Anderson localisation in tight-binding models with flat bands

We consider the effect of weak disorder on eigenstates in a special class of tight-binding models. Models in this class have short-range hopping on periodic lattices; their defining feature is that the clean systems have some energy bands that are dispersionless throughout the Brillouin zone. We show that states derived from these flat bands are generically critical in the presence of weak disorder, being neither Anderson localised nor spatially extended. Further, we establish a mapping between this localisation problem and the one of resonances in random impedance networks, which previous work has suggested are also critical. Our conclusions are illustrated using numerical results for a two-dimensional lattice, known as the square lattice with crossings or the planar pyrochlore lattice.Comment: 5 pages, 3 figures, as published (this version includes minor corrections

Thermodynamics of protein folding: a random matrix formulation

The process of protein folding from an unfolded state to a biologically active, folded conformation is governed by many parameters e.g the sequence of amino acids, intermolecular interactions, the solvent, temperature and chaperon molecules. Our study, based on random matrix modeling of the interactions, shows however that the evolution of the statistical measures e.g Gibbs free energy, heat capacity, entropy is single parametric. The information can explain the selection of specific folding pathways from an infinite number of possible ways as well as other folding characteristics observed in computer simulation studies.Comment: 21 Pages, no figure

Towards a common thread in Complexity: an accuracy-based approach

The complexity of a system, in general, makes it difficult to determine some or almost all matrix elements of its operators. The lack of accuracy acts as a source of randomness for the matrix elements which are also subjected to an external potential due to existing system conditions. The fluctuation of accuracy due to varying system-conditions leads to a diffusion of the matrix elements. We show that, for the single well potentials, the diffusion can be described by a common mathematical formulation where system information enters through a single parameter. This further leads to a characterization of physical properties by an infinite range of single parametric universality classes

The potential of siRNA based drug delivery in respiratory disorders: recent advances and progress

© 2019 Wiley Periodicals, Inc. Lung diseases are the leading cause of mortality worldwide. The currently available therapies are not sufficient, leading to the urgent need for new therapies with sustained anti-inflammatory effects. Small/short or silencing interfering RNA (siRNA) has potential therapeutic implications through post-transcriptional downregulation of the target gene expression. siRNA is essential in gene regulation, so is more favorable over other gene therapies due to its small size, high specificity, potency, and no or low immune response. In chronic respiratory diseases, local and targeted delivery of siRNA is achieved via inhalation. The effectual delivery can be attained by the generation of aerosols via inhalers and nebulizers, which overcomes anatomical barriers, alveolar macrophage clearance and mucociliary clearance. In this review, we discuss the different siRNA nanocarrier systems for chronic respiratory diseases, for safe and effective delivery. siRNA mediated pro-inflammatory gene or miRNA targeting approach can be a useful approach in combating chronic respiratory inflammatory conditions and thus providing sustained drug delivery, reduced therapeutic dose, and improved patient compliance. This review will be of high relevance to the formulation, biological and translational scientists working in the area of respiratory diseases

Alternative Technique for "Complex" Spectra Analysis

. The choice of a suitable random matrix model of a complex system is very sensitive to the nature of its complexity. The statistical spectral analysis of various complex systems requires, therefore, a thorough probing of a wide range of random matrix ensembles which is not an easy task. It is highly desirable, if possible, to identify a common mathematcal structure among all the ensembles and analyze it to gain information about the ensemble- properties. Our successful search in this direction leads to Calogero Hamiltonian, a one-dimensional quantum hamiltonian with inverse-square interaction, as the common base. This is because both, the eigenvalues of the ensembles, and, a general state of Calogero Hamiltonian, evolve in an analogous way for arbitrary initial conditions. The varying nature of the complexity is reflected in the different form of the evolution parameter in each case. A complete investigation of Calogero Hamiltonian can then help us in the spectral analysis of complex systems.Comment: 20 pages, No figures, Revised Version (Minor Changes

A Case of Problematic Diffusion

Sex determination techniques have diffused rapidly in India, and are being used to detect female fetuses and subsequently to abort them. This technology has spread rapidly because it imparts knowledge that is of great value within the Indian context, and because it fits in neatly with the modernization dynamic within India, which itself has enmeshed with traditional patriarchal institutions to oppress Indian women. More research needs to be done on ways to stem the adoption of problematic innovations.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/68396/2/10.1177_107554709401500301.pd

