Physical Sciences and Mathematics Commons^™

On Adaptivity And Randomness For Streaming Algorithms, Manuel Stoeckl

Dartmouth College Ph.D Dissertations

A streaming algorithm has a limited amount of memory and reads a long sequence (data stream) of input elements, one by one, and computes an output depending on the input. Such algorithms may be used in an online fashion, producing a sequence of intermediate outputs corresponding to the prefixes of the data stream. Adversarially robust streaming algorithms are required to give correct outputs with a desired probability even when the data stream is adaptively generated by an adversary that can see all intermediate outputs of the algorithm. This thesis binds together research on a variety of problems related to the …

Say That Again: The Role Of Multimodal Redundancy In Communication And Context, Brandon Javier Dormes

Cognitive Science Senior Theses

With several modes of expression, such as facial expressions, body language, and speech working together to convey meaning, social communication is rich in redundancy. While typically relegated to signal preservation, this study investigates the role of cross-modal redundancies in establishing performance context, focusing on unaided, solo performances. Drawing on information theory, I operationalize redundancy as predictability and use an array of machine learning models to featurize speakers' facial expressions, body poses, movement speeds, acoustic features, and spoken language from 24 TEDTalks and 16 episodes of Comedy Central Stand-Up Presents. This analysis demonstrates that it is possible to distinguish between these …

Cyclic Mixed-Radix Dense Gray Codes, Jessica Cheng

Computer Science Senior Theses

A Gray code is a sequence of n binary integers in the range 0 to n-1 that has the Gray-code property: each integer in the sequence differs from the integer before it in a single digit. Gray codes have many applications, ranging from rotary encoders to Boolean circuit minimization. We refer to Gray codes where the first and last
codewords in the sequence fulfill the Gray-code property as cyclic. Additionally, we refer to a Gray code as dense if the sequence of n numbers consists of a permutation of ⟨0, 1, . . . , n − 1⟩. This thesis …

Space-Efficient Algorithms And Verification Schemes For Graph Streams, Prantar Ghosh

Dartmouth College Ph.D Dissertations

Structured data-sets are often easy to represent using graphs. The prevalence of massive data-sets in the modern world gives rise to big graphs such as web graphs, social networks, biological networks, and citation graphs. Most of these graphs keep growing continuously and pose two major challenges in their processing: (a) it is infeasible to store them entirely in the memory of a regular server, and (b) even if stored entirely, it is incredibly inefficient to reread the whole graph every time a new query appears. Thus, a natural approach for efficiently processing and analyzing such graphs is reading them as …

A Machine-Verified Proof Of Linearizability For A Queue Algorithm, Ugur Yavuz

Dartmouth College Master’s Theses

Proofs of linearizability are typically intricate and lengthy, and readers may find it difficult to verify their correctness. We present a unique technique for producing proofs of linearizability that are fully verifiable by a mechanical proof system, thereby eliminating the need for any manual verification. Specifically, we reduce the burden of proving linearizable object implementations correct to the proof of a particular invariant whose correctness can be shown inductively. Noting that the latter is a task that many proof systems (such as the TLA+ Proof System we chose to work with) are well-suited to handle, this technique allows us to …

Counting And Sampling Small Structures In Graph And Hypergraph Data Streams, Themistoklis Haris

Dartmouth College Undergraduate Theses

In this thesis, we explore the problem of approximating the number of elementary substructures called simplices in large k-uniform hypergraphs. The hypergraphs are assumed to be too large to be stored in memory, so we adopt a data stream model, where the hypergraph is defined by a sequence of hyperedges.

First we propose an algorithm that (ε, δ)-estimates the number of simplices using O(m^1+1/k / T) bits of space. In addition, we prove that no constant-pass streaming algorithm can (ε, δ)- approximate the number of simplices using less than O( m ^1+1/k / T ) bits of space. Thus …

Object Manipulation With Modular Planar Tensegrity Robots, Maxine Perroni-Scharf

Dartmouth College Undergraduate Theses

This thesis explores the creation of a novel two-dimensional tensegrity-based mod- ular system. When individual planar modules are linked together, they form a larger tensegrity robot that can be used to achieve non-prehensile manipulation. The first half of this dissertation focuses on the study of preexisting types of tensegrity mod- ules and proposes different possible structures and arrangements of modules. The second half describes the construction and actuation of a modular 2D robot com- posed of planar three-bar tensegrity structures. We conclude that tensegrity modules are suitably adapted to object manipulation and propose a future extension of the modular 2D …