challenges to the intended receiver, which must synchronize correlator processing to match the code every time it changes. High-order phase shift keying (PSK) spread modulations do, however, provide an overall whiter spectral response than legacy direct sequence spread spectrum (DSSS) signals. Further, the unique ability to color the output signal spectrum offers new advantages to optimize transmission in a non-white frequency channel and to mitigate observed interference. In high data rate applications, the opportunity to inject a time-aligned co-channel underlay-based watermark for authentication at the receiver is an effective method to enhance physical layer (PHY) security for virtually any primary network waveform. This thesis presents a series of options to enhance the implementation of arbitrary-phase chaotic sequence-based spread spectrum waveforms, including techniques to significantly reduce fallthrough correlator hardware resources in low-power sensing devices for only minor performance loss, capabilities for programming chosen frequency domain spectra into the resulting spread spectrum signal, and design considerations for underlay watermark-based PHY-layer firewalls. A number of hardware validated prototypes were built on an Intel Arria 10 SoC FPGA to provide measurable results, achieving substantial computational resource gains and implementation flexibility. / Master of Science / This thesis presents a series of options for enhancing the implementation of arbitrary-phase spread spectrum waveforms, a highly-secure class of wireless technologies, in order to reduce design complexity with minimal loss, provide methods for real-time performance adaptations, and extend the traditional application space for increased security of communications in other networks. A number of enhanced hardware prototypes were implemented to provide measurable results, achieving substantial computational resource gains and design flexibility. Given the computational resources and power constraints of devices in the Internet of Things (IoT), the signal detection loss of 2.10 dB for reducing the hardware logic utilization of the brute force fallthrough correlator by more than 76% (and eliminating the need to dedicate computationally-expensive embedded multipliers) is a very reasonable trade. While the waveform is fundamentally designed for increased security, adapting to widespread and/or commercial use may allow some sacrifice of the signal’s ability to avoid interception/detection to improve performance in undesirable operating conditions. In a similar, yet reversed, case, injecting a watermarking signature at the physical layer (PHY) of less-secure wireless technologies for receiver-side authentication also proves to be beneficial.

<p dir="ltr">This paper examines the resilience of global food and energy supply chains against the background of recent world disruptions such as China-US trade war, novel coronavirus disease 2019 (COVID-19) pandemic, and Russia’s incursion into Ukraine. It aims at improving forecast methodologies and providing early indications of market stressors by considering three key cracks or spreads within the food and energy industries soy crush spread, crude crack spread, and cattle finish spread. The study uses Autoregressive Integrated Moving Average (ARIMA), Exponential Smoothing State Space (ETS) and Vector Error Correction Model (VECM). The profit relationships are examined in these models with regard to potential problems for supply chains in the soybean crushing industry, cattle finishing, and crude oil refining sectors. It also compares forecasting approaches like univariate (ARIMA & ETS) and multivariate (VECM). This means that it tries to gauge how accurate each one is in predicting where a given sector may be heading or where there are risks likely to happen. The situation is further complicated by on-going capacity expansions in these sectors which are expected to face more challenges due to geopolitical tensions as well as efforts to mitigate climate change internationally.The overall goal of the research is to develop forecasting methods to help industry participants, policymakers, and small producers make informed decisions amid volatility and the threat of imminent supply chain disruptions.</p>

The objective of this thesis is to determine the average probability of bit error of an asynchronous, noncoherent, direct-sequence, code-division multiple-access (CDMA) system using wideband M-ary FSK as bandpass modulation. The immediate analysis and determination of the average probability of bit error is made inherently more difficult because of two random effects. The first disturbance encountered in the analysis is the existence of additive, white, Gaussian noise and multi-user noise. The second disturbance, which is more difficult to analyze, is the effect of multipath fading, which is caused by reflections of the transmitted signal through the propagating medium to the receiver. / Master of Science

