Maximal regularity for second order non-autonomous Cauchy problems

We consider some non-autonomous second order Cauchy problems of the form u + B(t)(u) over dot + A(t)u = f (t is an element of [0, T]), u(0) = (u) over dot(0) = 0. We assume that the first order problem (u) over dot + B(t)u = f (t is an element of [0, T]), u(0) = 0, has L-p-maximal regularity. Then we establish L-p-maximal regularity of the second order problem in situations when the domains of B(t(1)) and A(t(2)) always coincide, or when A(t) = kappa B(t).

On the maximal rate of non-square STBCs from complex orthogonal designs

A Linear Processing Complex Orthogonal Design (LPCOD) is a p x n matrix epsilon, (p >= n) in k complex indeterminates x(1), x(2),..., x(k) such that (i) the entries of epsilon are complex linear combinations of 0, +/- x(i), i = 1,..., k and their conjugates, (ii) epsilon(H)epsilon = D, where epsilon(H) is the Hermitian (conjugate transpose) of epsilon and D is a diagonal matrix with the (i, i)-th diagonal element of the form l(1)((i))vertical bar x(1)vertical bar(2) + l(2)((i))vertical bar x(2)vertical bar(2)+...+ l(k)((i))vertical bar x(k)vertical bar(2) where l(j)((i)), i = 1, 2,..., n, j = 1, 2,...,k are strictly positive real numbers and the condition l(1)((i)) = l(2)((i)) = ... = l(k)((i)), called the equal-weights condition, holds for all values of i. For square designs it is known. that whenever a LPCOD exists without the equal-weights condition satisfied then there exists another LPCOD with identical parameters with l(1)((i)) = l(2)((i)) = ... = l(k)((i)) = 1. This implies that the maximum possible rate for square LPCODs without the equal-weights condition is the same as that or square LPCODs with equal-weights condition. In this paper, this result is extended to a subclass of non-square LPCODs. It is shown that, a set of sufficient conditions is identified such that whenever a non-square (p > n) LPCOD satisfies these sufficient conditions and do not satisfy the equal-weights condition, then there exists another LPCOD with the same parameters n, k and p in the same complex indeterminates with l(1)((i)) = l(2)((i)) = ... = l(k)((i)) = 1.

On the maximal rate of (n+1) x n and (n+2) x n complex orthogonal designs

For p x n complex orthogonal designs in k variables, where p is the number of channels uses and n is the number of transmit antennas, the maximal rate L of the design is asymptotically half as n increases. But, for such maximal rate codes, the decoding delay p increases exponentially. To control the delay, if we put the restriction that p = n, i.e., consider only the square designs, then, the rate decreases exponentially as n increases. This necessitates the study of the maximal rate of the designs with restrictions of the form p = n+1, p = n+2, p = n+3 etc. In this paper, we study the maximal rate of complex orthogonal designs with the restrictions p = n+1 and p = n+2. We derive upper and lower bounds for the maximal rate for p = n+1 and p = n+2. Also for the case of p = n+1, we show that if the orthogonal design admit only the variables, their negatives and multiples of these by root-1 and zeros as the entries of the matrix (other complex linear combinations are not allowed), then the maximal rate always equals the lower bound.

A Novel Construction of Complex Orthogonal Designs with Maximal Rate and Low-PAPR

Space-time block codes based on orthogonal designs are used for wireless communications with multiple transmit antennas which can achieve full transmit diversity and have low decoding complexity. However, the rate of the square real/complex orthogonal designs tends to zero with increase in number of antennas, while it is possible to have a rate-1 real orthogonal design (ROD) for any number of antennas.In case of complex orthogonal designs (CODs), rate-1 codes exist only for 1 and 2 antennas. In general, For a transmit antennas, the maximal rate of a COD is 1/2 + l/n or 1/2 + 1/n+1 for n even or odd respectively. In this paper, we present a simple construction for maximal-rate CODs for any number of antennas from square CODs which resembles the construction of rate-1 RODs from square RODs. These designs are shown to be amenable for construction of a class of generalized CODs (called Coordinate-Interleaved Scaled CODs) with low peak-to-average power ratio (PAPR) having the same parameters as the maximal-rate codes. Simulation results indicate that these codes perform better than the existing maximal rate codes under peak power constraint while performing the same under average power constraint.

