Elliptic Solutions of Dynamical Lucas Sequences.

We study two types of dynamical extensions of Lucas sequences and give elliptic solutions for them. The first type concerns a level-dependent (or discrete time-dependent) version involving commuting variables. We show that a nice solution for this system is given by elliptic numbers. The second type involves a non-commutative version of Lucas sequences which defines the non-commutative (or abstract) Fibonacci polynomials introduced by Johann Cigler. If the non-commuting variables are specialized to be elliptic-commuting variables the abstract Fibonacci polynomials become non-commutative elliptic Fibonacci polynomials. Some properties we derive for these include their explicit expansion in terms of normalized monomials and a non-commutative elliptic Euler-Cassini identity.

Predicting the Incremental Hospital Cost of Adverse Events Among Medicare Beneficiaries in the Comprehensive Joint Replacement Program During Fiscal Year 2014.

BACKGROUND: The Medicare program's Comprehensive Care for Joint Replacement (CJR) payment model places hospitals at financial risk for the treatment cost of Medicare beneficiaries (MBs) undergoing lower extremity joint replacement (LEJR). METHODS: This study uses Medicare Provider Analysis and Review File and identified 674,777 MBs with LEJR procedure during fiscal year 2014. Adverse events (death, acute myocardial infarction, pneumonia, sepsis or shock, surgical site bleeding, pulmonary embolism, mechanical complications, and periprosthetic joint infection) were studied. Multivariable regressions were modeled to estimate the incremental hospital cost of treating each adverse event. RESULTS: The risk-adjusted estimated hospital cost of treating adverse events varied from a high of $29,061 (MBs experiencing hip fracture and joint infection) to a low of $6308 (MBs without hip fracture that experienced pulmonary embolism). CONCLUSION: Avoidance of adverse events in the LEJR hospitalization will play an important role in managing episode hospital costs in the Comprehensive Care for Joint Replacement program.

Lack of neuropathological changes in rats administered tedizolid phosphate for nine months.

Tedizolid, a novel oxazolidinone antibacterial, was administered to Long Evans rats by oral gavage once daily for up to 9 months at doses near the maximum tolerated dose (MTD) to evaluate for potential neurotoxicity. Mean plasma exposures of tedizolid at the low-, medium-, and high-dose levels (7.5, 15, and 30 mg/kg of body weight/day for males; 2.5, 5, and 10 mg/kg/day for females) were similar between males and females and were 1.8-, 3.9-, and 8.0-fold greater than exposures in patients at the therapeutic dose (200 mg once daily). Evaluated endpoints included survival, clinical observations, body weight, and food consumption. At 1, 3, 6, and 9 months, ophthalmic examinations, functional observational batteries, and locomotor activity measures were conducted, brain weights/sizes were recorded, and perfusion-fixed tissues were collected from 12 rats/sex/group/time point. A detailed morphological assessment was conducted on brain, eyes, optic nerve/tract, spinal cord, peripheral nerves (includes sciatic, sural, tibial, peroneal, trigeminal), and skeletal muscle. At the end of 9 months, less body weight gain was seen in high-dose males (-6.7%) and females (-5.8%) compared with that seen in controls. There were no tedizolid-related adverse neurobehavioral effects or tedizolid-related histopathologic changes in the central/peripheral nervous systems, including the optic nerve. Results of this study indicate that tedizolid was not neurotoxic when administered long term to pigmented rats at doses near the MTD, which were up to 8-fold higher than the human therapeutic exposure.

On the infinite Borwein product raised to a positive real power.

In this paper, we study properties of the coefficients appearing in the q-series expansion of ∏n≥1[(1-qn)/(1-qpn)]δ, the infinite Borwein product for an arbitrary prime p, raised to an arbitrary positive real power δ. We use the Hardy-Ramanujan-Rademacher circle method to give an asymptotic formula for the coefficients. For p=3 we give an estimate of their growth which enables us to partially confirm an earlier conjecture of the first author concerning an observed sign pattern of the coefficients when the exponent δ is within a specified range of positive real numbers. We further establish some vanishing and divisibility properties of the coefficients of the cube of the infinite Borwein product. We conclude with an Appendix presenting several new conjectures on precise sign patterns of infinite products raised to a real power which are similar to the conjecture we made in the p=3 case.

Three families of q-supercongruences modulo the square and cube of a cyclotomic polynomial.

