Decomposition of a complete graph into trails of given lengths

AbstractLet n be an even positive integer and l1, l2,…ls be a sequence of positive integers with a sum equal to 12n(n−1). We prove that Kn, the complete graph of order n, can be decomposed into trails of lengths l1, l2,…,ls if, and only if, s⩾12n

Topological transversals to a family of convex sets

Let $\mathcal F$ be a family of compact convex sets in $\mathbb R^d$. We say that $\mathcal F$ has a \emph{topological $\rho$-transversal of index $(m,k)$} ($\rho<m$, $0<k\leq d-m$) if there are, homologically, as many transversal $m$-planes to $\mathcal F$ as $m$-planes containing a fixed $\rho$-plane in $\mathbb R^{m+k}$. Clearly, if $\mathcal F$ has a $\rho$-transversal plane, then $\mathcal F$ has a topological $\rho$-transversal of index $(m,k),$ for $\rho<m$ and $k\leq d-m$. The converse is not true in general. We prove that for a family $\mathcal F$ of $\rho+k+1$ compact convex sets in $\mathbb R^d$ a topological $\rho$-transversal of index $(m,k)$ implies an ordinary $\rho$-transversal. We use this result, together with the multiplication formulas for Schubert cocycles, the Lusternik-Schnirelmann category of the Grassmannian, and different versions of the colorful Helly theorem by B\'ar\'any and Lov\'asz, to obtain some geometric consequences

Poly(2-propylacrylic acid)/poly(lactic-co-glycolic acid) blend microparticles as a targeted antigen delivery system to direct either CD4+ or CD8+ T cell activation.

Poly(lactic-co-glycolic acid) (PLGA) based microparticles (MPs) are widely investigated for their ability to load a range of molecules with high efficiency, including antigenic proteins, and release them in a controlled manner. Micron-sized PLGA MPs are readily phagocytosed by antigen presenting cells, and localized to endosomes. Due to low pH and digestive enzymes, encapsulated protein cargo is largely degraded and processed in endosomes for MHC-II loading and presentation to CD4+ T cells, with very little antigen delivered into the cytosol, limiting MHC-I antigenic loading and presentation to CD8+ T cells. In this work, PLGA was blended with poly(2-propylacrylic acid) (PPAA), a membrane destabilizing polymer, in order to incorporate an endosomal escape strategy into PLGA MPs as an easily fabricated platform with diverse loading capabilities, as a means to enable antigen presentation to CD8+ T cells. Ovalbumin (OVA)-loaded MPs were fabricated using a water-in-oil double emulsion with a 0% (PLGA only), 3 and 10% PPAA composition. MPs were subsequently determined to have an average diameter of 1 µm, with high loading and a release profile characteristic of PLGA. Bone marrow derived dendritic cells (DCs) were then incubated with MPs in order to evaluate localization, processing, and presentation of ovalbumin. Endosomal escape of OVA was observed only in DC groups treated with PPAA/PLGA blends, which promoted high levels of activation of CD8+ OVA-specific OT-I T cells, compared to DCs treated with OVA-loaded PLGA MPs which were unable activate CD8+ T cells. In contrast, DCs treated with OVA-loaded PLGA MPs promoted OVA-specific OT-II CD4+ T cell activation, whereas PPAA incorporation into the MP blend did not permit CD4+ T cell activation. These studies demonstrate PLGA MP blends containing PPAA are able to provide an endosomal escape strategy for encapsulated protein antigen, enabling the targeted delivery of antigen for tunable presentation and activation of either CD4+ or CD8+ T cells

Combustion Modeling Approach for the Optimization of a Temperature Controlled Reactivity Compression Ignition Engine Fueled with Iso-Octane

In this study, an innovative Low Temperature Combustion (LTC) system named Temperature Controlled Reactivity Compression Ignition (TCRCI) is presented, and a numerical optimization of the hardware and the operating parameters is proposed. The studied combustion system aims to reduce the complexity of the Reaction Controlled Compression Ignition engine (RCCI), replacing the direct injection of high reactivity fuel with a heated injection of low reactivity fuel. The combustion system at the actual state of development is presented, and its characteristics are discussed. Hence, it is clear that the performances are highly limited by the actual diesel-derived hardware, and a dedicated model must be designed to progress in the development of this technology. A Computational Fluid Dynamics (CFD) model suitable for the simulation of this type of combustion is proposed, and it is validated with the available experimental operating conditions. The Particle Swarm Optimization (PSO) algorithm was integrated with the Computational Fluid Dynamic (CFD) software to optimize the engine combustion system by means of computational simulation. The operating condition considered has a relatively high load with a fixed fuel mass and compression ratio. The parameters to optimize are the piston bowl geometry, injection parameters and the boosting pressure. The achieved system configuration is characterized by a wider piston bowl and injection angle, and it is able to increase the net efficiency of 3% and to significantly reduce CO emissions from 0.407 to 0.136 mg

Addendum to: Capillary floating and the billiard ball problem

We compare the results of our earlier paper on the floating in neutral equilibrium at arbitrary orientation in the sense of Finn-Young with the literature on its counterpart in the sense of Archimedes. We add a few remarks of personal and social-historical character.Comment: This is an addendum to my article Capillary floating and the billiard ball problem, Journal of Mathematical Fluid Mechanics 14 (2012), 363 -- 38

On recurrence and ergodicity for geodesic flows on noncompact periodic polygonal surfaces

