Minimal Castelnuovo-Mumford regularity for a given Hilbert polynomial

Let $K$ be an algebraically closed field of null characteristic and $p(z)$ a Hilbert polynomial. We look for the minimal Castelnuovo-Mumford regularity $m_{p(z)}$ of closed subschemes of projective spaces over $K$ with Hilbert polynomial $p(z)$. Experimental evidences led us to consider the idea that $m_{p(z)}$ could be achieved by schemes having a suitable minimal Hilbert function. We give a constructive proof of this fact. Moreover, we are able to compute the minimal Castelnuovo-Mumford regularity $m_p(z)^{\varrho}$ of schemes with Hilbert polynomial $p(z)$ and given regularity $\varrho$ of the Hilbert function, and also the minimal Castelnuovo-Mumford regularity $m_u$ of schemes with Hilbert function $u$. These results find applications in the study of Hilbert schemes. They are obtained by means of minimal Hilbert functions and of two new constructive methods which are based on the notion of growth-height-lexicographic Borel set and called ideal graft and extended lifting.Comment: 21 pages. Comments are welcome. More concise version with a slight change in the title. A further revised version has been accepted for publication in Experimental Mathematic

Achieving full diversity in multi-antenna two-way relay networks via symbol-based physical-layer network coding

This paper considers physical-layer network coding (PNC) with M-ary phase-shift keying (MPSK) modulation in two-way relay channel (TWRC). A low complexity detection technique, termed symbol-based PNC (SPNC), is proposed for the relay. In particular, attributing to the outer product operation imposed on the superposed MPSK signals at the relay, SPNC obtains the network-coded symbol (NCS) straightforwardly without having to detect individual symbols separately. Unlike the optimal multi-user detector (MUD) which searches over the combinations of all users’ modulation constellations, SPNC searches over only one modulation constellation, thus simplifies the NCS detection. Despite the reduced complexity, SPNC achieves full diversity in multi-antenna relay as the optimal MUD does. Specifically, antenna selection based SPNC (AS-SPNC) scheme and signal combining based SPNC (SC-SPNC) scheme are proposed. Our analysis of these two schemes not only confirms their full diversity performance, but also implies when SPNC is applied in multi-antenna relay, TWRC can be viewed as an effective single-input multiple-output (SIMO) system, in which AS-PNC and SC-PNC are equivalent to the general AS scheme and the maximal-ratio combining (MRC) scheme. Moreover, an asymptotic analysis of symbol error rate (SER) is provided for SC-PNC considering the case that the number of relay antennas is sufficiently large

Current Knowledge and Attitudes Concerning Cost-Effectiveness in Glaucoma Pharmacotherapy: A Glaucoma Specialists Focus Group Study.

Background:Rising healthcare costs motivate continued cost-reduction efforts. To help lower costs associated with open-angle glaucoma (OAG), a prevalent, progressive disease with substantial direct and indirect costs, clinicians need to understand the cost-effectiveness of intraocular pressure (IOP)-lowering pharmacotherapies. There is little published information on clinicians' knowledge and attitudes about cost-effectiveness in glaucoma treatment. Purpose:This pilot focus group study aimed to explore clinician attitudes and perspectives around the costs and cost drivers of glaucoma therapy; the implementation of cost-effectiveness decisions; the clinical utility of cost-effectiveness studies; and the cost-effectiveness of available treatments. Methods:Six US glaucoma specialists participated in two separate teleconferencing sessions (three participants each), managed by an independent, skilled moderator (also a glaucoma specialist) using a discussion guide. Participants reviewed recent publications (n=25) on health economics outcomes research in glaucoma prior to the sessions. Results:Participants demonstrated a clear understanding of the economic burden of glaucoma therapy and identified medications, diagnostics, office visits, and treatment changes as key cost drivers. They considered cost-effectiveness an appropriate component of treatment decision-making but identified the need for additional data to inform these decisions. Participants indicated that there were only a few recent studies on health economics outcomes in glaucoma which evaluate parameters important to patient care, such as quality of life and medication adherence, and that longitudinal data were scant. In addition to efficacy, participants felt patient adherence and side-effect profile should be included in economic evaluations of glaucoma pharmacotherapy. Recently approved medications were evaluated in this context. Conclusion:Clinicians deem treatment decisions based on cost-effectiveness data as clinically appropriate. Newer IOP-lowering therapies with potentially greater efficacy and favorable side-effect and adherence profiles may help optimize cost-effectiveness. Future studies should include: clinicians' perspectives; lack of commercial bias; analysis of long-term outcomes/costs; more comprehensive parameters; real-world (including quality-of-life) data; and a robust Markov model

Effect of metal clusters on the swelling of gold-fluorocarbon-polymer composite films

We have investigated the phenomenon of swelling due to acetone diffusion in fluorocarbon polymer films doped with different gold concentrations below the percolation threshold. The presence of the gold clusters in the polymer is shown to improve the mixing between the fluorocarbon polymer and the acetone, which is not a good solvent for this kind of polymers. In order to explain the experimental results the stoichiometry and the morphology of the polymer--metal system have been studied and a modified version of the Flory--Huggins model has been developed

Design of an innovative polymerase chain reaction device based on buoyancy driven flow

