Levi-flat Minimal Hypersurfaces in Two-dimensional Complex Space Forms

The purpose of this article is to classify the real hypersurfaces in complex space forms of dimension 2 that are both Levi-flat and minimal. The main results are as follows: When the curvature of the complex space form is nonzero, there is a 1-parameter family of such hypersurfaces. Specifically, for each one-parameter subgroup of the isometry group of the complex space form, there is an essentially unique example that is invariant under this one-parameter subgroup. On the other hand, when the curvature of the space form is zero, i.e., when the space form is complex 2-space with its standard flat metric, there is an additional `exceptional' example that has no continuous symmetries but is invariant under a lattice of translations. Up to isometry and homothety, this is the unique example with no continuous symmetries.

Capacity Investment in Renewable and Conventional Energy Sources

This dissertation studies capacity investments in energy sources, with a focus on renewable technologies, such as solar and wind energy. We develop analytical models to provide insights for policymakers and use real data from the state of Texas to corroborate our findings.

We first take a strategic perspective and focus on electricity pricing policies. Specifically, we investigate the capacity investments of a utility firm in renewable and conventional energy sources under flat and peak pricing policies. We consider generation patterns and intermittency of solar and wind energy in relation to the electricity demand throughout a day. We find that flat pricing leads to a higher investment level for solar energy and it can still lead to more investments in wind energy if considerable amount of wind energy is generated throughout the day.

In the second essay, we complement the first one by focusing on the problem of matching supply with demand in every operating period (e.g., every five minutes) from the perspective of a utility firm. We study the interaction between renewable and conventional sources with different levels of operational flexibility, i.e., the possibility

of quickly ramping energy output up or down. We show that operational flexibility determines these interactions: renewable and inflexible sources (e.g., nuclear energy) are substitutes, whereas renewable and flexible sources (e.g., natural gas) are complements.

In the final essay, rather than the capacity investments of the utility firms, we focus on the capacity investments of households in rooftop solar panels. We investigate whether or not these investments may cause a utility death spiral effect, which is a vicious circle of increased solar adoption and higher electricity prices. We observe that the current rate-of-return regulation may lead to a death spiral for utility firms. We show that one way to reverse the spiral effect is to allow the utility firms to maximize their profits by determining electricity prices.

Division of labor in frontal eye field neurons during presaccadic remapping of visual receptive fields.

Our percept of visual stability across saccadic eye movements may be mediated by presaccadic remapping. Just before a saccade, neurons that remap become visually responsive at a future field (FF), which anticipates the saccade vector. Hence, the neurons use corollary discharge of saccades. Many of the neurons also decrease their response at the receptive field (RF). Presaccadic remapping occurs in several brain areas including the frontal eye field (FEF), which receives corollary discharge of saccades in its layer IV from a collicular-thalamic pathway. We studied, at two levels, the microcircuitry of remapping in the FEF. At the laminar level, we compared remapping between layers IV and V. At the cellular level, we compared remapping between different neuron types of layer IV. In the FEF in four monkeys (Macaca mulatta), we identified 27 layer IV neurons with orthodromic stimulation and 57 layer V neurons with antidromic stimulation from the superior colliculus. With the use of established criteria, we classified the layer IV neurons as putative excitatory (n = 11), putative inhibitory (n = 12), or ambiguous (n = 4). We found that just before a saccade, putative excitatory neurons increased their visual response at the RF, putative inhibitory neurons showed no change, and ambiguous neurons increased their visual response at the FF. None of the neurons showed presaccadic visual changes at both RF and FF. In contrast, neurons in layer V showed full remapping (at both the RF and FF). Our data suggest that elemental signals for remapping are distributed across neuron types in early cortical processing and combined in later stages of cortical microcircuitry.

SAFE: A Declarative Trust-Agile System with Linked Credentials

Secure Access For Everyone (SAFE), is an integrated system for managing trust

using a logic-based declarative language. Logical trust systems authorize each

request by constructing a proof from a context---a set of authenticated logic

statements representing credentials and policies issued by various principals

in a networked system. A key barrier to practical use of logical trust systems

is the problem of managing proof contexts: identifying, validating, and

assembling the credentials and policies that are relevant to each trust

decision.

SAFE addresses this challenge by (i) proposing a distributed authenticated data

repository for storing the credentials and policies; (ii) introducing a

programmable credential discovery and assembly layer that generates the

appropriate tailored context for a given request. The authenticated data

repository is built upon a scalable key-value store with its contents named by

secure identifiers and certified by the issuing principal. The SAFE language

provides scripting primitives to generate and organize logic sets representing

credentials and policies, materialize the logic sets as certificates, and link

them to reflect delegation patterns in the application. The authorizer fetches

the logic sets on demand, then validates and caches them locally for further

use. Upon each request, the authorizer constructs the tailored proof context

and provides it to the SAFE inference for certified validation.

Delegation-driven credential linking with certified data distribution provides

flexible and dynamic policy control enabling security and trust infrastructure

to be agile, while addressing the perennial problems related to today's

certificate infrastructure: automated credential discovery, scalable

revocation, and issuing credentials without relying on centralized authority.

We envision SAFE as a new foundation for building secure network systems. We

used SAFE to build secure services based on case studies drawn from practice:

(i) a secure name service resolver similar to DNS that resolves a name across

multi-domain federated systems; (ii) a secure proxy shim to delegate access

control decisions in a key-value store; (iii) an authorization module for a

networked infrastructure-as-a-service system with a federated trust structure

(NSF GENI initiative); and (iv) a secure cooperative data analytics service

that adheres to individual secrecy constraints while disclosing the data. We

present empirical evaluation based on these case studies and demonstrate that

SAFE supports a wide range of applications with low overhead.