Sets Characterized by Missing Sums and Differences in Dilating Polytopes

A sum-dominant set is a finite set $A$ of integers such that $|A+A| > |A-A|$. As a typical pair of elements contributes one sum and two differences, we expect sum-dominant sets to be rare in some sense. In 2006, however, Martin and O'Bryant showed that the proportion of sum-dominant subsets of $\{0,\dots,n\}$ is bounded below by a positive constant as $n\to\infty$. Hegarty then extended their work and showed that for any prescribed $s,d\in\mathbb{N}_0$, the proportion $\rho^{s,d}_n$ of subsets of $\{0,\dots,n\}$ that are missing exactly $s$ sums in $\{0,\dots,2n\}$ and exactly $2d$ differences in $\{-n,\dots,n\}$ also remains positive in the limit. We consider the following question: are such sets, characterized by their sums and differences, similarly ubiquitous in higher dimensional spaces? We generalize the integers in a growing interval to the lattice points in a dilating polytope. Specifically, let $P$ be a polytope in $\mathbb{R}^D$ with vertices in $\mathbb{Z}^D$, and let $\rho_n^{s,d}$ now denote the proportion of subsets of $L(nP)$ that are missing exactly $s$ sums in $L(nP)+L(nP)$ and exactly $2d$ differences in $L(nP)-L(nP)$. As it turns out, the geometry of $P$ has a significant effect on the limiting behavior of $\rho_n^{s,d}$. We define a geometric characteristic of polytopes called local point symmetry, and show that $\rho_n^{s,d}$ is bounded below by a positive constant as $n\to\infty$ if and only if $P$ is locally point symmetric. We further show that the proportion of subsets in $L(nP)$ that are missing exactly $s$ sums and at least $2d$ differences remains positive in the limit, independent of the geometry of $P$. A direct corollary of these results is that if $P$ is additionally point symmetric, the proportion of sum-dominant subsets of $L(nP)$ also remains positive in the limit.Comment: Version 1.1, 23 pages, 7 pages, fixed some typo

Prospects for measuring supermassive black hole masses with future extremely large telescopes

The next generation of giant-segmented mirror telescopes ($>$ 20 m) will enable us to observe galactic nuclei at much higher angular resolution and sensitivity than ever before. These capabilities will introduce a revolutionary shift in our understanding of the origin and evolution of supermassive black holes by enabling more precise black hole mass measurements in a mass range that is unreachable today. We present simulations and predictions of the observations of nuclei that will be made with the Thirty Meter Telescope (TMT) and the adaptive optics assisted integral-field spectrograph IRIS, which is capable of diffraction-limited spectroscopy from $Z$ band (0.9 $\mu$m) to $K$ band (2.2 $\mu$m). These simulations, for the first time, use realistic values for the sky, telescope, adaptive optics system, and instrument, to determine the expected signal-to-noise ratio of a range of possible targets spanning intermediate mass black holes of $\sim10^4$ \msun to the most massive black holes known today of $>10^{10}$ $M_\odot$. We find that IRIS will be able to observe Milky Way-mass black holes out the distance of the Virgo cluster, and will allow us to observe many more brightest cluster galaxies where the most massive black holes are thought to reside. We also evaluate how well the kinematic moments of the velocity distributions can be constrained at the different spectral resolutions and plate scales designed for IRIS. We find that a spectral resolution of $\sim8000$ will be necessary to measure the masses of intermediate mass black holes. By simulating the observations of galaxies found in SDSS DR7, we find that over $10^5$ massive black holes will be observable at distances between $0.005 < z < 0.18$ with the estimated sensitivity and angular resolution provided by access to $Z$-band (0.9 $\mu$m) spectroscopy from IRIS and the TMT adaptive optics system. (Abridged)Comment: 19 pages, 20 figures, accepted to A

Fully Endoscopic Microvascular Decompression for Trigeminal Neuralgia

Trigeminal neuralgia (TN) is a chronic, progressive facial pain disorder characterized by severe paroxysmal episodes in the distribution of the trigeminal nerve. The most common cause of (TN) is compression of the trigeminal nerve by a vascular structure within the posterior fossa at the dorsal root entry zone (DREZ). Initially described by Dr. Peter Janetta, microvascular decompression has been clearly demonstrated to be a safe and effective treatment for TN with excellent immediate and long-term pain relief.1 Although neuroimaging has advanced significantly allowing for improved pre-operative visualization of the trigeminal nerve and determination of vascular conflict, most neurosurgeons continue to practice the MVD procedure in a very similar manner to Dr. Janetta’s 1967 description.2 While the retrosigmoid craniotomy and operative microscope allows for an excellent view of the posterior aspect of the trigeminal nerve within the cerebellopontine angle, visualization of the anterior aspect of the nerve is limited. Additionally, adequate visualization of the DREZ may be difficult and require additional retraction of the cerebellum, potentially resulting in complications such as hearing loss and cerebellar injury. As neurosurgical experience with the endoscope has grown, a variety of authors have described performing microvascular decompression with endoscopic assistance which involves using the endoscope to inspect the trigeminal nerve for sites of compression but performing the decompression under the microscope. While the main advantage of the endoscopic approach compared to the microscopic approach is improved visualization of the trigeminal nerve from the DREZ to Meckel’s cave including its inferior, anterior and superior surfaces, evolution of the procedure to a fully endoscopic approach has the additional benefits of being less invasive with minimal soft tissue dissection and cerebellar retraction allowing for reduced patient discomfort and accelerated recovery. In this technical review, we describe our approach to performing a fully endoscopic microvascular decompression including the surgical nuances that allow the procedure to be performed safely and efficiently. Pages 2-