This paper was presented at the 2nd Micro and Nano Flows Conference (MNF2009), which was held at Brunel University, West London, UK. The conference was organised by Brunel University and supported by the Institution of Mechanical Engineers, IPEM, the Italian Union of Thermofluid dynamics, the Process Intensification Network, HEXAG - the Heat Exchange Action Group and the Institute of Mathematics and its Applications.Polymerase Chain Reaction (PCR) plays a central role in the field of molecular biology. The miniaturization of PCR systems is promising as it potentially minimizes costly reagent consumption and time required for analysis. In PCR microdevices a sample solution is usually handled by external pumps. An alternative solution relies on temperature-induced density difference in the presence of a body force to induce buoyancy driven flow. This alternative method is easy to be used and does not require expensive setup, but, to date, the thermo-fluid-dynamic field in the micro-channels still needs to be optimized. The present study focuses on the design of micro-channels, having innovative and optimized shapes to obtain proper fluid actuation and DNA sample amplification within buoyancy driven flow PCR devices. A parametric study is carried out by means of computational thermal fluid dynamic modeling: several channel geometry configurations were compared in terms of time required for analysis, temperature distribution and priming volume. The advantages and disadvantages of such configurations are discussed

Regularity bounds by minimal generators and Hilbert function

Let $\rho_C$ be the regularity of the Hilbert function of a projective curve $C$ in \mbox {P}^n_K over an algebraically closed field $K$ and $\beta_1, \ldots, \beta_{n-1}$ be degrees for which there exists a complete intersection of type ($\beta_1, \ldots, \beta_{n-1}$) containing properly $C$. Then the Castelnuovo-Mumford regularity of $C$ is bounded above by max $\{\rho_C +1, \beta 1 + \ldots + \beta_n-1 -(n-1)\}$ .We investigate the sharpness of the above bound, which is achieved by curves algebraically linked to ones having degenerate general hyperplane section

POOL File Catalog, Collection and Metadata Components

The POOL project is the common persistency framework for the LHC experiments to store petabytes of experiment data and metadata in a distributed and grid enabled way. POOL is a hybrid event store consisting of a data streaming layer and a relational layer. This paper describes the design of file catalog, collection and metadata components which are not part of the data streaming layer of POOL and outlines how POOL aims to provide transparent and efficient data access for a wide range of environments and use cases - ranging from a large production site down to a single disconnected laptops. The file catalog is the central POOL component translating logical data references to physical data files in a grid environment. POOL collections with their associated metadata provide an abstract way of accessing experiment data via their logical grouping into sets of related data objects.Comment: Talk from the 2003 Computing in High Energy and Nuclear Physics (CHEP03), La Jolla, Ca, USA, March 2003, 4 pages, 1 eps figure, PSN MOKT00

An independently validated nomogram for isocitrate dehydrogenase-wild-type glioblastoma patient survival.

BackgroundIn 2016, the World Health Organization reclassified the definition of glioblastoma (GBM), dividing these tumors into isocitrate dehydrogenase (IDH)-wild-type and IDH-mutant GBM, where the vast majority of GBMs are IDH-wild-type. Nomograms are useful tools for individualized estimation of survival. This study aimed to develop and independently validate a nomogram for IDH-wild-type patients with newly diagnosed GBM.MethodsData were obtained from newly diagnosed GBM patients from the Ohio Brain Tumor Study (OBTS) and the University of California San Francisco (UCSF) for diagnosis years 2007-2017 with the following variables: age at diagnosis, sex, extent of resection, concurrent radiation/temozolomide (TMZ) status, Karnofsky Performance Status (KPS), O6-methylguanine-DNA methyltransferase (MGMT) methylation status, and IDH mutation status. Survival was assessed using Cox proportional hazards regression, random survival forests, and recursive partitioning analysis, with adjustment for known prognostic factors. The models were developed using the OBTS data and independently validated using the UCSF data. Models were internally validated using 10-fold cross-validation and externally validated by plotting calibration curves.ResultsA final nomogram was validated for IDH-wild-type newly diagnosed GBM. Factors that increased the probability of survival included younger age at diagnosis, female sex, having gross total resection, having concurrent radiation/TMZ, having a high KPS, and having MGMT methylation.ConclusionsA nomogram that calculates individualized survival probabilities for IDH-wild-type patients with newly diagnosed GBM could be useful to physicians for counseling patients regarding treatment decisions and optimizing therapeutic approaches. Free software for implementing this nomogram is provided: https://gcioffi.shinyapps.io/Nomogram_For_IDH_Wildtype_GBM_H_Gittleman/

Computational and experimental investigation of mixing in microchannels

This paper was presented at the 2nd Micro and Nano Flows Conference (MNF2009), which was held at Brunel University, West London, UK. The conference was organised by Brunel University and supported by the Institution of Mechanical Engineers, IPEM, the Italian Union of Thermofluid dynamics, the Process Intensification Network, HEXAG - the Heat Exchange Action Group and the Institute of Mathematics and its Applications.Mixing is a key process for the successful of all chemical or biochemical reactions, so effective micromixers represent essential components for micro total analysis systems (μTAS) or lab-on-a-chip. In the present study a combined computational and experimental approach was adopted to evaluate how the efficiency of a Y-mixer can be enhanced by modifying its downstream geometry. Three different geometries were studied and compared: Y-straight channel, Y-sine channel and Y-wrinkled wall channel. For each of them the influence of perfusing flow rates and channel cross section aspect ratio was investigated. Physical prototypes were built using a simple technique based on a xerographic process, and their mixing performance was experimentally evaluated. Computational models of the designed micromixers were generated: the Navier-Stokes equations for an incompressible Newtonian fluid and the advection-diffusion equation were solved with an uncoupled approach by means of the finite volume method. The computational and experimental results were critically compared, revealing Y-wrinkled wall mixer as the best performer among those considered and suggesting criteria of possible improvements and optimization