Berkowitz's Algorithm and Clow Sequences

We present a combinatorial interpretation of Berkowitz's algorithm. Berkowitz's algorithm is the fastest known parallel algorithm for computing the characteristic polynomial of a matrix. Our combinatorial interpretation is based on ``loop covers'' introduced by Valiant, and ``clow sequences.'' Clow sequences turn out to capture very succinctly the computations performed by Berkowitz's algorithm, which otherwise is quite difficult to analyze. The main contribution of this paper is a proof of correctness of Berkowitz's algorithm in terms of clow sequences.Comment: Submitted to ELA (Electronic Journal of Linear Algebra

An exact upper bound on the size of minimal clique covers

Indeterminate strings have received considerable attention in the recent past; see for example Christodoulakis et al 2015 and Helling et al 2017. This attention is due to their applicability in bioinformatics, and to the natural correspondence with undirected graphs. One aspect of this correspondence is the fact that the minimal alphabet size of indeterminates representing any given undirected graph corresponds to the size of the minimal clique cover of this graph. This paper solves a related problem proposed in Helling et al 2017: compute $\Theta_n(m)$, which is the size of the largest possible minimal clique cover (i.e., an exact upper bound), and hence alphabet size of the corresponding indeterminate, of any graph on $n$ vertices and $m$ edges

A polytime proof of correctness of the Rabin-Miller algorithm from Fermat's little theorem

Although a deterministic polytime algorithm for primality testing is now known, the Rabin-Miller randomized test of primality continues being the most efficient and widely used algorithm. We prove the correctness of the Rabin-Miller algorithm in the theory V1 for polynomial time reasoning, from Fermat's little theorem. This is interesting because the Rabin-Miller algorithm is a polytime randomized algorithm, which runs in the class RP (i.e., the class of polytime Monte-Carlo algorithms), with a sampling space exponential in the length of the binary encoding of the input number. (The class RP contains polytime P.) However, we show how to express the correctness in the language of V1, and we also show that we can prove the formula expressing correctness with polytime reasoning from Fermat's Little theorem, which is generally expected to be independent of V1. Our proof is also conceptually very basic in the sense that we use the extended Euclid's algorithm, for computing greatest common divisors, as the main workhorse of the proof. For example, we make do without proving the Chinese Reminder theorem, which is used in the standard proofs

WordPress on AWS: a Communication Framework

Every organization needs to communicate with its audience, and social media is an attractive and inexpensive way to maintain dialogic communication. About 1/3 of the Internet web pages are powered by WordPress, and about a million companies have moved their IT infrastructure to the AWS cloud. Together, AWS and WordPress offer an attractive, effective and inexpensive way for companies, both large and small, to maintain their presence on the web

Density functional theory study of quasi-free-standing graphene layer on 4H-SiC(0001) surface decoupled by hydrogen atoms

Epitaxial graphene, grown on SiC(0001) surface, has been widely studied both experimentally and theoretically. It was found that first epitaxial graphene layer in such structures is a buffer layer i.e. there are no characteristic Dirac cones in the band structure associated with it. However, C. Riedl et al. (Phys. Rev. Lett. 103, 246804 (2009)) in their experimental work observed recently that hydrogen intercalation of SiC-graphene samples can recover electronic properties typical to selfstanding graphene. The possible scenarios of hydrogen intercalation inducing graphene layer decoupling, including both the hydrogen penetration paths and energetically stable positions of hydrogen atoms, were modeled in ab initio DFT calculations. From the obtained results it follows that, due to intercalation, the graphene layer moves away to achieve about 3.9 A distance from the SiC surface. Electronic band structure, calculated for such quasi free standing graphene, exhibits Dirac-cone behavior which is in agreement with ARPES measurements.Comment: 4 pages, 5 figure

Comparative Toxicity of Cryoprotectants on Staphylococcus aureus at Room Temperature

Staphylococcus aureus and Methicillin-Resistant S. aureus (MRSA) are important human and veterinary pathogens. Each year, thousands of researchers study these bacteria in detail; therefore, it is common practice for many S. aureus and MRSA isolates to be cryopreserved. Cryopreservation is a method by which bacterial samples are prepared and frozen for long periods of time, enabling future analysis and research. However, a comparison of different cryoprotectant methods for S. aureus preservation has not yet been done. The objective of this study was to determine which cryoprotectant is the most efficient in preserving S. aureus. Dimethyl sulfoxide (DMSO) is a commonly used cryoprotectant, but is also considered highly toxic to bacteria at room temperature. Alternative cryoprotectants such as 60% glycerol, a 50:50 solution of 7% milk and 60% glycerol, or a commercially available kit could be less toxic and thus better suited for cryoprotection. In our study, the four aforementioned cryoprotectants were compared by freezing eight strains of MRSA and two strains of Methicillin Susceptible S. aureus (MSSA) with each method. The samples were then thawed and allowed to sit at room temperature for up to 72 hours, with sampling occurring at predetermined intervals. The samples were serially diluted and plated on Mueller-Hinton agar, and colony-forming units were counted after 24 hours of incubation at 37°C to determine concentration and loss in bacterial population over time. Upon thawing, all samples showed a decrease in initial concentration of at least 80%. Within 72 hours at room temperature, the concentration of bacteria preserved with DMSO showed an additional decrease of 99.52% from the concentration determined at thawing. Samples preserved with glycerol, milk and glycerol solution, and the commercial kit decreased by 71.67%, 67.69%, and 35.10% respectively. No differences were observed between MRSA and MSSA. This suggests that using DMSO as a cryoprotectant is a potential risk because of its high bacterial toxicity. The use of glycerol, milk and glycerol solution, or a commercial kit is recommended based on their lower toxicities. Careful selection of a cryoprotectant is key to preserving valuable strains of S. aureus for future study.The Ohio State University: Undergraduate Research OfficeThe Ohio State University: College of Food, Agricultural, and Environmental SciencesNo embarg

When is the condition of order preservation met?

This article explores a relationship between inconsistency in the pairwise comparisons method and conditions of order preservation. A pairwise comparisons matrix with elements from an alo-group is investigated. This approach allows for a generalization of previous results. Sufficient conditions for order preservation based on the properties of elements of pairwise comparisons matrix are derived. A numerical example is presented.Comment: 19 page

Breaking | Grounding | Growing: Expanding the Rhode Island gardening reentry programs as a pathway towards stability

What happens to the over two million people incarcerated in U.S. prisons and jails? Changing in sentencing laws and policies have created a cycle of imprisonment, racially isolating and oppressing BIPOC communities. Reintegration and reentry programs are an avenue to break the cycle of recidivism. Through my work, I have developed hands-on, structured opportunities for justice-involved adults to rebuild a life for themselves by increasing the accessibility of gardening reentry programs. This project creates a space for mentorship and support for Rhode Island’s formerly incarcerated people with the goal of helping them to develop vital life skills through growing and gardening management. It is time to meet people where they are and grow a space to foster a more inclusive community during this challenging transitional period

Cloudifying the Curriculum with AWS

The Cloud has become a principal paradigm of computing in the last ten years, and Computer Science curricula must be updated to reflect that reality. This paper examines simple ways to accomplish curriculum cloudification using Amazon Web Services (AWS), for Computer Science and other disciplines such as Business, Communication and Mathematics