Stable multivariate WW-Eulerian polynomials

We prove a multivariate strengthening of Brenti's result that every root of the Eulerian polynomial of type $B$ is real. Our proof combines a refinement of the descent statistic for signed permutations with the notion of real stability-a generalization of real-rootedness to polynomials in multiple variables. The key is that our refined multivariate Eulerian polynomials satisfy a recurrence given by a stability-preserving linear operator. Our results extend naturally to colored permutations, and we also give stable generalizations of recent real-rootedness results due to Dilks, Petersen, and Stembridge on affine Eulerian polynomials of types $A$ and $C$. Finally, although we are not able to settle Brenti's real-rootedness conjecture for Eulerian polynomials of type $D$, nor prove a companion conjecture of Dilks, Petersen, and Stembridge for affine Eulerian polynomials of types $B$ and $D$, we indicate some methods of attack and pose some related open problems.Comment: 17 pages. To appear in J. Combin. Theory Ser.

Lattice Point Generating Functions and Symmetric Cones

We show that a recent identity of Beck-Gessel-Lee-Savage on the generating function of symmetrically contrained compositions of integers generalizes naturally to a family of convex polyhedral cones that are invariant under the action of a finite reflection group. We obtain general expressions for the multivariate generating functions of such cones, and work out the specific cases of a symmetry group of type A (previously known) and types B and D (new). We obtain several applications of the special cases in type B, including identities involving permutation statistics and lecture hall partitions.Comment: 19 page

Optimal Human Navigation in Steep Terrain: a Hamilton-Jacobi-Bellman Approach

We present a method for determining optimal walking paths in steep terrain using the level set method and an optimal control formulation. By viewing the walking direction as a control variable, we can determine the optimal control by solving a Hamilton-Jacobi-Bellman equation. We then calculate the optimal walking path by solving an ordinary differential equation. We demonstrate the effectiveness of our method by computing optimal paths which travel throughout mountainous regions of Yosemite National Park. We include details regarding the numerical implementation of our model and address a specific application of a law enforcement agency patrolling a nationally protected area.Comment: 19 pages, 11 figure

A Randomized, Double‐Blind Study Comparing Pharmacokinetics and Pharmacodynamics of Proposed Biosimilar ABP 798 With Rituximab Reference Product in Subjects With Moderate to Severe Rheumatoid Arthritis

ABP 798 is a proposed biosimilar to rituximab reference product (RP), an anti-CD20 monoclonal antibody. Pharmacokinetics (PK), pharmacodynamics (PD), and safety results from the comparative clinical study that evaluated the PK, PD, safety, efficacy, and immunogenicity of ABP 798 versus rituximab RP are presented here. Subjects with moderate to severe rheumatoid arthritis (RA) received 2 doses of ABP 798, United States-sourced RP (rituximab US) or European Union-sourced RP (rituximab EU), each consisting of two 1000-mg infusions 2 weeks apart. For the second dose (week 24), ABP 798- and rituximab EU-treated subjects received the same treatment; rituximab US-treated subjects transitioned to ABP 798. End points included area under the serum concentration-time curve from time 0 extrapolated to infinity and maximum observed serum concentration following the second infusion of the first dose (PK) and percentage of subjects with complete CD19+ cell depletion days 1-33 (PD). Primary analysis established PK similarity between ABP 798 and rituximab RP based on 90% confidence intervals of the adjusted geometric mean ratios being within a prespecified equivalence margin of 0.8 and 1.25. Complete CD19+ B-cell depletion on day 3 among groups confirmed PD similarity. These findings demonstrated PK/PD similarity between ABP 798 and rituximab RP in subjects with moderate to severe RA

Three-dimensional coherent X-ray diffraction imaging of a ceramic nanofoam: determination of structural deformation mechanisms

Ultra-low density polymers, metals, and ceramic nanofoams are valued for their high strength-to-weight ratio, high surface area and insulating properties ascribed to their structural geometry. We obtain the labrynthine internal structure of a tantalum oxide nanofoam by X-ray diffractive imaging. Finite element analysis from the structure reveals mechanical properties consistent with bulk samples and with a diffusion limited cluster aggregation model, while excess mass on the nodes discounts the dangling fragments hypothesis of percolation theory.Comment: 8 pages, 5 figures, 30 reference

Psycho-behavioural responses of the general population to COVID-19 after mass vaccination: a cross-sectional study

Abstract Background Previous studies have examined public psycho-behavioural responses in the early stages of the epidemic, little is known after mass vaccination has been implemented. This study aimed to investigate the public's behavioural (adoption of COVID-19 precautionary measures) and psychological (depression, anxiety and stress) responses to COVID-19 and their relationships after the launch of the territory-wide vaccination programme in Hong Kong. Methods A cross-sectional survey study using anonymous online or face-to-face questionnaires was conducted between June 2021 and September 2021. A convenience sample of Hong Kong Chinese residents aged ⩾18 years were recruited online by referrals and from a university-run community vaccination centre. Results A total of 1893 valid questionnaires were received. The results showed that Hong Kong residents have high levels of adoption of precautionary measures and low levels of depression, anxiety and stress after the mass vaccination. Hierarchical regression analysis identified that in the fully adjusted model, the adoption of precautionary measures was a consistent protective factor (β ranged −1.51 to −1.67, p < 0.001) for depression, anxiety and stress amid the COVID-19 pandemic. Conclusions This study offers new information on the public's psycho-behavioural responses to the pandemic, as well as insights into public health planning after introducing the mass vaccination