Renyi entropies of free bosons on the torus and holography

We analytically evaluate the Renyi entropies for the two dimensional free boson CFT. The CFT is considered to be compactified on a circle and at finite temperature. The Renyi entropies S-n are evaluated for a single interval using the two point function of bosonic twist fields on a torus. For the case of the compact boson, the sum over the classical saddle points results in the Riemann-Siegel theta function associated with the A(n-1) lattice. We then study the Renyi entropies in the decompactification regime. We show that in the limit when the size of the interval becomes the size of the spatial circle, the entanglement entropy reduces to the thermal entropy of free bosons on a circle. We then set up a systematic high temperature expansion of the Renyi entropies and evaluate the finite size corrections for free bosons. Finally we compare these finite size corrections both for the free boson CFT and the free fermion CFT with the one-loop corrections obtained from bulk three dimensional handlebody spacetimes which have higher genus Riemann surfaces as its boundary. One-loop corrections in these geometries are entirely determined by quantum numbers of the excitations present in the bulk. This implies that the leading finite size corrections contributions from one-loop determinants of the Chern-Simons gauge field and the Dirac field in the dual geometry should reproduce that of the free boson and the free fermion CFT respectively. By evaluating these corrections both in the bulk and in the CFT explicitly we show that this expectation is indeed true.

Maximal Contractive Tuples

Maximality of a contractive tuple of operators is considered. A characterization for a contractive tuple to be maximal is obtained. The notion of maximality for a submodule of the Drury-Arveson module on the -dimensional unit ball is defined. For , it is shown that every submodule of the Hardy module over the unit disc is maximal. But for we prove that any homogeneous submodule or submodule generated by polynomials is not maximal. A characterization of maximal submodules is obtained.

Conformal perturbation theory and higher spin entanglement entropy on the torus

We study the free fermion theory in 1+1 dimensions deformed by chemical potentials for holomorphic, conserved currents at finite temperature and on a spatial circle. For a spin-three chemical potential mu, the deformation is related at high temperatures to a higher spin black hole in hs0] theory on AdS(3) spacetime. We calculate the order mu(2) corrections to the single interval Renyi and entanglement entropies on the torus using the bosonized formulation. A consistent result, satisfying all checks, emerges upon carefully accounting for both perturbative and winding mode contributions in the bosonized language. The order mu(2) corrections involve integrals that are finite but potentially sensitive to contact term singularities. We propose and apply a prescription for defining such integrals which matches the Hamiltonian picture and passes several non-trivial checks for both thermal corrections and the Renyi entropies at this order. The thermal corrections are given by a weight six quasi-modular form, whilst the Renyi entropies are controlled by quasi-elliptic functions of the interval length with modular weight six. We also point out the well known connection between the perturbative expansion of the partition function in powers of the spin-three chemical potential and the Gross-Taylor genus expansion of large-N Yang-Mills theory on the torus. We note the absence of winding mode contributions in this connection, which suggests qualitatively different entanglement entropies for the two systems.

On the Bounds of Certain Maximal Linear Codes in a Projective Space

The set of all subspaces of F-q(n) is denoted by P-q(n). The subspace distance d(S)(X, Y) = dim(X) + dim(Y)-2dim(X boolean AND Y) defined on P-q(n) turns it into a natural coding space for error correction in random network coding. A subset of P-q(n) is called a code and the subspaces that belong to the code are called codewords. Motivated by classical coding theory, a linear coding structure can be imposed on a subset of P-q(n). Braun et al. conjectured that the largest cardinality of a linear code, that contains F-q(n), is 2(n). In this paper, we prove this conjecture and characterize the maximal linear codes that contain F-q(n).

