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Boolean functions with high correlation immunity can be used in cryptosystems to defend against correlation attacks. These functions are rare and difficult to find. As the variables increase, this task becomes exponentially more complex and time consuming. Three different ways to execute a program to find the correlation immunity of a function are compared in this thesis. First, a program was written in C and executed on a conventional CPU. The same program was then executed on an FPGA on the SRC-6 reconfigurable computer. A similar program was written in Verilog and executed on the FPGA. By taking advantage of the parallel processing ability of the SRC-6, a wellprogrammed Verilog macro can find functions with high correlation immunity at a much faster rate. The SRC-6 reconfigurable computer is used in this thesis to find the correlation immunity of millions of functions up to six variables. Rotation symmetric and balanced functions were examined to find subsets that contain a high percentage of functions with good correlation immunity. The nonlinearity and correlation immunity of functions of four and five variables were compared to find functions with the best balance to fend off both correlation and linear attacks on a cryptosystem.

 Boolean functions are perhaps the most basic objects of study in theoretical computer science. They also arise in other areas of mathematics, including combinatorics, statisti cal physics, and mathematical social choice. The field of analysis of Boolean functions seeks to understand them via their Fourier transform and other analytic methods. This text gives a thorough overview of the field, beginning with the most basic definitions and proceeding to advanced topics such as hypercontractivity and isoperimetry. Each chapter includes a “highlight application” such as Arrow’s theorem from economics, the Goldreich-Levin algorithm from cryptography/learning theory, H˚astad’s NP-hardness of approximation results, and “sharp threshold” theorems for random graph properties. The book includes nearly 500 exercises and can be used as the basis of a one-semester graduate course. It should appeal to advanced undergraduates, graduate students, and researchers in computer science theory and related mathematical fields.

Evolutionary algorithms (EAs) are population-based general-purpose optimization algorithms, and have been successfully applied in various real-world optimization tasks. However, previous theoretical studies often employ EAs with only a parent or offspring population and focus on specific problems. Furthermore, they often only show upper bounds on the running time, while lower bounds are also necessary to get a complete understanding of an algorithm. In this paper, we analyze the running time of the ($\mu$+$\lambda$)-EA (a general population-based EA with mutation only) on the class of pseudo-Boolean functions with a unique global optimum. By applying the recently proposed switch analysis approach, we prove the lower bound $\Omega(n \ln n+ \mu + \lambda n\ln\ln n/ \ln n)$ for the first time. Particularly on the two widely-studied problems, OneMax and LeadingOnes, the derived lower bound discloses that the ($\mu$+$\lambda$)-EA will be strictly slower than the (1+1)-EA when the population size $\mu$ or $\lambda$ is above a moderate order. Our results imply that the increase of population size, while usually desired in practice, bears the risk of increasing the lower bound of the running time and thus should be carefully considered.

A list of open problems in the field of analysis of boolean functions, compiled February 2012 for the Simons Symposium.

Boolean functions with high correlation immunity can be used in cryptosystems to defend against correlation attacks. These functions are rare and difficult to find. As the variables increase, this task becomes exponentially more complex and time consuming. Three different ways to execute a program to find the correlation immunity of a function are compared in this thesis. First, a program was written in C and executed on a conventional CPU. The same program was then executed on an FPGA on the SRC-6 reconfigurable computer. A similar program was written in Verilog and executed on the FPGA. By taking advantage of the parallel processing ability of the SRC-6, a wellprogrammed Verilog macro can find functions with high correlation immunity at a much faster rate. The SRC-6 reconfigurable computer is used in this thesis to find the correlation immunity of millions of functions up to six variables. Rotation symmetric and balanced functions were examined to find subsets that contain a high percentage of functions with good correlation immunity. The nonlinearity and correlation immunity of functions of four and five variables were compared to find functions with the best balance to fend off both correlation and linear attacks on a cryptosystem.

Boolean functions with high correlation immunity can be used in cryptosystems to defend against correlation attacks. These functions are rare and difficult to find. As the variables increase, this task becomes exponentially more complex and time consuming. Three different ways to execute a program to find the correlation immunity of a function are compared in this thesis. First, a program was written in C and executed on a conventional CPU. The same program was then executed on an FPGA on the SRC-6 reconfigurable computer. A similar program was written in Verilog and executed on the FPGA. By taking advantage of the parallel processing ability of the SRC-6, a wellprogrammed Verilog macro can find functions with high correlation immunity at a much faster rate. The SRC-6 reconfigurable computer is used in this thesis to find the correlation immunity of millions of functions up to six variables. Rotation symmetric and balanced functions were examined to find subsets that contain a high percentage of functions with good correlation immunity. The nonlinearity and correlation immunity of functions of four and five variables were compared to find functions with the best balance to fend off both correlation and linear attacks on a cryptosystem.

