Comparing Powers of Edge Ideals

Given a nontrivial homogeneous ideal $I\subseteq k[x_1,x_2,\ldots,x_d]$, a problem of great recent interest has been the comparison of the $r$th ordinary power of $I$ and the $m$th symbolic power $I^{(m)}$. This comparison has been undertaken directly via an exploration of which exponents $m$ and $r$ guarantee the subset containment $I^{(m)}\subseteq I^r$ and asymptotically via a computation of the resurgence $\rho(I)$, a number for which any $m/r > \rho(I)$ guarantees $I^{(m)}\subseteq I^r$. Recently, a third quantity, the symbolic defect, was introduced; as $I^t\subseteq I^{(t)}$, the symbolic defect is the minimal number of generators required to add to $I^t$ in order to get $I^{(t)}$. We consider these various means of comparison when $I$ is the edge ideal of certain graphs by describing an ideal $J$ for which $I^{(t)} = I^t + J$. When $I$ is the edge ideal of an odd cycle, our description of the structure of $I^{(t)}$ yields solutions to both the direct and asymptotic containment questions, as well as a partial computation of the sequence of symbolic defects.Comment: Version 2: Revised based on referee suggestions. Lemma 5.12 was added to clarify the proof of Theorem 5.13. To appear in the Journal of Algebra and its Applications. Version 1: 20 pages. This project was supported by Dordt College's undergraduate research program in summer 201

Automated Termination Analysis for Logic Programs with Cut

Termination is an important and well-studied property for logic programs. However, almost all approaches for automated termination analysis focus on definite logic programs, whereas real-world Prolog programs typically use the cut operator. We introduce a novel pre-processing method which automatically transforms Prolog programs into logic programs without cuts, where termination of the cut-free program implies termination of the original program. Hence after this pre-processing, any technique for proving termination of definite logic programs can be applied. We implemented this pre-processing in our termination prover AProVE and evaluated it successfully with extensive experiments

Nonlinear spectroscopy of exciton-polaritons in a GaAs-based microcavity

We present a systematic investigation of two-photon excitation processes in a GaAs-based microcavity in the strong-coupling regime. We observe second harmonic generation resonant to the upper and lower polariton level, which exhibits a strong dependence on the photonic fraction of the corresponding polariton. In addition we have performed two-photon excitation spectroscopy to identify $2p$ exciton states which are crucial for the operation as a terahertz lasing device, which was suggested recently [A. V. Kavokin et al., Phys. Rev. Lett. \textbf{108}, 197401 (2012)]. However, no distinct signatures of a $2p$ exciton state could be identified, which indicates a low two-photon pumping efficiency

The Importance of Health Literacy: A Student-Led Workshop on Lay Communication

The purpose of this experiential senior project workshop was to advance the knowledge and practice of health communication by (a) delivering a training workshop to Cal Poly undergraduate students and (b) by exploring the relationship between health literacy and effective communication through completion of a rapid review of the literature. The reviewed literature served the purpose of helping the student further design the workshop to elicit a foundational understanding of the elements of effective communication of health information as well as the history and evolution of health literacy as a concept. The workshop revised and delivered by the student was first developed by Dr. Jafrā Thomas (2020) with the stated goal to provide undergraduate students with an awareness of health literacy, the role of plain language in promoting health literacy, and to equip students with practical skills for effectively communicating health information to a lay adult audience. This submission presents the student reflection on their experiential project, the rapid review of literature produced by the student, the elements identified for a successful workshop on the topic, evaluation and analysis of participant pre-and post-workshop surveys, and finally, suggestions for ways to improve the workshop which was guided by the student’s review of literature and experiential reflection. After the conclusion of the workshop, student participants were successfully able to define health literacy and identify at least two tips for effective communication of health information. Some proposed improvements for future workshop revisions include the addition of personal anecdotes and health-related case studies

Effective parallelisation for machine learning

We present a novel parallelisation scheme that simplifies the adaptation of learning algorithms to growing amounts of data as well as growing needs for accurate and confident predictions in critical applications. In contrast to other parallelisation techniques, it can be applied to a broad class of learning algorithms without further mathematical derivations and without writing dedicated code, while at the same time maintaining theoretical performance guarantees. Moreover, our parallelisation scheme is able to reduce the runtime of many learning algorithms to polylogarithmic time on quasi-polynomially many processing units. This is a significant step towards a general answer to an open question [21] on efficient parallelisation of machine learning algorithms in the sense of Nick’s Class (NC). The cost of this parallelisation is in the form of a larger sample complexity. Our empirical study confirms the potential of our parallelisation scheme with fixed numbers of processors and instances in realistic application scenarios

Assessment of the National Test Strategy on the Development of the COVID-19 Pandemic in Denmark