Immunization of male rabbits with sheep luteal receptor to LH results in production of antibodies exhibiting hormone-agonistic and -antagonistic activities

Antibodies to LH/chorionic gonadotrophin receptor (LH/CG-R; molecular weight 67 000), isolated in a homogenous state (established by SDS-PAGE and ligand blotting) from sheep luteal membrane using human CG (hCG)-Sepharose affinity chromatography, were raised in three adult male rabbits (R-I, R-II and R-III). Each of the rabbits received 20-30 mu g oi the purified receptor in Freund's complete adjuvant at a time. Primary immunization was followed by booster injection at intervals. Production of receptor antibodies was monitored by (1) determining the dilution of the serum (IgG fraction) that could specifically bind 50% of I-125-LH/CG-R added and (2) analysing sera for any chance in testosterone levels. Following primary immunization and the first booster, all three rabbits exhibited a 2.5- to 6.0-fold increase in serum testosterone over basal levels and this effect was spread over a period of time (similar to 40 days) coinciding with the rise and fall of receptor antibodies. The maximal antibody titre (ED(50)) produced at this time ranged from 1:350 to 1:100 to below detectable limits for R-I, R-II and R-III respectively. Subsequent immunizations followed by the second booster resulted in a substantial increase in antibody titre (ED(50) of 1:5000) in R-I, but this was not accompanied by any change in serum testosterone over preimmune levels, suggesting that with the progress of immunization the character of the antibody produced had also changed. Two pools of antisera from R-I collected 10 days following the booster (at day 70 (bleed I) and day 290 (bleed II)) were used in further experiments. IgG isolated from bleed I but not from bleed II antiserum showed a dose-dependent stimulation of testosterone production by mouse Leydig cells in vitro, thus confirming the in vivo hormone-mimicking activity antibodies generated during the early immunization phase. The IgG fractions from both bleeds were, however, capable of inhibiting (1) I-125-hCG binding to crude sheep luteal membrane (EC(50) of 1:70 and 1:350 for bleed I and II antisera respectively) and (2) ovine LH-stimulated testosterone production by mouse Leydig cells in vitro, indicating the presence oi antagonistic antibodies irrespective of the period of time during which the rabbits were immunized. The: fact that bleed I-stimulated testosterone production could be inhibited in a dose-dependent manner by the addition of IgG from bleed II to the mouse Leydig cell in vitro assay system showed that the agonistic activity is intrinsic to the bleed I antibody. The receptor antibody (bleed II) was also capable of blocking LH action in vivo, as rabbits passively (for 24 h with LH/CG-R antiserum) as well as actively (for 130 days) immunized against LH/CG-R failed to respond to a bolus injection of LH (50 mu g). At no time, however, was the serum testosterone reduced below the basal level. This study clearly shows that, unlike with LH antibody, attempts to achieve an LH deficiency effect in vivo by resorting to immunization with hole LH receptor is difficult, as receptor antibodies exhibit both hormone-mimicking (agonistic) as well as hormone-blocking (antagonistic) activities.

Hyperexpression of biologically active human chorionic gonadotropin using the methylotropic yeast, Pichia pastoris

Human chorionic gonadotropin (hCG), a heterodimeric glycoprotein hormone, is composed of an alpha subunit noncovalentlv associated with the hormone-specific beta subunit. The objective of the present study was recombinant expression of properly folded, biologically active hCG and its subunits using an expression system that could be used for structure-function studies while providing adequate quantities of the hormone for immunocontraceptive studies. We report here expression of biologically active hCG and its subunits using a yeast expression system, Pichia pastoris. The recombinant hGG alpha and hCG beta subunits were secreted into the medium and the levels of expression achieved at shake culture level were 24 and 2.7-3 mg/l secretory medium respectively. Go-expression of both subunits in the same cell resulted in secretion of heterodimeric hGG into the medium. The pichia-expressed hCG was immunologically similar to the native hormone, capable of binding to the LH receptors and stimulating a biological response in vitro. Surprisingly, the maximal response obtained was twice that obtained with the native hGG. The le level of expression of hCG achieved was 12-16 mg/l secretory medium and is expected to increase several-fold in a fermenter. Thus the Pichia expression system is capable of hyperexpressing properly folded, biologically active hGG and is suitable for structure-function studies of the hormone.