The Effects of Pet Ownership on Anxiety and Depression Among Trauma-Exposed College Students

Rates of anxiety and depression are prevalent in college students and can be attributed in part to stress and trauma-related events. However, studies suggest that pet ownership has the possibility of alleviating symptoms of anxiety, depression, negative emotions, and suicide. The purpose of this study was to determine the relationship between pet ownership and levels of anxiety and depression among those who have experienced a traumatic event. The sample was comprised of five hundred and forty-seven VCU students who completed an online survey from Spit for Science during their junior year. Linear regressions were performed to determine the nature and strength of the relationship between our two variables. After controlling for gender, race/ethnicity, personality, social support, and resiliency, we found statistically significant lower levels of anxiety and depression among pet owners compared to non-pet owners (p=0.004). This study reinforces how pets can impact our mental health, and lends further research to support programs such as VCU’s Center for Human-Animal Interaction (CHAI) and their Dogs on Call program.https://scholarscompass.vcu.edu/uresposters/1238/thumbnail.jp

Risk of SARS-CoV-2 Transmission During Flexible Laryngoscopy: A Systematic Review.

IMPORTANCE: Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) reportedly infected otolaryngologists disproportionately in the early parts of the coronavirus disease 2019 pandemic. Recommendations from national and international health organizations suggest minimizing the use of flexible laryngoscopy as a result. OBJECTIVE: To review evidence on the risks of aerosolization and transmission of SARS-CoV-2 from patients to health care personnel during endoscopy of the upper aerodigestive tract. EVIDENCE REVIEW: A comprehensive review of literature was performed on April 19, 2020, using the PubMed/MEDLINE (1966-April 2020), Embase (1975-April 2020), and Web of Science (1900-April 2020) databases. All English-language primary research studies were included if they assessed the transmission of SARS-CoV-2 or SARS-CoV-1 during procedures in the upper aerodigestive tract. The primary outcome measure was disease transmission among health care workers. The Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines were used for accuracy of reporting. FINDINGS: The queries for SARS-CoV-2 and SARS-CoV-1 identified 6 articles for systematic review. No studies included in this review provided data for SARS-CoV-2 transmission during flexible laryngoscopy. A total of 204 of 1264 health care workers (16.1%) had procedure-specific infections of SARS-CoV-1 or SARS-CoV-2. Among those, 53 of 221 (24.0%) were exposed during intubation, 1 of 15 (6.7%) during bronchoscopy, and 1 of 1 (100%) during endoscopy-assisted intubation. CONCLUSIONS AND RELEVANCE: A substantial lack of research precludes formal conclusions about the safety of flexible laryngoscopy and transmission of SARS-CoV-2 from patients to health care workers. The use of appropriate precautionary measures and personal protective equipment appears to reduce the risk of transmission. Given the uncertainty in transmission and the known benefits of safety precautions, upper airway endoscopy may be reasonable to perform if precautionary steps are taken

Unknown Rectal Lesions: A Case of Severe Proctitis Secondary to Mpox in the Setting of Concomitant HIV, Syphilis, HSV, and Chlamydia

Introduction: Mpox emerged as a public health crisis with limited research describing co-occurring HIV and sexually transmitted infections (STIs). We present a case of severe proctitis secondary to Mpox with concomitant HIV (Human Immunodeficiency Virus), syphilis, HSV (Herpes Simplex Virus), and chlamydia and review presentation, diagnosis, treatment, and prevention of Mpox with concurrent STIs. Case Presentation: 34-year-old male living with HIV (LWH) presenting with worsening rectal pain, multiple anal papules, and fever. His laboratory workup revealed simultaneous positive results for orthopoxvirus, chlamydia, and HSV-1 PCR. We initiated tecovirimat due to rectal involvement and uncontrolled pain. He subsequently developed lesions on hands as rectal pain improved. He completed tecovirimat treatment and the lesions cleared by outpatient follow-up. Discussion: Among published studies of Mpox patients, 40% were LWH, and a significant percent were found to have co-occurring gonorrhea (23%), chlamydia (20%), syphilis (8%), and HSV (1%) with presentations including fever (62%), lymphadenopathy (49%), malaise (39%), and rectal pain (25%). We recommend Mpox and full STI diagnostic testing for unknown anogenital lesions and early treatment should be considered. Early initiation of Tecovirimat treatment should be considered in severe disease, immune deficiency, or those at high-risk for serious sequelae, in accordance with CDC guidelines. Learning Points: Identify the differential diagnosis for unknown rectal lesions Describe the clinical presentation of Mpox Summarize the diagnostic approach and interpretation of diagnostic results Identify treatment options and considerations by patient populations Review preventative strategies and high-risk populations for Mpox transmissio

Comparison of the diagnostic accuracy of three current guidelines for the evaluation of asymptomatic pancreatic cystic neoplasms.

