Search results for "topological"
showing 10 items of 420 documents
Verso una dimensione narrativa delle mappe
2021
Tra il pensiero e la costruzione dell’architettura il disegno ha un ruolo baricentrico per connettere i diversi protagonisti di una realizzazione e per coinvolgere la collettività facendo percepire inedite prospettive. La scrittura si rivela utile per esplicitare ciò che nella grafica è sotteso e per stabilire un ordine nuovo nel ragionamento progettuale. I rapporti fra segni e significati si moltiplicano nei sistemi informativi recenti in cui si ha la sensazione di poter dire moltissimo (dati numerici e spaziali) ma a volte sfugge quella sintesi indispensabile per una interpretazione concreta, finalizzata alla costruzione di possibili esperienze fisiche. Per l’esplorazione dell’uso di dive…
Topological Devil's staircase in atomic two-leg ladders
2019
Abstract We show that a hierarchy of topological phases in one dimension—a topological Devil’s staircase—can emerge at fractional filling fractions in interacting systems, whose single-particle band structure describes a topological or a crystalline topological insulator. Focusing on a specific example in the BDI class, we present a field-theoretical argument based on bosonization that indicates how the system, as a function of the filling fraction, hosts a series of density waves. Subsequently, based on a numerical investigation of the low-lying energy spectrum, Wilczek–Zee phases, and entanglement spectra, we show that they are symmetry protected topological phases. In sharp contrast to t…
A characterization of Hajłasz–Sobolev and Triebel–Lizorkin spaces via grand Littlewood–Paley functions
2010
Abstract In this paper, we establish the equivalence between the Hajlasz–Sobolev spaces or classical Triebel–Lizorkin spaces and a class of grand Triebel–Lizorkin spaces on Euclidean spaces and also on metric spaces that are both doubling and reverse doubling. In particular, when p ∈ ( n / ( n + 1 ) , ∞ ) , we give a new characterization of the Hajlasz–Sobolev spaces M ˙ 1 , p ( R n ) via a grand Littlewood–Paley function.
Observation of topological gravity-capillary waves in a water wave crystal
2019
The discovery of topological phases of matter, initially driven by theoretical advances in quantum condensed matter physics, has been recently extended to classical wave systems, reaching out to a wealth of novel potential applications in signal manipulation and energy concentration. Despite the fact that many realistic wave media (metals at optical frequencies, polymers at ultrasonic frequencies) are inherently dispersive, topological wave transport in photonic and phononic crystals has so far been limited to ideal situations and proof-of-concept experiments involving dispersionless media. Here, we report the first experimental demonstration of topological edge states in a classical water …
Cardinal inequalities involving the Hausdorff pseudocharacter
2023
We establish several bounds on the cardinality of a topological space involving the Hausdorff pseudocharacter $H\psi(X)$. This invariant has the property $\psi_c(X)\leq H\psi(X)\leq\chi(X)$ for a Hausdorff space $X$. We show the cardinality of a Hausdorff space $X$ is bounded by $2^{pwL_c(X)H\psi(X)}$, where $pwL_c(X)\leq L(X)$ and $pwL_c(X)\leq c(X)$. This generalizes results of Bella and Spadaro, as well as Hodel. We show additionally that if $X$ is a Hausdorff linearly Lindel\"of space such that $H\psi(X)=\omega$, then $|X|\le 2^\omega$, under the assumption that either $2^{<\mathfrak{c}}=\mathfrak{c}$ or $\mathfrak{c}<\aleph_\omega$. The following game-theoretic result is shown: i…
Getting discriminant functions of antibacterial activity from physicochemical and topological parameters.
2001
Linear discriminant analysis has been demonstrated to be a very useful tool in the selection and design of new drugs. Up to now we have used it through the search of a topological pattern of activity. In this work our goal is to calculate a complete set of physicochemical parameters using semiempirical (quantum chemical) calculations as well as topological indices (TIs) and try to find out any discriminant function for antibacterial activity through the combined use of both types of descriptors. The physicochemical parameters, such as heat of formation, HOMO, LUMO, dipole moment, polarizability, hyperpolarizability, PM3 generated IR vibrational frequencies, etc., were calculated using PM3 H…
On a topological interpretation of electronic and vibrational molecular energies
1998
Abstract A relationship between Randic's connectivity index and various quantum mechanical parameters derived from the Huckel Molecular Orbital (HMO) approach is demonstrated. When applied to conjugated hydrocarbons, this index represents the measure of the global π electron molecular energy and, therefore, of the resonance energy. Moreover, the development of the procedure, allows the introduction of a new definition of the bond order which, in turn, makes possible a better prediction not only for bond lengths of naphtalene but also for the resonance integral and conjugation energy for butadiene. Also, a corrected value for the Randic index is deduced, which allows for the reduction of the…
ChemInform Abstract: Getting Discriminant Functions of Antibacterial Activity from Physicochemical and Topological Parameters.
2010
Linear discriminant analysis has been demonstrated to be a very useful tool in the selection and design of new drugs. Up to now we have used it through the search of a topological pattern of activity. In this work our goal is to calculate a complete set of physicochemical parameters using semiempirical (quantum chemical) calculations as well as topological indices (TIs) and try to find out any discriminant function for antibacterial activity through the combined use of both types of descriptors. The physicochemical parameters, such as heat of formation, HOMO, LUMO, dipole moment, polarizability, hyperpolarizability, PM3 generated IR vibrational frequencies, etc., were calculated using PM3 H…
Some Relationships between Molecular Energy-Topology and Symmetry
2001
Molecular Topology (M.T.) has demonstrated its efficiency in the prediction of many experimental parameters. The application of the topological indices to the prediction of pharmacological properties, and, above all, to its inverse problem, the drug design, is particularly interesting [1,2]. Several attempts to explain the reasons of such efficiency have been carried out [3,4]. So far, we are not close to a definitive answer.
Topological structure analysis of chromatin interaction networks.
2019
Abstract Background Current Hi-C technologies for chromosome conformation capture allow to understand a broad spectrum of functional interactions between genome elements. Although significant progress has been made into analysis of Hi-C data to identify biologically significant features, many questions still remain open, in particular regarding potential biological significance of various topological features that are characteristic for chromatin interaction networks. Results It has been previously observed that promoter capture Hi-C (PCHi-C) interaction networks tend to separate easily into well-defined connected components that can be related to certain biological functionality, however, …