In this paper, three parametric q-supercongruences for truncated very-well-poised basic hypergeometric series are proved, one of them modulo the square, the other two modulo the cube of a cyclotomic polynomial. The main ingredients of proof include a basic hypergeometric summation by George Gasper, the method of creative microscoping (a method recently introduced by the first author in collaboration with Wadim Zudilin), and the Chinese remainder theorem for coprime polynomials.

New q-Analogues of Van Hamme's (E.2) Supercongruence and of a Supercongruence by Swisher.

In this paper, a couple of q-supercongruences for truncated basic hypergeometric series are proved, most of them modulo the cube of a cyclotomic polynomial. One of these results is a new q-analogue of the (E.2) supercongruence by Van Hamme, another one is a new q-analogue of a supercongruence by Swisher, while the other results are closely related q-supercongruences. The proofs make use of special cases of a very-well-poised 6 ϕ 5 summation. In addition, the proofs utilize the method of creative microscoping (which is a method recently introduced by the first author in collaboration with Wadim Zudilin), and the Chinese remainder theorem for coprime polynomials.

Some q-supercongruences modulo the square and cube of a cyclotomic polynomial.

Two q-supercongruences of truncated basic hypergeometric series containing two free parameters are established by employing specific identities for basic hypergeometric series. The results partly extend two q-supercongruences that were earlier conjectured by the same authors and involve q-supercongruences modulo the square and the cube of a cyclotomic polynomial. One of the newly proved q-supercongruences is even conjectured to hold modulo the fourth power of a cyclotomic polynomial.

A New Family of q-Supercongruences Modulo the Fourth Power of a Cyclotomic Polynomial.

We establish a new family of q-supercongruences modulo the fourth power of a cyclotomic polynomial, and give several related results. Our main ingredients are q-microscoping and the Chinese remainder theorem for polynomials.

Some New q-Congruences for Truncated Basic Hypergeometric Series: Even Powers.

We provide several new q-congruences for truncated basic hypergeometric series with the base being an even power of q. Our results mainly concern congruences modulo the square or the cube of a cyclotomic polynomial and complement corresponding ones of an earlier paper containing q-congruences for truncated basic hypergeometric series with the base being an odd power of q. We also give a number of related conjectures including q-congruences modulo the fifth power of a cyclotomic polynomial and a congruence for a truncated ordinary hypergeometric series modulo the seventh power of a prime greater than 3.

Reduced post-operative opioid use decreases length of stay and readmission rates in patients undergoing hip and knee joint arthroplasty.

BACKGROUND: While adequate pain relief is central to patient recovery and satisfaction, opioid use is associated with side effects, adverse drug events and opioid use disorder and therefore is under increased scrutiny. Enhanced surgical recovery protocols include multimodal pain management as a key process, but the impact of opioid dose as an independent variable has not been examined. METHODS: Retrospective analysis of 51,824 hip and knee arthroplasty encounters in a large healthcare system. RESULTS: Overall, patients receiving treatment with lower doses of opiates had shorter median length of stay (p < 0.001); this earlier discharge had no negative consequences on readmission rates. In particular, patients discharged on day 1 received a lower median morphine milligram equivalent (MME) per day than those who were not discharged (32.5 [IQR: 19.0-50.0] versus 45.0 [26.7-71.2], respectively, p < 0.001). The probability of discharge on day 1 was 41.2% and 19.6% for those patients on lower versus higher MME/day, respectively. Similarly, there was a reduction in odds of readmission of 15.2% (95% CI 5.8-23.6%) for patients on lower doses of MME/day. CONCLUSION: Lower MME/day following joint arthroplasty is linked to the probability of discharge on both days 1 and 2 post-surgery as well as reduced odds of readmission. These findings persisted even when adjusting for all other factors, including participation in the enhanced surgical recovery program, the use of a multi-modal analgesic regimen, the presence of complications, patient demographics, and other baseline characteristics. Efforts to reduce opioid use in the peri- and immediate post-operative period, regardless of the mechanism, demonstrated a significant effect on patient outcomes.

OSWG Recommendations for Genotoxicity Testing of Novel Oligonucleotide-Based Therapeutics.