Asymptomatic pancreatic cysts are a common clinical problem but only a minority of these cases progress to cancer. Our aim was to compare the accuracy to detect malignancy of the 2015 American Gastroenterological Association (AGA), the 2012 International Consensus/Fukuoka (Fukuoka guidelines [FG]), and the 2010 American College of Radiology (ACR) guidelines.We conducted a retrospective study at 3 referral centers for all patients who underwent resection for an asymptomatic pancreatic cyst between January 2008 and December 2013. We compared the accuracy of 3 guidelines in predicting high-grade dysplasia (HGD) or cancer in resected cysts. We performed logistic regression analyses to examine the association between cyst features and risk of HGD or cancer.A total of 269 patients met inclusion criteria. A total of 228 (84.8%) had a benign diagnosis or low-grade dysplasia on surgical pathology, and 41 patients (15.2%) had either HGD (n = 14) or invasive cancer (n = 27). Of the 41 patients with HGD or cancer on resection, only 3 patients would have met the AGA guideline\u27s indications for resection based on the preoperative cyst characteristics, whereas 30/41 patients would have met the FG criteria for resection and 22/41 patients met the ACR criteria. The sensitivity, specificity, positive predictive value, negative predictive value of HGD, and/or cancer of the AGA guidelines were 7.3%, 88.2%, 10%, and 84.1%, compared to 73.2%, 45.6%, 19.5%, and 90.4% for the FG and 53.7%, 61%, 19.8%, and 88% for the ACR guidelines. In multivariable analysis, cyst size \u3e3 cm, compared to ≤3 cm, (odds ratio [OR] = 2.08, 95% confidence interval [CI] = 1.11, 4.2) and each year increase in age (OR = 1.07, 95% CI = 1.03, 1.11) were positively associated with risk of HGD or cancer on resection.In patients with asymptomatic branch duct-intraductal papillary mucinous neoplasms or mucinous cystic neoplasms who underwent resection, the prevalence rate of HGD or cancer was 15.2%. Using the 2015 AGA criteria for resection would have missed 92.6% of patients with HGD or cancer. The more inclusive FG and ACR had a higher sensitivity for HGD or cancer but lower specificity. Given the current deficiencies of these guidelines, it will be important to determine the acceptable rate of false-positives in order to prevent a single true-positive

Identification of phenolic compounds in pomegranate (Punica Granatum) seeds and soybean (Glicine Max) oils and its stabilization by spray drying.

Pomegranate seed oil (PSO), even though highly sensitive to oxidation, has been extensively studied due to its bioactive potentials, assigned to the punicic acid, a polyunsaturated fatty acid, and several phenolic compounds. Combined with soybean oil (SO) we get an affordable product, rich in essential fatty acids. In this study we evaluate PSO and SO for phenolic and fatty acids compositions and encapsulate it by spray drying to increase its shelf life. Modified starch, maltodextrin and gum arabic are evaluated by a mixture design to get the better wall material composition. The content of punicic, a conjugated linolenic acid, and linoleic acids in PSO and SO were, respectively 75% and 54%. As expected, the phenolic acids were found at low concentration in PSO and SO, but in high content in pressing cake. The better response for spray drying process yield and oxidative stability were achieved at using modified starch and gum arabic at the same proportion as wall material.Food: the tree that sustains life

Endonasal Vascularized Flaps For Cranial Base Reconstruction

Since the introduction of extended endoscopic cranial base surgery, postoperative cerebrospinal fluid (CSF) leak has been a formidable and troublesome issue resulting in complications such meningitis, pneumocephalus, and the need for additional surgical interventions. Establishment of a watertight cranial base reconstruction is the most critical step in preventing postoperative CSF leakage. Historically, various free grafts, both synthetic and autologous, were utilized as repair materials for reconstruction of the cranial base defect often in combination with temporary CSF diversion. Free grafts are often sufficient for repair of small low flow, low pressure dural defects. High postoperative CSF leak rates reported in the initial endoscopic skull base literature are evidence that free grafts do not provide a reliably competent repair for large defects or direct high-flow CSF leaks. The introduction of the Hadad-Bassagasteguy vascularized nasoseptal flap has significantly reduced the reported CSF leak rate with a recent meta-analysis reporting that use of the vascularized flap is associated with a 7% rate of postoperative CSF leakage compared to 16% with free grafts alone for large dural defects.6 Since the initial description of the vascularized pedicled nasoseptal flap in 2006, many surgeons have developed a variety of alternative vascularized flaps for endonasal cranial base reconstruction. In this article, we summarize and compare several of the most clinically useful vascularized flaps including their harvest technique, indications and limitations, and potential complications. Pages: 28-3