Novel Theorems and Algorithms Relating to the Collatz Conjecture

Proposed in 1937, the Collatz conjecture has remained in the spotlight for mathematicians and computer scientists alike due to its simple proposal, yet intractable proof. In this paper, we propose several novel theorems, corollaries, and algorithms that explore relationships and properties between the natural numbers, their peak values, and the conjecture. These contributions primarily analyze the number of Collatz iterations it takes for a given integer to reach 1 or a number less than itself, or the relationship between a starting number and its peak value.Comment: 17 pages, 4 figures, 4 tables, 3 algorithms, 10 theorems, 2 corollaries, GitHub cod

Dynamic Population Models with Temporal Preferential Sampling to Infer Phenology

To study population dynamics, ecologists and wildlife biologists use relative abundance data, which are often subject to temporal preferential sampling. Temporal preferential sampling occurs when sampling effort varies across time. To account for preferential sampling, we specify a Bayesian hierarchical abundance model that considers the dependence between observation times and the ecological process of interest. The proposed model improves abundance estimates during periods of infrequent observation and accounts for temporal preferential sampling in discrete time. Additionally, our model facilitates posterior inference for population growth rates and mechanistic phenometrics. We apply our model to analyze both simulated data and mosquito count data collected by the National Ecological Observatory Network. In the second case study, we characterize the population growth rate and abundance of several mosquito species in the Aedes genus.Comment: 29 pages, 5 figures, 1 tabl

From START to FINISH : the influence of osmotic stress on the cell cycle

Peer reviewedPublisher PD

Resolving Intravoxel White Matter Structures in the Human Brain Using Regularized Regression and Clustering

The human brain is a complex system of neural tissue that varies significantly between individuals. Although the technology that delineates these neural pathways does not currently exist, medical imaging modalities, such as diffusion magnetic resonance imaging (dMRI), can be leveraged for mathematical identification. The purpose of this work is to develop a novel method employing machine learning techniques to determine intravoxel nerve number and direction from dMRI data. The method was tested on multiple synthetic datasets and showed promising estimation accuracy and robustness for multi-nerve systems under a variety of conditions, including highly noisy data and imprecision in parameter assumptions

Yeast IME2 Functions Early in Meiosis Upstream of Cell Cycle-Regulated SBF and MBF Targets

BACKGROUND: In Saccharomyces cerevisiae, the G1 cyclin/cyclin-dependent kinase (CDK) complexes Cln1,-2,-3/Cdk1 promote S phase entry during the mitotic cell cycle but do not function during meiosis. It has been proposed that the meiosis-specific protein kinase Ime2, which is required for normal timing of pre-meiotic DNA replication, is equivalent to Cln1,-2/Cdk1. These two CDK complexes directly catalyze phosphorylation of the B-type cyclin/CDK inhibitor Sic1 during the cell cycle to enable its destruction. As a result, Clb5,-6/Cdk1 become activated and facilitate initiation of DNA replication. While Ime2 is required for Sic1 destruction during meiosis, evidence now suggests that Ime2 does not directly catalyze Sic1 phosphorylation to target it for destabilization as Cln1,-2/Cdk1 do during the cell cycle. METHODOLOGY/PRINCIPAL FINDINGS: We demonstrated that Sic1 is eventually degraded in meiotic cells lacking the IME2 gene (ime2Δ), supporting an indirect role of Ime2 in Sic1 destruction. We further examined global RNA expression comparing wild type and ime2Δ cells. Analysis of these expression data has provided evidence that Ime2 is required early in meiosis for normal transcription of many genes that are also periodically expressed during late G1 of the cell cycle. CONCLUSIONS/SIGNIFICANCE: Our results place Ime2 at a position in the early meiotic pathway that lies upstream of the position occupied by Cln1,-2/Cdk1 in the analogous cell cycle pathway. Thus, Ime2 may functionally resemble Cln3/Cdk1 in promoting S phase entry, or it could play a role even further upstream in the corresponding meiotic cascade

Establishment of Cohesion at the Pericentromere by the Ctf19 Kinetochore Subcomplex and the Replication Fork-Associated Factor, Csm3

The cohesin complex holds sister chromatids together from the time of their duplication in S phase until their separation during mitosis. Although cohesin is found along the length of chromosomes, it is most abundant at the centromere and surrounding region, the pericentromere. We show here that the budding yeast Ctf19 kinetochore subcomplex and the replication fork-associated factor, Csm3, are both important mediators of pericentromeric cohesion, but they act through distinct mechanisms. We show that components of the Ctf19 complex direct the increased association of cohesin with the pericentromere. In contrast, Csm3 is dispensable for cohesin enrichment in the pericentromere but is essential in ensuring its functionality in holding sister centromeres together. Consistently, cells lacking Csm3 show additive cohesion defects in combination with mutants in the Ctf19 complex. Furthermore, delaying DNA replication rescues the cohesion defect observed in cells lacking Ctf19 complex components, but not Csm3. We propose that the Ctf19 complex ensures additional loading of cohesin at centromeres prior to passage of the replication fork, thereby ensuring its incorporation into functional linkages through a process requiring Csm3

