On Convergence of Differential Evolution Over a Class of Continuous Functions With Unique Global Optimum

Differential evolution (DE) is arguably one of the most powerful stochastic real-parameter optimization algorithms of current interest. Since its inception in the mid 1990s, DE has been finding many successful applications in real-world optimization problems from diverse domains of science and engineering. This paper takes a first significant step toward the convergence analysis of a canonical DE (DE/rand/1/bin) algorithm. It first deduces a time-recursive relationship for the probability density function (PDF) of the trial solutions, taking into consideration the DE-type mutation, crossover, and selection mechanisms. Then, by applying the concepts of Lyapunov stability theorems, it shows that as time approaches infinity, the PDF of the trial solutions concentrates narrowly around the global optimum of the objective function, assuming the shape of a Dirac delta distribution. Asymptotic convergence behavior of the population PDF is established by constructing a Lyapunov functional based on the PDF and showing that it monotonically decreases with time. The analysis is applicable to a class of continuous and real-valued objective functions that possesses a unique global optimum (but may have multiple local optima). Theoretical results have been substantiated with relevant computer simulations.

Trapped fermions in a synthetic non-Abelian gauge field

On increasing the coupling strength (lambda) of a non-Abelian gauge field that induces a generalized Rashba spin-orbit interaction, the topology of the Fermi surface of a homogeneous gas of noninteracting fermions of density rho similar to k(F)(3) undergoes a change at a critical value, lambda(T) approximate to k(F) [Phys. Rev. B 84, 014512 ( 2011)]. In this paper we analyze how this phenomenon affects the size and shape of a cloud of spin-1/2 fermions trapped in a harmonic potential such as those used in cold atom experiments. We develop an adiabatic formulation, including the concomitant Pancharatnam-Berry phase effects, for the one-particle states in the presence of a trapping potential and the gauge field, obtaining approximate analytical formulas for the energy levels for some high symmetry gauge field configurations of interest. An analysis based on the local density approximation reveals that, for a given number of particles, the cloud shrinks in a characteristic fashion with increasing.. We explain the physical origins of this effect by a study of the stress tensor of the system. For an isotropic harmonic trap, the local density approximation predicts a spherical cloud even for anisotropic gauge field configurations. We show, via a calculation of the cloud shape using exact eigenstates, that for certain gauge field configurations there is a systematic and observable anisotropy in the cloud shape that increases with increasing gauge coupling lambda. The reasons for this anisotropy are explained using the analytical energy levels obtained via the adiabatic approximation. These results should be useful in the design of cold atom experiments with fermions in non-Abelian gauge fields. An important spin-off of our adiabatic formulation is that it reveals exciting possibilities for the cold-atom realization of interesting condensed matter Hamiltonians by using a non-Abelian gauge field in conjunction with another potential. In particular, we show that the use of a spherical non-Abelian gauge field with a harmonic trapping potential produces a monopole field giving rise to a spherical geometry quantum Hall-like Hamiltonian in the momentum representation.

An Algorithm for Testing 2-Asummability of Boolean Functions

Simple algorithms have been developed to generate pairs of minterms forming a given 2-sum and thereby to test 2-asummability of switching functions. The 2-asummability testing procedure can be easily implemented on the computer. Since 2-asummability is a necessary and sufficient condition for a switching function of upto eight variables to be linearly separable (LS), it can be used for testing LS switching functions of upto eight variables.

Measurement of probability-distribution functions sensitive technique for the study of conduction phenomena in liquid dielectrics

The paper outlines a technique for sensitive measurement of conduction phenomena in liquid dielectrics. The special features of this technique are the simplicity of the electrical system, the inexpensive instrumentation and the high accuracy. Detection, separation and analysis of a random function of current that is superimposed on the prebreakdown direct current forms the basis of this investigation. In this case, prebreakdown direct current is the output data of a test cell with large electrodes immersed in a liquid medium subjected to high direct voltages. Measurement of the probability-distribution function of a random fluctuating component of current provides a method that gives insight into the mechanism of conduction in a liquid medium subjected to high voltages and the processes that are responsible for the existence of the fluctuating component of the current.

Waring and Riedel Functions for the Liquid-Vapor Coexistence Curve

There exists a minimum in the Waring function, psi(T) = -d(ln p)/d(1/T), and in the Riedel function, alpha(T) = d(ln p)/d(In T), in the liquid-vapor coexistence curve for most fluids. By analyzing National Institute of Standards and Technology data for the molar enthalpy of vaporization and the compressibility variation at the liquid-vapor phase change of 105 fluids, we find that the temperatures of these minima are linearly correlated with the critical temperature, T-c. Using reduced coordinates, we also demonstrate that the minima are well-correlated with the acentric factor. These correlations are used for testing four well-known vapor pressure equations in the Pitzer corresponding states scheme.

