Zero-knowledge protocols enable one party, called a prover, to "convince" another party, called a verifier, the validity of a mathematical statement such that the verifier "learns nothing" other than the fact that the proven statement is true. The different ways of formulating the terms "convince" and "learns nothing" gives rise to four classes of languages having zero-knowledge protocols, which are: statistical zero-knowledge proof systems, computational zero-knowledge proof systems, statistical zero-knowledge argument systems, and computational zero-knowledge argument systems. We establish complexity-theoretic characterization of the classes of languages in NP having zero-knowledge argument systems. Using these characterizations, we show that for languages in NP: -- Instance-dependent commitment schemes are necessary and sufficient for zero-knowledge protocols. Instance-dependent commitment schemes for a given language are commitment schemes that can depend on the instance of the language, and where the hiding and binding properties are required to hold only on the YES and NO instances of the language, respectively. -- Computational zero knowledge and computational soundness (a property held by argument systems) are symmetric properties. Namely, we show that the class of languages in NP intersect co-NP having zero-knowledge arguments is closed under complement, and that a language in NP has a statistical zero-knowledge **argument** system if and only if its complement has a **computational** zero-knowledge proof system. -- A method of transforming any zero-knowledge protocol that is secure only against an honest verifier that follows the prescribed protocol into one that is secure against malicious verifiers. In addition, our transformation gives us protocols with desirable properties like having public coins, being black-box simulatable, and having an efficient prover. The novelty of our results above is that they are **unconditional**, meaning that they do not rely on any unproven complexity assumptions such as the existence of one-way functions. Moreover, in establishing our complexity-theoretic characterizations, we give the first construction of statistical zero-knowledge argument systems for NP based on any one-way function.

The Hilbert scheme of \(n\) points in the projective plane parameterizes degree \(n\) zero-dimensional subschemes of the projective plane. We examine the dual cones of effective divisors and moving curves on the Hilbert scheme. By studying interpolation, restriction, and stability properties of certain vector bundles on the plane we fully determine these cones for just over three fourths of all values of \(n\). A general Steiner bundle on \(\mathbb{P}^N\) is a vector bundle \(E\) admitting a resolution of the form \(0 \rightarrow \mathcal{O}_{\mathbb{P}^N} (−1)^s {M \atop \rightarrow} \mathcal{O}^{s+r}_{\mathbb{P}^N} \rightarrow E \rightarrow 0\), where the map \(M\) is general. We complete the classification of slopes of semistable Steiner bundles on \(\mathbb{P}^N\) by showing every admissible slope is realized by a bundle which restricts to a balanced bundle on a rational curve. The proof involves a basic question about multiplication of polynomials on \(\mathbb{P}^1\) which is interesting in its own right. / Mathematics

published_or_final_version / Public Administration / Master / Master of Social Sciences

Let Md be the moduli space of algebraic maps (morphisms) of degree d from P^1 to a fixed Grassmannian. The main purpose of this thesis is to provide an explicit construction of a compactification of Md satisfying the following property: the compactification is a smooth projective variety and the boundary is a simple normal crossing divisor. The main tool of the construction is blowing-up. We start with a smooth compactification given by Quot scheme, which we denote by Qd. The boundary Qd\Md is singular and of high codimension. Next, we give a filtration of the boundary Qd\Md by closed subschemes: Zd,0 subset Zd,1 subset ... Zd,d-1=Qd\Md. Then we blow up the Quot scheme Qd along these subschemes succesively, and prove that the final outcome is a compactification satisfying the desired properties. The proof is based on the key observation that each Zd,r has a smooth projective variety which maps birationally onto it. This smooth projective variety, denoted by Qd,r, is a relative Quot scheme over the Quot-scheme compactification Qr for Mr. The map from Qd,r to Zd,r is an isomorphism when restricted to the preimage of Zd,r\ Zd,r-1. With the help of the Qd,r's, one can show that the final outcome of the successive blowing-up is a smooth compactification whose boundary is a simple normal crossing divisor.