Epileptiform activity contralateral to unilateral hippocampal sclerosis does not cause the expression of brain damage markers

OBJECTIVE: Patients with epilepsy often ask if recurrent seizures harm their brain and aggravate their epileptic condition. This crucial question has not been specifically addressed by dedicated experiments. We analyze here if intense bilateral seizure activity induced by local injection of kainic acid (KA) in the right hippocampus produces brain damage in the left hippocampus. METHODS: Adult guinea pigs were bilaterally implanted with hippocampal electrodes for continuous video-electroencephalography (EEG) monitoring. Unilateral injection of 1 μg KA in the dorsal CA1 area induced nonconvulsive status epilepticus (ncSE) characterized by bilateral hippocampal seizure discharges. This treatment resulted in selective unilateral sclerosis of the KA-injected hippocampus. Three days after KA injection, the animals were killed, and the brains were submitted to ex vivo magnetic resonance imaging (MRI) and were processed for immunohistochemical analysis. RESULTS: During ncSE, epileptiform activity was recorded for 27.6 ± 19.1 hours in both the KA-injected and contralateral hippocampi. Enhanced T1-weighted MR signal due to gadolinium deposition, mean diffusivity reduction, neuronal loss, gliosis, and blood-brain barrier permeability changes was observed exclusively in the KA-injected hippocampus. Despite the presence of a clear unilateral hippocampal sclerosis at the site of KA injection, no structural alterations were detected by MR and immunostaining analysis performed in the hippocampus contralateral to KA injection 3 days and 2 months after ncSE induction. Fluoro-Jade and terminal deoxynucleotidyl transferase dUTP nick end labeling (TUNEL) staining at the same time points confirmed the absence of degenerating cells in the hippocampi contralateral to KA injection. SIGNIFICANCE: We demonstrate that intense epileptiform activity during ncSE does not cause obvious brain damage in the hippocampus contralateral to unilateral hippocampal KA injection. These findings argue against the hypothesis that epileptiform activity per se contributes to focal brain injury in previously undamaged cortical regions

International consensus statement on allergy and rhinology: Olfaction.

BACKGROUND The literature regarding clinical olfaction, olfactory loss, and olfactory dysfunction has expanded rapidly over the past two decades, with an exponential rise in the past year. There is substantial variability in the quality of this literature and a need to consolidate and critically review the evidence. It is with that aim that we have gathered experts from around the world to produce this International Consensus on Allergy and Rhinology: Olfaction (ICAR:O). METHODS Using previously described methodology, specific topics were developed relating to olfaction. Each topic was assigned a literature review, evidence-based review, or evidence-based review with recommendations format as dictated by available evidence and scope within the ICAR:O document. Following iterative reviews of each topic, the ICAR:O document was integrated and reviewed by all authors for final consensus. RESULTS The ICAR:O document reviews nearly 100 separate topics within the realm of olfaction, including diagnosis, epidemiology, disease burden, diagnosis, testing, etiology, treatment, and associated pathologies. CONCLUSION This critical review of the existing clinical olfaction literature provides much needed insight and clarity into the evaluation, diagnosis, and treatment of patients with olfactory dysfunction, while also clearly delineating gaps in our knowledge and evidence base that we should investigate further

International consensus statement on allergy and rhinology: Olfaction

Background: The literature regarding clinical olfaction, olfactory loss, and olfactory dysfunction has expanded rapidly over the past two decades, with an exponential rise in the past year. There is substantial variability in the quality of this literature and a need to consolidate and critically review the evidence. It is with that aim that we have gathered experts from around the world to produce this International Consensus on Allergy and Rhinology: Olfaction (ICAR:O). Methods: Using previously described methodology, specific topics were developed relating to olfaction. Each topic was assigned a literature review, evidence-based review, or evidence-based review with recommendations format as dictated by available evidence and scope within the ICAR:O document. Following iterative reviews of each topic, the ICAR:O document was integrated and reviewed by all authors for final consensus. Results: The ICAR:O document reviews nearly 100 separate topics within the realm of olfaction, including diagnosis, epidemiology, disease burden, diagnosis, testing, etiology, treatment, and associated pathologies. Conclusion: This critical review of the existing clinical olfaction literature provides much needed insight and clarity into the evaluation, diagnosis, and treatment of patients with olfactory dysfunction, while also clearly delineating gaps in our knowledge and evidence base that we should investigate further