On concave univalent functions

We consider functions that map the open unit disc conformally onto the complement of an unbounded convex set with opening angle pa, a ? (1, 2], at infinity. In this paper, we show that every such function is close-to-convex of order (a - 1) and is included in the set of univalent functions of bounded boundary rotation. Many interesting consequences of this result are obtained. We also determine the extreme points of the set of concave functions with respect to the linear structure of the Hornich space.

Glycodelin-A interferes with IL-2/IL-2R signalling to induce cell growth arrest, loss of effector functions and apoptosis in T-lymphocytes

The progesterone-regulated glycoprotein glycodelin-A (GdA), secreted by the decidualized endometrium at high concentrations in primates, inhibits the maternal immune response against fetal antigens and thereby contributes to the tolerance of the semi-allogenic fetus during a normal pregnancy. Our earlier studies demonstrated the ability of GdA to induce an intrinsic apoptotic cascade in CD4 T-lymphocytes and suppress the cytolytic effector function of CD8 T-lymphocytes. In this report, we investigated further into the mechanism of action of GdA controlling perforin and granzyme B expression in CD8 T-lymphocytes and the mechanism of action of GdA leading to lymphocyte death. Flow cytometry analysis was performed to check for the surface expression of interleukin-2 receptor (IL-2R) and intracellular eomesodermin (Eomes) in activated T-lymphocytes, whereas quantitative RTPCR analysis was used to find out their mRNA profile upon GdA treatment. Western analysis was carried out to confirm the protein level of Bax and Bcl-2. GdA reduces the surface expression of the high-affinity IL-2R complex by down-regulating the synthesis of IL-2R (CD25). This disturbs the optimal IL-2 signalling and decreases the Eomes expression, which along with IL-2 directly regulates perforin and granzymes expression. Consequently, the CD8 T-lymphocytes undergo growth arrest and are unable to mature into competent cytotoxic T-lymphocytes. In the CD4 T-lymphocytes, growth factor IL-2 deprivation leads to proliferation inhibition, decreased Bcl-2/enhanced Bax expression, culminating in mitochondrial stress and cell death. GdA spurs cell cycle arrest, loss of effector functions and apoptosis in different T-cell subsets by making T-lymphocytes unable to respond to IL-2.

Structure and Mechanistic Insights into Novel Iron-mediated Moonlighting Functions of Human J-protein Cochaperone, Dph4

J-proteins are obligate cochaperones of Hsp70s and stimulate their ATPase activity via the J-domain. Although the functions of J-proteins have been well understood in the context of Hsp70s, their additional co-evolved ``physiological functions'' are still elusive. We report here the solution structure and mechanism of novel iron-mediated functional roles of human Dph4, a type III J-protein playing a vital role in diphthamide biosynthesis and normal development. The NMR structure of Dph4 reveals two domains: a conserved J-domain and a CSL-domain connected via a flexible linker-helix. The linker-helix modulates the conformational flexibility between the two domains, regulating thereby the protein function. Dph4 exhibits a unique ability to bind iron in tetrahedral coordination geometry through cysteines of its CSL-domain. The oxidized Fe-Dph4 shows characteristic UV-visible and electron paramagnetic resonance spectral properties similar to rubredoxins. Iron-bound Dph4 (Fe-Dph4) also undergoes oligomerization, thus potentially functioning as a transient ``iron storage protein,'' thereby regulating the intracellular iron homeostasis. Remarkably, Fe-Dph4 exhibits vital redox and electron carrier activity, which is critical for important metabolic reactions, including diphthamide biosynthesis. Further, we observed that Fe-Dph4 is conformationally better poised to perform Hsp70-dependent functions, thus underlining the significance of iron binding in Dph4. Yeast Jjj3, a functional ortholog of human Dph4 also shows a similar iron-binding property, indicating the conserved nature of iron sequestration across species. Taken together, our findings provide invaluable evidence in favor of additional co-evolved specialized functions of J-proteins, previously not well appreciated.

