Non-uniform non-tensor product local interpolatory subdivision surfaces

In this paper we exploit a class of univariate, C1 interpolating four-point subdivision schemes featured by a piecewise uniform parameterization, to define non-tensor product subdivision schemes interpolating regular grids of control points and generating C1 limit surfaces with a better behavior than the well-established tensor product subdivision and spline surfaces. As a result, it is emphasized that subdivision methods can be more effective than splines, not only, as widely acknowledged, for the representation of surfaces of arbitrary topology, but also for the generation of smooth interpolants of regular grids of points. To our aim, the piecewise uniform parameterization of the univariate case is generalized to an augmented parameterization, where the knot intervals of the kth level grid of points are computed from the initial ones by an updating relation that keeps the subdivision algorithm linear. The particular parameters configuration, together with the structure of the subdivision rules, turn out to be crucial to prove the continuity and smoothness of the limit surface

Non-uniform interpolatory curve subdivision with edge parameters built upon compactly supported fundamental splines

In this paper we present a family of Non-Uniform Local Interpolatory (NULI) subdivision schemes, derived from compactly supported cardinal splines with non-uniform knots (NULICS). For this spline family, the knot partition is defined by a sequence of break points and by one additional knot, arbitrarily placed along each knot-interval. The resulting refinement algorithms are linear and turn out to contain a set of edge parameters that, when fixed to a value in the range [0,1], allow us to move each auxiliary knot to any position between the break points to simulate the behavior of the NULICS interpolants. Among all the members of this new family of schemes, we will then especially analyze the NULI 4-point refinement. This subdivision scheme has all the fundamental features of the quadratic cardinal spline basis it is originated from, namely compact support, C 1 smoothness, second order polynomials reproduction and approximation order 3. In addition the NULI 4-point subdivision algorithm has the possibility of setting consecutive edge parameters to simulate triple knots - that are not achievable when using the corresponding spline basis - thus allowing for limit curves with crease vertices, without using an ad hoc mask. Numerical examples and comparisons with other methods will be given to the aim of illustrating the performance of the NULI 4-point scheme in the case of highly non-uniform initial data

Construction and characterization of non-uniform local interpolating polynomial splines

This paper presents a general framework for the construction of piecewise-polynomial local interpolants with given smoothness and approximation order, defined on non-uniform knot partitions. We design such splines through a suitable combination of polynomial interpolants with either polynomial or rational, compactly supported blending functions. In particular, when the blending functions are rational, our approach provides spline interpolants having low, and sometimes minimum degree. Thanks to its generality, the proposed framework also allows us to recover uniform local interpolating splines previously proposed in the literature, to generalize them to the non-uniform case, and to complete families of arbitrary support width. Furthermore it provides new local interpolating polynomial splines with prescribed smoothness and polynomial reproduction properties

Host defense pathways against fungi: the basis for vaccines and immunotherapy.

Fungal vaccines have long been a goal in the fields of immunology and microbiology to counter the high mortality and morbidity rates owing to fungal diseases, particularly in immunocompromised patients. However, the design of effective vaccination formulations for durable protection to the different fungi has lagged behind due to the important differences among fungi and their biology and our limited understanding of the complex host-pathogen interactions and immune responses. Overcoming these challenges is expected to contribute to improved vaccination strategies aimed at personalized efficacy across distinct target patient populations. This likely requires the integration of multifaceted approaches encompassing advanced immunology, systems biology, immunogenetics, and bioinformatics in the fields of fungal and host biology and their reciprocal interactions

Immunogenetic profiling to predict risk of invasive fungal diseases: where are we now?

Invasive fungal diseases remain nowadays life-threatening conditions affecting multiple clinical settings. The onset of these diseases is dependent on numerous factors, of which the "immunocompromised" phenotype of the patients is the more often acknowledged. However, and despite comparable immune dysfunction, not all patients are ultimately susceptible to disease, suggesting that additional risk factors, likely of genetic nature, may also be important. In the last years, genetic variants in several immune-related genes have also been proposed as major determinants of the susceptibility pattern of high-risk patients to invasive fungal diseases. Altogether, these findings highlighted the crucial significance of the individual genetic make-up in defining susceptibility to infection, providing a compelling rationale for the introduction of the immunogenetic profile as a risk prediction measure that may ultimately help to guide clinicians in the use of prophylaxis and preemptive fungal therapy in high-risk patients