Biological invasions represent both an urgent conservation problem and an opportunity to advance ecological theory. Development of pertinent research questions and proactive management strategies require knowledge of which introduced species are present and of spatiotemporal trends in the distribution of natives and invaders. In Chapter 2 we developed a quantitative framework to identify spreaders and decliners and estimate invasion chronologies based on a historical fish presence data set for upper and middle New River (UMNR) tributaries. Our framework accounts for spatiotemporal variability in sampling effort by aggregating presences by watershed and expressing range size as a function of the number of watersheds sampled per time period. The majority (55%) of fish species present in the study area were introduced, 51% of which were spreaders. Most spreaders (84%) appeared to be spreading exponentially. The rate of new introductions detected in the study area has slowed since the mid-20th century. Two natives, the mound-spawning bluehead chub Nocomis leptocephalus and its strong nest associate (reproductive mutualist), mountain redbelly dace Chrosomus oreas, were among the most rapid spreaders. Four natives showed evidence of decline. Our framework leverages historical presence data to reconstruct temporal trends in species distributions. It sets the stage for further study of factors driving stream fish invasions and declines in the Appalachian region, and is transferable to diverse taxonomic groups and geographic regions. Species traits and human activities mediating stream-fish invasions remain poorly understood. In Chapter 3 we modeled the contribution of species traits to invasion success of UMNR tributary fishes during the colonization and spread stages. Biological traits accurately explained colonization and spread success, whereas ecological traits resulted in less accurate models. Colonization success was positively related to time since introduction, benthic feeding, an equilibrium life history, and nest spawning. Successful spread was positively related to winter air temperature in the native range and an equilibrium life history. Variables estimating human use and propagule pressure were non-informative. Traits that influenced invasion success were consistent with the hypothesis that human land-use practices have increased the invasibility of highland watersheds by creating novel conditions suited to lowland and equilibrium invaders. / Master of Science

Many industries are turning to wireless communication systems to track their assets. One example of such an industry is the shipping industry, where — under the growing emphasis on homeland security — tracking cargo containers and their contents has become a high priority. There are several beacons on the commercial market that will meet this need if the required beacon does not need to be independently powered or to have global coverage. This thesis attempts to find a design solution for a beacon that transmits location data, is battery powered, and has world-wide coverage. The beacon is intended to be a low power, transmit only device, and the receiver will not be designed to operate in real-time. Several communication systems were evaluated on these conditions, and the Globalstar Satellite System was selected to use as the communication system for the beacon. The Globalstar Satellite System is a low earth orbiting (LEO) satellite system and uses Code Division Multiple Access (CDMA) to allocate system resources to the maximum number of users possible. Discussions of spread spectrum techniques and theory, Rake receivers, and error correction codes are included as a background for the design. This thesis examines the initial steps in the design of the transmitter beacon and aims to determine the minimum required beacon transmit power for good receiver performance. A portion of the correlator in the Globalstar receiver is simulated for several scenarios: a single user case with varying transmit power, and a multiple user case with fixed transmit power. Although not likely to occur, the single user case was used to baseline system performance and to verify the multi-user case results. The simulated correlator employed a parallel search strategy and used a truncated version of the Globalstar system code sequence. Finally, a threshold analysis was performed to determine if better receiver performance could be obtained. / Master of Science

The purpose of this paper is to compare the liquidity and the components of the bid-ask spread for thinly traded firms switching from a dealer market (Emerging Stock Market (ESM)) to an order driven market (Taiwan Stock Exchanges (TSE) or GreTai Securities Market (GTSM)). Firstly, we follow Christie and Huang’s (1994) method to measure the liquidity performance. Our finding shows that thinly traded firms could improve their liquidity by switching from a dealer market to an order driven market. Secondly, we apply Huang and Stoll’s (1997) and Lin et al.’s (1995) model to estimate the bid-ask spread components. Our results show that the adverse selection cost is significantly smaller on ESM than TSE or GTSM using both Huang and Stoll’s (1997) and Lin et al.’s (1995) model. The inventory holding cost is lower on ESM than TSE or GTSM estimated by Huang and Stoll’s (1997) model. However, the estimates of order processing cost and the probability of trade reversal do not produce consistent results by applying Huang and Stoll’s (1997) and Lin et al.’s (1995) model.