Serine/Threonine/Tyrosine Protein Kinase Phosphorylates Oleosin, a Regulator of Lipid Metabolic Functions

Plant oils are stored in oleosomes or oil bodies, which are surrounded by a monolayer of phospholipids embedded with oleosin proteins that stabilize the structure. Recently, a structural protein, Oleosin3 (OLE3), was shown to exhibit both monoacylglycerol acyltransferase and phospholipase A(2) activities. The regulation of these distinct dual activities in a single protein is unclear. Here, we report that a serine/threonine/tyrosine protein kinase phosphorylates oleosin. Using bimolecular fluorescence complementation analysis, we demonstrate that this kinase interacts with OLE3 and that the fluorescence was associated with chloroplasts. Oleosin-green fluorescent protein fusion protein was exclusively associated with the chloroplasts. Phosphorylated OLE3 exhibited reduced monoacylglycerol acyltransferase and increased phospholipase A(2) activities. Moreover, phosphatidylcholine and diacylglycerol activated oleosin phosphorylation, whereas lysophosphatidylcholine, oleic acid, and Ca2+ inhibited phosphorylation. In addition, recombinant peanut (Arachis hypogaea) kinase was determined to predominantly phosphorylate serine residues, specifically serine-18 in OLE3. Phosphorylation levels of OLE3 during seed germination were determined to be higher than in developing peanut seeds. These findings provide direct evidence for the in vivo substrate selectivity of the dual-specificity kinase and demonstrate that the bifunctional activities of oleosin are regulated by phosphorylation.

Interacting fermions in synthetic non-Abelian gauge fields

Generation and study of synthetic gauge fields has enhanced the possibility of using cold atom systems as quantum emulators of condensed matter Hamiltonians. In this article we describe the physics of interacting spin -1/2 fermions in synthetic non-Abelian gauge fields which induce a Rashba spin-orbit interaction on the motion of the fermions. We show that the fermion system can evolve to a Bose-Einstein condensate of a novel boson which we call rashbon. The rashbon-rashbon interaction is shown to be independent of the interaction between the constituent fermions. We also show that spin-orbit coupling can help enhancing superfluid transition temperature of weak superfluids to the order of Fermi temperature. A non-Abelian gauge field, when used in conjunction with another potential, can generate interesting Hamiltonians such as that of a magnetic monopole.

Context dependent splicing functions of Bud31/Ycr063w define its role in budding and cell cycle progression

The yeast Bud31 protein, a Prp19 complex (NTC) member, aids spliceosome assembly and thus promotes efficient pre-mRNA splicing. The bud31 null cells show mild budding abnormalities at optimal growth temperatures and, at higher temperatures, have growth defects with aberrant budding. Here we have assessed cell cycle transitions which require Bud31. We find Bud31 facilitates passage through G1-S regulatory point (Start) but is not needed for G2-M transition or for exit from mitosis. To co-relate Bud31 functions in cell division with splicing, we studied the splicing status of transcripts that encode proteins involved in budding. We find Bud31 promotes efficient splicing of only some of these pre-mRNAs, for example, ARP2 and SRC1. Wild type cells have a long and a short isoform of SRC1 mRNA and protein, out of which the shorter mRNA splice variant is predominant. bud31 Delta cells show inefficient SRC1 splicing and entirely lack the shorter SRC1 spliced mRNA isoform. Yeast PRP17, another NTC sub-complex member, is also required for G1-S and G2-M cell cycle transitions. We examined genetic interactions between BUD31 and PRP17. While both factors were needed for efficient cell cycle dependent gene expression, our data indicate that distinct pre-mRNAs depend on each of these non-essential splicing factors.

Sum rules and three point functions

Sum rules constraining the R-current spectral densities are derived holographically for the case of D3-branes, M2-branes and M5-branes all at finite chemical potentials. In each of the cases the sum rule relates a certain integral of the spectral density over the frequency to terms which depend both on long distance physics, hydrodynamics and short distance physics of the theory. The terms which which depend on the short distance physics result from the presence of certain chiral primaries in the OPE of two it-currents which are turned on at finite chemical potential. Since these sum rules contain information of the OPE they provide an alternate method to obtain the structure constants of the two R-currents and the chiral primary. As a consistency check we show that the 3 point function derived from the sum rule precisely matches with that obtained using Witten diagrams.

Diverse functions of restriction-modification systems in addition to cellular defense

Restriction-modification (R-M) systems are ubiquitous and are often considered primitive immune systems in bacteria. Their diversity and prevalence across the prokaryotic kingdom are an indication of their success as a defense mechanism against invading genomes. However, their cellular defense function does not adequately explain the basis for their immaculate specificity in sequence recognition and nonuniform distribution, ranging from none to too many, in diverse species. The present review deals with new developments which provide insights into the roles of these enzymes in other aspects of cellular function. In this review, emphasis is placed on novel hypotheses and various findings that have not yet been dealt with in a critical review. Emerging studies indicate their role in various cellular processes other than host defense, virulence, and even controlling the rate of evolution of the organism. We also discuss how R-M systems could have successfully evolved and be involved in additional cellular portfolios, thereby increasing the relative fitness of their hosts in the population.