During the COVID-19 pandemic, Denmark has pursued a mass testing strategy culminating in the testing of 12.167 individuals per 100,000 inhabitants per day during the spring of 2021. The strategy included free access to COVID-19 testing, and since 2021, compulsory documentation for negative tests or vaccination has been required for access to workplace, educational institutions, restaurants, and many other places. Testing and subsequent isolation if testing was positive were voluntary. The present study provides an analysis of whether testing frequency in Denmark showed any correlation to hospitalizations throughout the relevant stages of the pandemic. Mass testing was found not to correlate significantly with the number of hospitalizations during the pandemic. Interestingly, during the highest level of testing in spring 2021 the fraction of positive tests increased slightly; thus, the Danish mass testing strategy, at its best, failed to reduce the prevalence of COVID-19. Furthermore, the relationship between positives in antigen testing and in rt-PCR testing indicated that many patients were not tested early in their infection when the risk of transmission was at the highest. In conclusion, the Danish mass testing strategy for COVID-19 does not appear to have a detectable correlation to the number of hospitalizations due to COVID-19

Zero-Knowledge User Authentication: An Old Idea Whose Time Has Come

User authentication can rely on various factors (e.g., a password, a cryptographic key, biometric data) but should not reveal any secret or private information. This seemingly paradoxical feat can be achieved through zero-knowledge proofs. Unfortunately, naive password-based approaches still prevail on the web. Multi-factor authentication schemes address some of the weaknesses of the traditional login process, but generally have deployability issues or degrade usability even further as they assume users do not possess adequate hardware. This assumption no longer holds: smartphones with biometric sensors, cameras, short-range communication capabilities, and unlimited data plans have become ubiquitous. In this paper, we show that, assuming the user has such a device, both security and usability can be drastically improved using an augmented password-authenticated key agreement (PAKE) protocol and message authentication codes.Comment: International Workshop on Security Protocols (SPW) 201

Improved Performance of Gene Set Analysis on Genome-Wide Transcriptomics Data When Using Gene Activity State Estimates

Gene set analysis methods continue to be a popular and powerful method of evaluating genome-wide transcriptomics data. These approach require a priori grouping of genes into biologically meaningful sets, and then conducting downstream analyses at the set (instead of gene) level of analysis. Gene set analysis methods have been shown to yield more powerful statistical conclusions than single-gene analyses due to both reduced multiple testing penalties and potentially larger observed effects due to the aggregation of effects across multiple genes in the set. Traditionally, gene set analysis methods have been applied directly to normalized, log-transformed, transcriptomics data. Recently, efforts have been made to transform transcriptomics data to scales yielding more biologically interpretable results. For example, recently proposed models transform log-transformed transcriptomics data to a confidence metric (ranging between 0 and 100%) that a gene is active (roughly speaking, that the gene product is part of an active cellular mechanism). In this manuscript, we demonstrate, on both real and simulated transcriptomics data, that tests for differential expression between sets of genes using are typically more powerful when using gene activity state estimates as opposed to log-transformed gene expression data. Our analysis suggests further exploration of techniques to transform transcriptomics data to meaningful quantities for improved downstream inference

Morphology of powerful suction organs from blepharicerid larvae living in raging torrents

Background: Suction organs provide powerful yet dynamic attachments for many aquatic animals, including octopus, squid, remora, and clingfish. While the functional morphology of suction organs from some cephalopods and fishes has been investigated in detail, there are only few studies on such attachment devices in insects. Here we characterise the morphology and ultrastructure of the suction attachment organs of net-winged midge larvae (genus Liponeura; Diptera: Blephariceridae) – aquatic insects that live on rocks in rapid alpine waterways where flow speeds can reach 3ms⁻¹– using scanning electron microscopy, confocal laser scanning microscopy, and X-ray computed micro-tomography (micro-CT). Furthermore, we study the function of these organs in vivo using interference reflection microscopy. Results: We identified structural adaptations important for the function of the suction attachment organs in L. cinerascens and L. cordata. First, a dense array of spine-like microtrichia covering each suction disc comes into contact with the substrate upon attachment, analogous to hairy structures on suction organs from octopus, clingfish, and remora fish. These spine-like microtrichia may contribute to the seal and provide increased shear force resistance in high-drag environments. Second, specialised rim microtrichia at the suction disc periphery were found to form a continuous ring in close contact and may serve as a seal on a variety of surfaces. Third, a V-shaped cut on the suction disc (“V-notch“) is actively opened via two cuticular apodemes inserting on its flanks. The apodemes are attached to dedicated V-notch opening muscles, thereby providing a unique detachment mechanism. The complex cuticular design of the suction organs, along with specialized muscles that attach to them, allows blepharicerid larvae to generate powerful attachments which can withstand strong hydrodynamic forces and quickly detach for locomotion. Conclusion: The suction organs from Liponeura are underwater attachment devices specialised for resisting extremely fast flows. Structural adaptations from these suction organs could translate into future bioinspired attachment systems that perform well on a wide range of surfaces