The Oligonucleotide Safety Working Group subcommittee on genotoxicity testing considers therapeutic oligonucleotides (ONs) unlikely to be genotoxic based on their properties and on the negative results for ONs tested to date. Nonetheless, the subcommittee believes that genotoxicity testing of new ONs is warranted because modified monomers could be liberated from a metabolized ON and incorporated into DNA and could hypothetically cause chain termination, miscoding, and/or faulty replication or repair. The standard test battery as described in Option 1 of International Conference on Harmonisation S2(R1) is generally adequate to assess such potential. However, for the in vitro assay for gene mutations, mammalian cells are considered more relevant than bacteria for most ONs due to their known responsiveness to nucleosides and their greater potential for ON uptake; on the other hand, bacterial assays may be more appropriate for ONs containing non-ON components. Testing is not recommended for ONs with only naturally occurring chemistries or for ONs with chemistries for which there is documented lack of genotoxicity in systems with demonstrated cellular uptake. Testing is recommended for ONs that contain non-natural chemical modifications and use of the complete drug product (including linkers, conjugates, and liposomes) is suggested to provide the most clinically relevant assessment. Documentation of uptake into cells comparable to those used for genotoxicity testing is proposed because intracellular exposure cannot be assumed for these large molecules. ONs could also hypothetically cause mutations through triple helix formation with genomic DNA and no tests are available for detection of such sequence-specific mutations across the entire genome. However, because the potential for triplex formation by therapeutic ONs is extremely low, this potential can be assessed adequately by sequence analysis.

Dietary Pectin Increases Intestinal Crypt Stem Cell Survival following Radiation Injury.

Gastrointestinal (GI) mucosal damage is a devastating adverse effect of radiation therapy. We have recently reported that expression of Dclk1, a Tuft cell and tumor stem cell (TSC) marker, 24h after high dose total-body gamma-IR (TBI) can be used as a surrogate marker for crypt survival. Dietary pectin has been demonstrated to possess chemopreventive properties, whereas its radioprotective property has not been studied. The aim of this study was to determine the effects of dietary pectin on ionizing radiation (IR)-induced intestinal stem cell (ISC) deletion, crypt and overall survival following lethal TBI. C57BL/6 mice received a 6% pectin diet and 0.5% pectin drinking water (pre-IR mice received pectin one week before TBI until death; post-IR mice received pectin after TBI until death). Animals were exposed to TBI (14 Gy) and euthanized at 24 and 84h post-IR to assess ISC deletion and crypt survival respectively. Animals were also subjected to overall survival studies following TBI. In pre-IR treatment group, we observed a three-fold increase in ISC/crypt survival, a two-fold increase in Dclk1+ stem cells, increased overall survival (median 10d vs. 7d), and increased expression of Dclk1, Msi1, Lgr5, Bmi1, and Notch1 (in small intestine) post-TBI in pectin treated mice compared to controls. We also observed increased survival of mice treated with pectin (post-IR) compared to controls. Dietary pectin is a radioprotective agent; prevents IR-induced deletion of potential reserve ISCs; facilitates crypt regeneration; and ultimately promotes overall survival. Given the anti-cancer activity of pectin, our data support a potential role for dietary pectin as an agent that can be administered to patients receiving radiation therapy to protect against radiation-induces mucositis.

Ablation of Doublecortin-Like Kinase 1 in the Colonic Epithelium Exacerbates Dextran Sulfate Sodium-Induced Colitis.

Doublecortin-like kinase 1 (Dclk1), a microtubule-associated kinase, marks the fifth lineage of intestinal epithelial cells called tuft cells that function as tumor stem cells in Apc mutant models of colon cancer. In order to determine the role of Dclk1 in dextran sulfate sodium (DSS) induced colonic inflammation both intestinal epithelial specific Dclk1 deficient (VillinCre;Dclk1f/f) and control (Dclk1f/f) mice were fed 3% DSS in drinking water for 9 days, allowed to recover for 2 days, and killed. The clinical and histological features of DSS-induced colitis were scored and immunohistochemical, gene expression, pro-inflammatory cytokines/chemokines, and immunoblotting analyses were used to examine epithelial barrier integrity, inflammation, and stem and tuft cell features. In DSS-induced colitis, VillinCre;Dclk1f/f mice demonstrated exacerbated injury including higher clinical colitis scores, increased epithelial barrier permeability, higher levels of pro-inflammatory cytokines and chemokines, decreased levels of Lgr5, and dysregulated Wnt/b-Catenin pathway genes. These results suggest that Dclk1 plays an important role in regulating colonic inflammatory response and colonic epithelial integrity.