<p>We study first order deformations of the tangent sheaf of resolutions of Calabi-Yau threefolds that are of the form $\CC^3/\ZZ_r$, focusing</p><p> on the cases where the orbifold has an isolated singularity. We prove a lower bound on the number </p><p>of deformations of the tangent bundle for any crepant resolution of this orbifold. We show that this lower bound is achieved when the resolution used is the </p><p>G-Hilbert scheme, and note that this lower bound can be found using a combinatorial count of (0,2)-deformation moduli fields for</p><p>N=(2,2) conformal field theories on the orbifold. We also find that in general this minimum is not achieved, and expect the discrepancy </p><p>to be explained by worldsheet instanton corrections coming from rational curves in the orbifold resolution. We show that </p><p>irreducible toric rational curves will account for some of the discrepancy, but also prove that there must be additional</p><p>worldsheet instanton corrections beyond those from smooth isolated rational curves.</p> / Dissertation

Consequences of global warming and climate change issues have become more apparent over the last several decades. Heat waves, floods, tornados and storms are not just natural disasters occurring elsewhere, but they are now serious environmental catastrophes threatening New Zealand (NZ) and nearby countries as a result of continously escalating greenhouse gas (GHG) emissions. Thus, the Kyoto Protocol was prepared for countries to work collaborately to provide a solution through encourging countries to commit themselves to reducing their individual share of the total GHG emissions. To date, NZ has gone through several phases of modification – introducing and revising two distinctive climate change policies (a Carbon Tax and an Emissions Trading Scheme [ETS]) as a tool to reduce GHG in NZ. These attempts to address climate change, coupled with the question raised by McDonald (Irish Times, 2009) doubting the actual effect of a tax on behaviour-change, provide an extensive basis for a case study in a NZ context involving an evaluation of the effectiveness of these regimes on incentivising behaviour-change to reduce and stablise the level of GHG emissions. In an attempt to answer the research question and conduct a case study in a NZ context, a triangulation approach incorporating both quantitative and qualitative research methods was undertaken. Statistical data analysis was conducted as a quantitative method to analyse and compare numerical changes 'with‘ and 'without‘ the existence of climate change policies. To enhance the results obtained from the quantitative research, qualitative information was also collected by interviewing politicians directly related to the introduction, implementation and the review process of the climate change policies in a semi-structured manner. The results of this study reinforced the need for regulations and policies to reduce and maintain the level of GHG emissions. Statistical data analysis proved that the existence of climate change policies results in lower level of GHG emissions. The interviewees also perceived that some sort of policy is definitely required to regulate the level of emissions, although whether the current, National-led Government‘s modfied-ETS is the 'right' approach is still uncertain. However, the majority of interviewees agreed that the type of tool does not matter, as long as it is correctly-designed to reflect the necessary policies to influence the decision making process of individuals and businesses, and ultimately change their behaviour as a result. However, in order to maintain NZ‘s relationship with other countries, it is preferable to retain its ETS regime until other countries decide to do otherwise.

The continual increase in electrical energy demand in South Africa has resulted in a precariously low reserve margin in supply from the primary utility, Eskom. This resulted in extensive load shedding throughout the country. Far-reaching measures had to be introduced in order to ensure a reliable supply of electricity. DSM interventions were shown to be very successful short term solutions for the mining industry, reducing the strain on the national grid. This resulted in an increasing number of investigations to broaden the base of DSM projects to other industries. One such intervention was the Usutu-Vaal water distribution scheme, situated near Standerton, South Africa. This scheme includes the Grootdraai, Tutuka, Grootfontein, Rietfontein and Naauwpoort pumping stations. With a combined installed capacity of 36.5MW and the extremely large water storage capacities, these pump stations have been identified as prime candidates for DSM interventions. This dissertation discusses the method followed for a DSM project intervention and the results of the implementation. The national grid was relieved by an average of 12.3 MW during the Eskom weekday peak period, by shifting the pumping load into the off-peak periods. Simulations have shown that an annual financial saving of approximately R4.7million may be expected. / Thesis (MIng (Mechanical Engineering))--North-West University, Potchefstroom Campus, 2013