Increasing complexity and interactions of oxidative stress in chronic respiratory diseases: An emerging need for novel drug delivery systems

© 2018 Elsevier B.V. Oxidative stress is intensely involved in enhancing the severity of various chronic respiratory diseases (CRDs) including asthma, chronic obstructive pulmonary disease (COPD), infections and lung cancer. Even though there are various existing anti-inflammatory therapies, which are not enough to control the inflammation caused due to various contributing factors such as anti-inflammatory genes and antioxidant enzymes. This leads to an urgent need of novel drug delivery systems to combat the oxidative stress. This review gives a brief insight into the biological factors involved in causing oxidative stress, one of the emerging hallmark feature in CRDs and particularly, highlighting recent trends in various novel drug delivery carriers including microparticles, microemulsions, microspheres, nanoparticles, liposomes, dendrimers, solid lipid nanocarriers etc which can help in combating the oxidative stress in CRDs and ultimately reducing the disease burden and improving the quality of life with CRDs patients. These carriers improve the pharmacokinetics and bioavailability to the target site. However, there is an urgent need for translational studies to validate the drug delivery carriers for clinical administration in the pulmonary clinic

Toward semiclassical theory of quantum level correlations of generic chaotic systems

In the present work we study the two-point correlation function $R(\epsilon)$ of the quantum mechanical spectrum of a classically chaotic system. Recently this quantity has been computed for chaotic and for disordered systems using periodic orbit theory and field theory. In this work we present an independent derivation, which is based on periodic orbit theory. The main ingredient in our approach is the use of the spectral zeta function and its autocorrelation function $C(\epsilon)$. The relation between $R(\epsilon)$ and $C(\epsilon)$ is constructed by making use of a probabilistic reasoning similar to that which has been used for the derivation of Hardy -- Littlewood conjecture. We then convert the symmetry properties of the function $C(\epsilon)$ into relations between the so-called diagonal and the off-diagonal parts of $R(\epsilon)$. Our results are valid for generic systems with broken time reversal symmetry, and with non-commensurable periods of the periodic orbits.Comment: 15 pages(twocolumn format), LaTeX, EPSF, (figures included

Glassy systems under time-dependent driving forces: application to slow granular rheology

We study the dynamics of a glassy model with infinite range interactions externally driven by an oscillatory force. We find a well-defined transition in the (Temperature-Amplitude-Frequency) phase diagram between (i) a `glassy' state characterized by the slow relaxation of one-time quantities, aging in two-time quantities and a modification of the equilibrium fluctuation-dissipation relation; and (ii) a `liquid' state with a finite relaxation time. In the glassy phase, the degrees of freedom governing the slow relaxation are thermalized to an effective temperature. Using Monte-Carlo simulations, we investigate the effect of trapping regions in phase space on the driven dynamics. We find that it alternates between periods of rapid motion and periods of trapping. These results confirm the strong analogies between the slow granular rheology and the dynamics of glasses. They also provide a theoretical underpinning to earlier attempts to present a thermodynamic description of moderately driven granular materials.Comment: Version accepted for publication - Physical Review

Cellular signalling pathways mediating the pathogenesis of chronic inflammatory respiratory diseases: an update

Respiratory disorders, especially non-communicable, chronic inflammatory diseases, are amongst the leading causes of mortality and morbidity worldwide. Respiratory diseases involve multiple pulmonary components, including airways and lungs that lead to their abnormal physiological functioning. Several signaling pathways have been reported to play an important role in the pathophysiology of respiratory diseases. These pathways, in addition, become the compounding factors contributing to the clinical outcomes in respiratory diseases. A range of signaling components such as Notch, Hedgehog, Wingless/Wnt, bone morphogenetic proteins, epidermal growth factor and fibroblast growth factor is primarily employed by these pathways in the eventual cascade of events. The different aberrations in such cell-signaling processes trigger the onset of respiratory diseases making the conventional therapeutic modalities ineffective. These challenges have prompted us to explore novel and effective approaches for the prevention and/or treatment of respiratory diseases. In this review, we have attempted to deliberate on the current literature describing the role of major cell signaling pathways in the pathogenesis of pulmonary diseases and discuss promising advances in the field of therapeutics that could lead to novel clinical therapies capable of preventing or reversing pulmonary vascular pathology in such patients