Doublecortin-like kinase 1 is elevated serologically in pancreatic ductal adenocarcinoma and widely expressed on circulating tumor cells.

Doublecortin-like kinase 1 (DCLK1) is a putative pancreatic stem cell marker and is upregulated in pancreatic cancer, colorectal cancer, and many other solid tumors. It marks tumor stem cells in mouse models of intestinal neoplasia. Here we sought to determine whether DCLK1 protein can be detected in the bloodstream and if its levels in archived serum samples could be quantitatively assessed in pancreatic cancer patients. DCLK1 specific ELISA, western blotting, and immunohistochemical analyses were used to determine expression levels in the serum and staining intensity in archived tumor tissues of pancreatic ductal adenocarcinoma (PDAC) patients and in pancreatic cancer mouse models. DCLK1 levels in the serum were elevated in early stages of PDAC (stages I and II) compared to healthy volunteers (normal controls). No differences were observed between stages III/IV and normal controls. In resected surgical tissues, DCLK1 expression intensity in the stromal cells was significantly higher than that observed in tumor epithelial cells. Circulating tumor cells were isolated from KPCY mice and approximately 52% of these cells were positive for Dclk1 staining. Dclk1 levels in the serum of KPC mice were also elevated. We have previously demonstrated that DCLK1 plays a potential role in regulating epithelial mesenchymal transition (EMT). Given the increasingly recognized role of EMT derived stem cells in cancer progression and metastasis, we hypothesize that DCLK1 may contribute to the metastatic process. Taken together, our results suggest that DCLK1 serum levels and DCLK1 positive circulating tumor cells should be further assessed for their potential diagnostic and prognostic significance.

DCLK1 is a broadly dysregulated target against epithelial-mesenchymal transition, focal adhesion, and stemness in clear cell renal carcinoma.

Renal clear cell carcinoma (RCC) is the most common type of kidney cancer and the 8th most common cancer overall in the US. RCC survival rates drop precipitously with regional and distant spread and recent studies have demonstrated that RCC presents an epithelial-mesenchymal transition (EMT) phenotype linked to increased recurrence and decreased survival. EMT is a key characteristic of tumor stem cells (TSCs) along with chemo-resistance and radio-resistance, which are also phenotypic of RCC. Targeting these factors is key to increasing the survival of RCC patients. Doublecortin-like kinase 1 (DCLK1) marks TSCs in pancreatic and colorectal cancer and regulates EMT and stemness. Analysis of the Cancer Genome Atlas' RCC dataset revealed that DCLK1 is overexpressed and dysregulated on the mRNA and epigenetic level in more than 93% of RCC tumors relative to adjacent normal tissue. Immunohistochemistry using α-DCLK1 antibody confirmed overexpression and demonstrated a major increase in immunoreactivity in stage II-III tumors compared to normal kidney and stage I tumors. Small-interfering RNA (siRNA) mediated knockdown of DCLK1 resulted in decreased expression of EMT and pluripotency factors and significantly reduced invasion, migration, focal adhesion, drug-resistance, and clonogenic capacity. These findings suggest that DCLK1 is a novel, overexpressed factor in RCC progression that may be targeted to suppress EMT, metastasis, and stemness in early-stage and advanced RCC to increase patient survival. Moreover, the possibility that DCLK1 may mark a population of tumor stem-like cells in RCC should be further investigated in light of these findings.

Amide proton transfer imaging of human brain tumors at 3T.

Amide proton transfer (APT) imaging is a technique in which the nuclear magnetization of water-exchangeable amide protons of endogenous mobile proteins and peptides in tissue is saturated, resulting in a signal intensity decrease of the free water. In this work, the first human APT data were acquired from 10 patients with brain tumors on a 3T whole-body clinical scanner and compared with T1- (T1w) and T2-weighted (T2w), fluid-attenuated inversion recovery (FLAIR), and diffusion images (fractional anisotropy (FA) and apparent diffusion coefficient (ADC)). The APT-weighted images provided good contrast between tumor and edema. The effect of APT was enhanced by an approximate 4% change in the water signal intensity in tumor regions compared to edema and normal-appearing white matter (NAWM). These preliminary data from patients with brain tumors show that the APT is a unique contrast that can provide complementary information to standard clinical MRI measures.