Background and problem: The capital gain tax was introduced in Sweden as late as 1991. Previous studies has shown that capital gain tax can explain differences in investors behaviour that can lead to trading changes and a lock-in effect on the stock market, which directly affects the liquidity of stocks. The problematic is that an illiquid stockmarket, among other things, could lead to that capitals stays in already mature companies and hamper IPOs. Purpose: The study ́s purpose is to study the relationship between capital gains tax and liquidity with control of others factors that might explain differences in liquidity on the stock market. Method: The study is conducted with a quantitative method and it ́s based on data collected from 1992-2000 for companies listed on Stockholm Stock Exchange. The method generated 939 observations for each variable and the study yielded a total of 5643 observations with a final loss of 34,6 % of the study ́s sample. We formed a hypothesis to answer the research question and achieve the purpose of the study. Conclusions: The study ́s results do not reject the study hypothesis of a negative relationship between capital gains tax and liquidity, which means that liquidity falls when capital gain tax rate increase in accordance with the existing theory. A negative correlation between capital gain tax and liquidity, might hamper IPOs of new companies, because the capital stays in the already mature companies and investors are discouraged from more productive investments. / Bakgrund och problem: Kapitalskatten infördes i Sverige så sent som 1991. Tidigarestudier har visat att kapitalskatt kan förklara skillnader i investerares beteende som kange upphov till tradingförändringar och en inlåsningseffekt på aktiemarknaden vilketdirekt påverkar aktiers likviditet. Med bakgrund av denna problematik skulle en illikvidaktiemarknad bland annat kunna leda till att kapital stannar i redan mogna bolag ochförsvårar börsintroduktioner. Syfte: Studiens syfte är att studera sambandet mellan kapitalskatt och likviditet medkontroll för andra faktorer som kan tänkas förklara skillnader i likviditet påaktiemarknaden. Metod: Studien genomförs med en kvantitativ undersökningsmetod och baseras på datainsamlad från åren 1992-2000 för företag noterade på Stockholmsbörsen. Denna metodgenererade 939 observationer för studiens respektive variabel vilket gav totalt 5643observationer med ett slutgiltigt bortfall på 34,6% av studiens mätpunkter. Vi utformadeen hypotes för att besvara studiens frågeställning och uppnå syftet med studien. Slutsatser: Studiens resultat förkastar inte studiens hypotes om ett negativt sambandmellan kapitalskatt och likviditet, vilket innebär att likviditeten sjunker närkapitalskattesatsen ökar i enlighet med befintlig teori. Eftersom ett negativt sambandföreligger mellan kapitalskatt och likviditet, finns risken att en hög kapitalskattförsvårar börsintroduktion av nya bolag, att kapital stannar i redan mogna bolag samt attinvesterare avskräcks från mer produktiva investeringar.

Atualmente tem aumentando o interesse na aplicação de sistemas caóticos no âmbito das telecomunicações. Esses sistemas apresentam certas peculiaridades, como geração de sinais com amplo espectro de freqüências e baixa correlação cruzada, o que os tornam altamente robustos para aplicação em esquemas de modulação caótica. Dentre tais esquemas, há aqueles em que a detecção é realizada utilizando alguma técnica de sincronismo. Neste trabalho, um circuito caótico é apresentado e sua performance é analisada. As técnicas de sincronismo Pecora-Carroll e sincronização por realimentação de erro são aplicadas ao circuito caótico apresentado. Utilizando este circuito caótico, são sugeridas as seguintes aplicações: um cifrador caótico e um sistema análogo ao spread spectrum. Os dois sistemas são implementados eletronicamente. Além disso, a avaliação da performance de cada sistema é realizada com o auxílio da técnica do diagrama de olho. / Nowadays it is increasing the interest in the application of the chaotic systems in the ambit of the telecommunications. These systems introduce some peculiarities, such as generation of wideband signals with low crosscorrelation, those characteristics make the systems strongly robust to application on chaotic modulation schemes. Among such schemes, there are ones where the detection is realized using techniques of synchronization. In this work, a chaotic circuit is introduced and its performance is evaluated. The Pecora-Carroll synchronization and error-feedback synchronization are applied on the chaotic circuit introduced. Using this chaotic circuit, the following applications are suggested: a chaotic cipher and a spread spectrum system. The two systems are implemented electronically. Besides, the performance of each system is evaluated using the eye pattern technique.