We study the recurrence and ergodicity for the billiard on noncompact polygonal surfaces with a free, cocompact action of $\Z$ or $\Z^2$. In the $\Z$-periodic case, we establish criteria for recurrence. In the more difficult $\Z^2$-periodic case, we establish some general results. For a particular family of $\Z^2$-periodic polygonal surfaces, known in the physics literature as the wind-tree model, assuming certain restrictions of geometric nature, we obtain the ergodic decomposition of directional billiard dynamics for a dense, countable set of directions. This is a consequence of our results on the ergodicity of \ZZ-valued cocycles over irrational rotations.Comment: 48 pages, 12 figure

Ecosystem carbon 7 dioxide fluxes after disturbance in forests of North America

Disturbances are important for renewal of North American forests. Here we summarize more than 180 site years of eddy covariance measurements of carbon dioxide flux made at forest chronosequences in North America. The disturbances included stand-replacing fire (Alaska, Arizona, Manitoba, and Saskatchewan) and harvest (British Columbia, Florida, New Brunswick, Oregon, Quebec, Saskatchewan, and Wisconsin) events, insect infestations (gypsy moth, forest tent caterpillar, and mountain pine beetle), Hurricane Wilma, and silvicultural thinning (Arizona, California, and New Brunswick). Net ecosystem production (NEP) showed a carbon loss from all ecosystems following a stand-replacing disturbance, becoming a carbon sink by 20 years for all ecosystems and by 10 years for most. Maximum carbon losses following disturbance (g C m−2y−1) ranged from 1270 in Florida to 200 in boreal ecosystems. Similarly, for forests less than 100 years old, maximum uptake (g C m−2y−1) was 1180 in Florida mangroves and 210 in boreal ecosystems. More temperate forests had intermediate fluxes. Boreal ecosystems were relatively time invariant after 20 years, whereas western ecosystems tended to increase in carbon gain over time. This was driven mostly by gross photosynthetic production (GPP) because total ecosystem respiration (ER) and heterotrophic respiration were relatively invariant with age. GPP/ER was as low as 0.2 immediately following stand-replacing disturbance reaching a constant value of 1.2 after 20 years. NEP following insect defoliations and silvicultural thinning showed lesser changes than stand-replacing events, with decreases in the year of disturbance followed by rapid recovery. NEP decreased in a mangrove ecosystem following Hurricane Wilma because of a decrease in GPP and an increase in ER

Dynamic habitat models reflect interannual movement of cetaceans within the California current ecosystem

This modeling project was funded by the Navy, Commander, U.S. Pacific Fleet (U.S. Navy), the Bureau of Ocean Energy Management (BOEM), and by the National Oceanic and Atmospheric Administration (NOAA), National Marine Fisheries Service (NMFS), Southwest Fisheries Science Center (SWFSC). The 2018 survey was conducted as part of the Pacific Marine Assessment Program for Protected Species (PacMAPPS), a collaborative effort between NOAA Fisheries, the U.S. Navy, and BOEM to collect data necessary to produce updated abundance estimates for cetaceans in the CCE study area. BOEM funding was provided via Interagency Agreement (IAA) M17PG00025, and Navy funding via IAA N0007018MP4C560, under the Mexican permit SEMARNAT/SGPA/DGVS/013212/18. The methods used to derive uncertainty estimates were developed as part of “DenMod: Working Group for the Advancement of Marine Species Density Surface Modeling” funded by OPNAV N45 and the SURTASS LFA Settlement Agreement, and managed by the U.S. Navy’s Living Marine Resources (LMR) program under Contract No. N39430-17-C-1982. Other permits included INEGI: Oficio núm. 400./331/2018, INEGI.GMA 1.03 SAGARPA de Oficio B00.02.04.1530/2018 NMFS Permit No. 19091.The distribution of wide-ranging cetacean species often cross national or jurisdictional boundaries, which creates challenges for monitoring populations and managing anthropogenic impacts, especially if data are only available for a portion of the species’ range. Many species found off the U.S. West Coast are known to have continuous distributions into Mexican waters, with highly variable abundance within the U.S. portion of their range. This has contributed to annual variability in design-based abundance estimates from systematic shipboard surveys off the U.S. West Coast, particularly for the abundance of warm temperate species such as striped dolphin, Stenella coeruleoalba, which increases off California during warm-water conditions and decreases during cool-water conditions. Species distribution models (SDMs) can accurately describe shifts in cetacean distribution caused by changing environmental conditions, and are increasingly used for marine species management. However, until recently, data from waters off the Baja California peninsula, México, have not been available for modeling species ranges that span from Baja California to the U.S. West Coast. In this study, we combined data from 1992–2018 shipboard surveys to develop SDMs off the Pacific Coast of Baja California for ten taxonomically diverse cetaceans. We used a Generalized Additive Modeling framework to develop SDMs based on line-transect surveys and dynamic habitat variables from the Hybrid Coordinate Ocean Model (HYCOM). Models were developed for ten species: long- and short-beaked common dolphins (Delphinus delphis delphis and D. d. bairdii), Risso’s dolphin (Grampus griseus), Pacific white-sided dolphin (Lagenorhynchus obliquidens), striped dolphin, common bottlenose dolphin (Tursiops truncatus), sperm whale (Physeter macrocephalus), blue whale (Balaenoptera musculus), fin whale (B. physalus), and humpback whale (Megaptera novaeangliae). The SDMs provide the first fine-scale (approximately 9 x 9 km grid) estimates of average species density and abundance, including spatially-explicit measures of uncertainty, for waters off the Baja California peninsula. Results provide novel insights into cetacean ecology in this region as well as quantitative spatial data for the assessment and mitigation of anthropogenic impacts.Publisher PDFPeer reviewe