Bernoulli polynomials and Pascal matrices in the context of Clifford analysis

AbstractThis paper describes an approach to generalized Bernoulli polynomials in higher dimensions by using Clifford algebras. Due to the fact that the obtained Bernoulli polynomials are special hypercomplex holomorphic (monogenic) functions in the sense of Clifford Analysis, they have properties very similar to those of the classical polynomials. Hypercomplex Pascal and Bernoulli matrices are defined and studied, thereby generalizing results recently obtained by Zhang and Wang (Z. Zhang, J. Wang, Bernoulli matrix and its algebraic properties, Discrete Appl. Math. 154 (11) (2006) 1622–1632)

Quantum chaos, dynamical stability and decoherence

We discuss the stability of quantum motion under system's perturbations in the light of the corresponding classical behavior. In particular we focus our attention on the so called "fidelity" or Loschmidt echo, its relation with the decay of correlations, and discuss the quantum-classical correspondence. We then report on the numerical simulation of the double-slit experiment, where the initial wave-packet is bounded inside a billiard domain with perfectly reflecting walls. If the shape of the billiard is such that the classical ray dynamics is regular, we obtain interference fringes whose visibility can be controlled by changing the parameters of the initial state. However, if we modify the shape of the billiard thus rendering classical (ray) dynamics fully chaotic, the interference fringes disappear and the intensity on the screen becomes the (classical) sum of intensities for the two corresponding one-slit experiments. Thus we show a clear and fundamental example in which transition to chaotic motion in a deterministic classical system, in absence of any external noise, leads to a profound modification in the quantum behavior

Equivalence between the Lovelock-Cartan action and a constrained gauge theory

We show that the four-dimensional Lovelock-Cartan action can be derived from a massless gauge theory for the $SO(1,3)$ group with an additional BRST trivial part. The model is originally composed by a topological sector and a BRST exact piece and has no explicit dependence on the metric, the vierbein or a mass parameter. The vierbein is introduced together with a mass parameter through some BRST trivial constraints. The effect of the constraints is to identify the vierbein with some of the additional fields, transforming the original action into the Lovelock-Cartan one. In this scenario, the mass parameter is identified with Newton's constant while the gauge field is identified with the spin-connection. The symmetries of the model are also explored. Moreover, the extension of the model to a quantum version is qualitatively discussed.Comment: 17 pages. No figures. Final version accepted for publication at the EPJ

Asymetric Triblock Copolymer Nanocarriers for Controlled Localization and pH-Sensitive Release of Proteins

Designing nanocarriers to release proteins under specific conditions is required to improve therapeutic approaches, especially in treating cancer and protein deficiency diseases. We present here supramolecular assemblies based on asymmetric poly(ethylene glycol)-b-poly(methylcaprolactone)-b-poly(2-(N,Ndiethylamino)ethyl methacrylate) (PEG-b-PMCL-b-PDMAEMA) copolymers for controlled localization and pH-sensitive release of proteins. Copolymers self-assembled in soft nanoparticles with a core domain formed by PMCL, and a hydrophilic domain based on PEG mainly embedded inside, and the branched PDMAEMA exposed at the particle surface. We selected as model proteins to be attached to the nanoparticles bovine serum albumin (BSA) and acid sphingomyelinase (ASM), the latter being an ideal candidate for protein replacement therapy. The hydrophilic/hydrophobic ratio, nanoparticle size, and the nature of biomolecules are key factors for modulating protein localization and attachment efficiency. The predominant outer shell of PDMAEMA allows efficient pH-triggered release of BSA and ASM, and in acidic conditions >70% of the bound proteins were released. Uptake of protein-attached nanoparticles by HELA cells, together with low toxicity and pH-responsive release, supports such protein-bound nanoparticles as efficient stimuli-responsive candidates for protein therapy

Nonlinear digital signal processing in mental health: characterization of major depression using instantaneous entropy measures of heartbeat dynamics

Nonlinear digital signal processing methods that address system complexity have provided useful computational tools for helping in the diagnosis and treatment of a wide range of pathologies. More specifically, nonlinear measures have been successful in characterizing patients with mental disorders such as Major Depression (MD). In this study, we propose the use of instantaneous measures of entropy, namely the inhomogeneous point-process approximate entropy (ipApEn) and the inhomogeneous point-process sample entropy (ipSampEn), to describe a novel characterization of MD patients undergoing affective elicitation. Because these measures are built within a nonlinear point-process model, they allow for the assessment of complexity in cardiovascular dynamics at each moment in time. Heartbeat dynamics were characterized from 48 healthy controls and 48 patients with MD while emotionally elicited through either neutral or arousing audiovisual stimuli. Experimental results coming from the arousing tasks show that ipApEn measures are able to instantaneously track heartbeat complexity as well as discern between healthy subjects and MD patients. Conversely, standard heart rate variability (HRV) analysis performed in both time and frequency domains did not show any statistical significance. We conclude that measures of entropy based on nonlinear point-process models might contribute to devising useful computational tools for care in mental health

Live Follow-Up of Enzymatic Reactions Inside the Cavities of Synthetic Giant Unilamellar Vesicles Equipped with Membrane Proteins Mimicking Cell Architecture

Compartmentalization of functional biological units, cells, and organelles serves as an inspiration for the development of biomimetic materials with unprecedented properties and applications in biosensing and medicine. Because of the complexity of cells, the design of ideal functional materials remains a challenge. An elegant strategy to obtain cell-like compartments as novel materials with biofunctionality is the combination of synthetic micrometer-sized giant unilamellar vesicles (GUVs) with biomolecules because it enables studying the behavior of biomolecules and processes within confined cavities. Here we introduce a functional cell-mimetic compartment formed by insertion of the model biopore bacterial membrane protein OmpF in thick synthetic membranes of an artificial GUV compartment that enclosesâEuro"as a modelâEuro"the oxidative enzyme horseradish peroxidase. In this manner, a simple and robust cell mimic is designed: the biopore serves as a gate that allows substrates to enter cavities of the GUVs, where they are converted into products by the encapsulated enzyme and then released in the environments of GUVs. Our bioequipped GUVs facilitate the control of specific catalytic reactions in confined microscale spaces mimicking cell size and architecture and thus provide a straightforward approach serving to obtain deeper insights into biological processes inside cells in real time