On the topological characterization of two-dimensional phase transitions

It is shown that for the two-dimensional planar-rotator model the variance of the number of vortices inside a large loop is proportional to the perimeter of the loop at all temperatures. A similar result holds for the variance of the charge inside a loop in the lattice Coulomb gas model. Hence a topological distinction between the high and low temperature phases of these models (area law versus perimeter law) is not possible.     

Symmetry adapted functions belonging to the dirac groups

An earlier analysis of the canonical form of a pair of invertible operators obeying the exchange rule is extended to cover a set of operators, between each pair of which a relation of this type exists; and for which a power of each operator is the unit matrix. Such relations define a system which may be regarded as a generalization of the Dirac matrices of relativistic quantum mechanics. We concentrate upon the group theoretic aspects of such a system and its matrix representations. Applications arise from the fact that all projective representations of finite abelian groups take the form of a Dirac Group. In particular, the representations of the magnetic space groups, which are projective representations of the lattice groups, arise in this manner.     

Quenched Averages for Self-Avoiding Walks and Polygons on Deterministic Fractals

We study rooted self avoiding polygons and self avoiding walks on deterministic fractal lattices of finite ramification index. Different sites on such lattices are not equivalent, and the number of rooted open walks W _n (S), and rooted self-avoiding polygons P _n (S) of n steps depend on the root S. We use exact recursion equations on the fractal to determine the generating functions for P _n (S), and W _n(S) for an arbitrary point S on the lattice. These are used to compute the averages ,, and over different positions of S. We find that the connectivity constant μ, and the radius of gyration exponent are the same for the annealed and quenched averages. However, , and , where the exponents and , take values different from the annealed case. These are expressed as the Lyapunov exponents of random product of finite-dimensional matrices. For the 3-simplex lattice, our numerical estimation gives and , to be compared with the known annealed values and .     

Scaling relation for determining the critical threshold for continuum percolation of overlapping discs of two sizes

We study continuum percolation of overlapping circular discs of two sizes. We propose a phenomenological scaling equation for the increase in the effective size of the larger discs due to the presence of the smaller discs. The critical percolation threshold as a function of the ratio of sizes of discs, for different values of the relative areal densities of two discs, can be described in terms of a scaling function of only one variable. The recent accurate Monte Carlo estimates of critical threshold by Quintanilla and Ziff [Phys. Rev. E76, 051115 (2007)] are in very good agreement with the proposed scaling relation.     

Multiobjective analog/RF circuit sizing using an improved brain storm optimization algorithm

This paper presents a multiobjective analog/RF circuit sizing tool using an improved brain storm optimization (IMBSO) algorithm with the purpose of analyzing the tradeoffs between competing performance specifications of analog/RF circuit block. A number of improvements are incorporated into IMBSO algorithm at different steps. At first, the clustering step of IMBSO algorithm is augmented with k-means\(++\) seeding technique to select the initial cluster centroids while clustering using k-means clustering technique. As a second improvement, the proposed IMBSO algorithm makes use of random probabilistic decision-making of river formation dynamics scheme to select optimal cluster centroids during population generation step. As a third improvement, an adaptive mutation operator is incorporated inside the IMBSO algorithm to generate new population. Finally, two separate constraint handling techniques are employed to handle both boundary and functional constraints during analog/RF circuit optimization. The performance of the proposed IMBSO algorithm is demonstrated in finding optimal Pareto fronts among different performance specifications of a two-stage operational amplifier circuit, a folded cascode amplifier circuit and a low noise amplifier circuit.     

The Conjugacy Class Number k(G): A Different Perspective

For a finite group G, let m(G) denote the least positive integer such that the union of any m(G) distinct nontrivial conjugacy classes of G together with the identity of G is a subgroup of G. We prove that m(G) = k(G) ?1 for all m(G) ≥2.     

On an M (X)/G/1 Retrial System with Two Types of Search of Customers from the Orbit

Single server retrial queueing models in which customers arrive according to a batch Poisson process are considered here. An arriving batch, finding the server busy, enters an orbit. Otherwise, one customer from the arriving batch enters for service immediately while the rest join the orbit. The customers from the orbit (the orbital customers) try to reach the server subsequently with the inter-retrial times exponentially distributed. Additionally, at each service completion epoch, two different search mechanisms, that is, type I and type II search, to bring the orbital customers by the system to service, are switched on. Thus, when the server is idle, a competition takes place among primary customers, customers who come by retrial and by two types of searches. The type I search selects a single customer whereas the type II search considers a batch of customers from the orbit. Depending on the maximum size of the batch being considered for service by a type II search, two cases are addressed here. In the first case, no restriction on batch size is assumed, whereas in the second case, maximum size of the batch is restricted to a pre-assigned value. We call the resulting models as model 1 and model 2 respectively. In all service modes other than type II search, only a single customer is qualified for service. Service times of the four types of customers, namely, primary, repeated, and those who come by two types of searches are arbitrarily distributed (with different distributions which are independent of each other). Steady state analysis is performed and stability conditions are established. A control problem for model 2 is considered and numerical illustrations are provided.     

Strategic engineering of alkyl spacer length for a pH-tolerant lysosome marker and dual organelle localization

Long-term visualization of lysosomal properties is extremely crucial to evaluate diseases related to their dysfunction. However, many of the reported lysotrackers are less conducive to imaging lysosomes precisely because they suffer from fluorescence quenching and other inherent drawbacks such as pH-sensitivity, polarity insensitivity, water insolubility, slow diffusibility, and poor photostability. To overcome these limitations, we have utilized an alkyl chain length engineering strategy and synthesized a series of lysosome targeting fluorescent derivatives namely NIMCs by attaching a morpholine moiety at the peri position of the 1,8-naphthalimide (NI) ring through varying alkyl spacers between morpholine and 1,8-naphthalimide. The structural and optical properties of the synthesized NIMCs were explored by ¹H-NMR, single-crystal X-ray diffraction, UV-Vis, and fluorescence spectroscopy. Afterward, optical spectroscopic measurements were carefully performed to identify a pH-tolerant, polarity sensitive, and highly photostable fluoroprobes for further live-cell imaging applications. NIMC6 displayed excellent pH-tolerant and polarity-sensitive properties. Consequently, all NIMCs were employed in kidney fibroblast cells (BHK-21) to investigate their applicability for lysosome targeting and probing lysosomal micropolarity. Interestingly, a switching of localization from lysosomes to the endoplasmic reticulum (ER) was also achieved by controlling the linker length and this phenomenon was subsequently applied in determining ER micropolarity. Additionally, the selected probe NIMC6 was also employed in BHK-21 cells for 3-D spheroid imaging and in Caenorhabditis elegans (C. elegans) for in vivo imaging, to evaluate its efficacy for imaging animal models.

A series naphthalimide-based fluorophores were designed by alkyl spacer length engineering to discover a pH-tolerant lysosomal marker. This approach also allows to probe lysosome-related organelles in C. elegans and communication between organelles.