Scribe notes from the 2012 Barbados Workshop on Computational Complexity. A series of lectures on Analysis of Boolean Functions by Ryan O'Donnell, with a guest lecture by Per Austrin.

Interaction graphs provide an important qualitative modeling approach for System Biology. This paper presents a novel approach for construction of interaction graph with the help of Boolean function decomposition. Each decomposition part (Consisting of 2-bits) of the Boolean functions has some important significance. In the dynamics of a biological system, each variable or node is nothing but gene or protein. Their regulation has been explored in terms of interaction graphs which are generated by Boolean functions. In this paper, different classes of Boolean functions with regards to Interaction Graph with biologically significant properties have been adumbrated.

1Animal Ghosts

By Elliott O'Donnell

This is a collection of ghost stories in which the antagonists are various animals. Divided up into chapters of ghost sightings by each group of animals, you will hear of hauntings by dogs, cats, birds, jungle animals, etc. (Summary by Allyson Hester)

2Werewolf -- Five Pieces

By Clemence Housman, Elliott O'Donnell, Saki and Carolyn Steward Taylor

Five stories and essays about werewolves. - Summary by david wales

3Dog Ghosts

By Elliott O'Donnell

Stories in which ghosts of dogs figure. This is chapter 2, Apparitions Of Dogs, of the book Animal Ghosts Or, Animal Hauntings and the Hereafter. - Summary by david wales

4Werwolves

By Elliott O'Donnell

Written in 1912 by a famous ghost hunter who was also an occult fantasy writer, this interesting book collects together folktales and traditions from across Europe, starting in the British Isles, through Spain, France, Belgium and Norway to Russia. The "scientific" accounts (including "How to Become a Werewolf") are embellished by anecdotes of the author's personal experiences with werewolves, ghosts and vampires.<br><br>From Chapter 1: It is an old belief that the souls of cataleptic and epileptic people, during the body's unconsciousness, adjourned temporarily to animals, and it is therefore only in keeping with such a view to suggest that on the deaths of such people their spirits take permanently the form of animals. (Summary by Beth Thomas)

5Twenty Years' Experience as a Ghost Hunter

By Elliott O'Donnell

After having a difficult time establishing a career as a novelist, O’Donnell discovered to his happy surprise that the reading public was very interested in his hobby of chasing ghosts, which he called “Superphysical Research.” After this, he made a habit of buttonholing friends and strangers to find out what experiences they had had with spirits and phantasms. He happily volunteered to camp out overnight in houses known to be haunted, and he made a concerted effort to discover any unhappy events that had, perhaps, led a ghost to inhabit. <br><br> This, then, is a collection of his juiciest remembrances of running down ghosts in Europe and America, both in peace and in the horrors of World War. ( Mark Smith)

6Sorcery Club

By Elliott O'Donnell

Leon Hamar and his friends were out-of-work and starving in San Francisco after the firm they worked for went out of business. Leon acquired a strange book and some cash in a trade for his watch-chain, one of his last posessions. He hated books and had no intention of reading the thing, but of course did, and discovered that it told the tale of Atlantis and the society of sorcerers who inhabited it. It not only told the story, but also gave specific instructions for initiation into the black arts. The friends decided they had little to lose and perhaps much to gain, even survival, if they underwent the tests and initiation into the ancient Atlantean black arts. What followed was not, perhaps, what they expected. - Summary by Don W. Jenkins

7Some Haunted Houses of England and Wales

By Elliott O'Donnell

Old buildings necessarily have a history. It is not always a happy history and folklore abounds. Sometimes unhappy souls come back to haunt the current residents or their guests. Whether you believe in ghosts or not, these narratives provide a fascinating insight into the history of the buildings and the hysteria they may induce. - Summary by Lynne Thompson

Bedtime is the time for strange and wonderful stories as we drift into slumber. This children's book is full of them and the adventures of all who climb that Ladder of Rickety Rungs each night. (Summary by Phil Chenevert)

9Scottish Ghost Stories

By Elliott O'Donnell

A public domain collection of Scottish Ghost tales by Elliott O'Donnell. 1911 - Summary by Sherry Morrow