The continual increase in electrical energy demand in South Africa has resulted in a precariously low reserve margin in supply from the primary utility, Eskom. This resulted in extensive load shedding throughout the country. Far-reaching measures had to be introduced in order to ensure a reliable supply of electricity. DSM interventions were shown to be very successful short term solutions for the mining industry, reducing the strain on the national grid. This resulted in an increasing number of investigations to broaden the base of DSM projects to other industries. One such intervention was the Usutu-Vaal water distribution scheme, situated near Standerton, South Africa. This scheme includes the Grootdraai, Tutuka, Grootfontein, Rietfontein and Naauwpoort pumping stations. With a combined installed capacity of 36.5MW and the extremely large water storage capacities, these pump stations have been identified as prime candidates for DSM interventions. This dissertation discusses the method followed for a DSM project intervention and the results of the implementation. The national grid was relieved by an average of 12.3 MW during the Eskom weekday peak period, by shifting the pumping load into the off-peak periods. Simulations have shown that an annual financial saving of approximately R4.7million may be expected. / Thesis (MIng (Mechanical Engineering))--North-West University, Potchefstroom Campus, 2013

ABSTRACT Bergman Trygg, E. 2014. Investigating the effect of monetary compensation on Human-Elephant Conflict, A qualitative study in Idodi and Pawaga Divisions, Tanzania. Department of Social and Economic Geography, Uppsatser: Kulturgeografiska institutionen, Uppsala University. The purpose of this study is to investigate how a compensation scheme affects farmers’ attitudes toward elephants, the Tanzanian government and the concept of conservation. Another purpose is to see what respondents know about the scheme in relation to what is written in the scheme documents. This was done by conducting 20 qualitative interviews with farmers in five different villages in Idodi and Pawaga Divisions, Tanzania. Respondents were divided into two groups: One who had received compensation and one who had not. This aimed to distinguish differences between respondent groups, hence evaluating the efficacy of the compensation scheme and how it affects their attitudes. More interviews were conducted with victims or their relatives who had been attacked by wild animals in order to see what these victims knew of the scheme and how authorities handled attacks.      Results showed small differences between the groups. Both had positive attitudes toward elephants and conservation, contradicting to what is presented in earlier studies. Attitudes toward the government were mainly negative due to suspicions of corruption. There were more positive attitudes toward the government among respondents who had received compensation. Knowledge of the scheme was low compared to what is written in the scheme documents.   Keywords: Human-elephant conflict, compensation scheme, attitudes, farmers, Tanzania   Supervisor: Bert Eriksson.

The relay channel plays an integral role in network communication systems. An intermediate node acts as a relay to facilitate the communication between the source and the destination. If the rate of codewords is less than the capacity of the source-relay link, the relay can decode the source's messages and forward them to the destination. On the contrary, if the rate of codewords is greater than the capacity of the source-relay link, the relay cannot decode the messages. Nevertheless, the relay can still compress its observations and then send them to the destination. Obviously, if the relay-destination link is of a capacity high enough such that the relay's observations can be losslessly sent to the destination, then the maximum message rate can be achieved as if the relay and the destination can jointly decode. However, when the relay-destination link is of a limited capacity such that the relay's observation cannot be losslessly forwarded to the destination, then what is the maximum achievable rate from the source to the destination? This problem was formulated by Cover in another perspective [7], i.e., what is the minimum rate of the relay-destination link such that the maximum message rate can be achieved? We try to answer this Cover's problem in this thesis. First, a sufficient rate to achieve the maximum message rate can be obtained by Slepian-Wolf coding, which gives us an upper bound on the optimal relay-destination link rate. In this thesis, we show that under some channel conditions, this sufficient condition is also necessary, which implies that Slepian-Wolf coding is already optimal. Hence, the upper bound meets exactly the minimum value of the required rate. In our approach, we start with the standard converse proof. First, we present a necessary condition for achieving the maximum message rate in the single-letter form. Following the condition, we derive a theorem, which is named as "single-letter criterion". The "single-letter criterion" can be easily utilized to verify different channels. Then we show that for two special cases: when the source-relay link and the source-destination link of the relay channel are both binary symmetric channels (BSCs), and when they are both binary erasure channels (BECs), Slepian-Wolf coding is optimal in achieving the maximum message rate. Moreover, the maximum message rates of these two special channels are also calculated in this thesis.