Latency, Power and Performance Trade-offs in Network-on-Chips by Link Microarchitecture Exploration

This paper presents a power, latency and throughput trade-off study on NoCs by varying microarchitectural (e.g. pipelining) and circuit level (e.g. frequency and voltage) parameters. We change pipelining depth, operating frequency and supply voltage for 3 example NoCs - 16 node 2D Torus, Tree network and Reduced 2D Torus. We use an in-house NoC exploration framework capable of topology generation and comparison using parameterized models of Routers and links developed in SystemC. The framework utilizes interconnect power and delay models from a low-level modelling tool called Intacte[1]1. We find that increased pipelining can actually reduce latency. We also find that there exists an optimal degree of pipelining which is the most energy efficient in terms of minimizing energy-delay product.

Detection of the protein dimers, multiple monomeric states and hydrated forms of Plasmodium falciparum triosephosphate isomerase in the gas phase

Dimeric and monomeric forms of the enzyme triosephosphate isomerase (TIM) from Plasmodium falciparum (Pf) have been detected under conditions of nanoflow by electrospray mass spectrometry. The dimer (M = 55 663 Da) exhibits a narrow charge state distribution with intense peaks limited to values of 18(+) to 21(+), maximal intensity being observed for charge states 19(+) and 20(+). A monomeric species with a charge state distribution ranging from 11(+) to 16(+) is also observed, which may be assigned to folded dissociated subunits. Complete dimer dissociation results under normal electrospray condition. The effects of solution pH and source temperature have been investigated. The observation of four distinct charge state distributions which may be assigned to a dimer, folded monomer, partially folded monomer and unfolded monomer is reported. Circular dichromism and fluorescence studies of Pf TIM at low pH support the retention of substantial secondary and tertiary structures. Satellite peaks in mass spectra corresponding to hydrated species are also observed and isotope shift upon deuteration is demonstrated. The analysis of all available independent crystal structures of Pf TIM and TIMs from other organisms permits identification of structurally conserved water molecules. Hydration observed in the dimer and folded monomeric forms in the gas phase may correspond to these conserved sites.

Effect of pregnant mare serum gonadotropin on the induction and degradation of FSH and LH receptors in the granulosa cell of the immature rat

The relative induction of FSH and LH receptors in the granulosa cells of immature rat ovary by pregnant mare serum gonadotropin (PMSG) has been studied. A single injection of PMSG (15 IU) brought about a 3- and 12-fold increase in FSH and LH receptor concentration,respectively, in the granulosa cells. Maximal concentration was reached by 72 h but the receptor levels showed a sharp decline during the next 24–48 h. The kinetic properties of the newly formed FSH receptors were indistinguishable from the pre-existing ones. The induced FSH receptors were functional as demonstrated by an increase in the in vitro responsiveness of the cells to exogenous FSH in terms of progesterone production. Treatment of immature rats with cyanoketone, an inhibitor of Δ5,3β-hydroxysteroid dehydrogenase, prior to PMSG injection effectively reduced the PMSG-stimulated increase in the serum estradiol, uterine weight and LH receptors but had no effect on the FSH receptor induction. The ability of PMSG to induce gonadotropin receptors can be arrested at any given time by injecting its antibody, thereby suggesting a continuous need for the hormonal inducer. Estrogen in the absence of the primary inducer was unable to maintain the induced LH and FSH receptor concentration. Inhibition of prostaglandin synthesis using indomethacin also had no effect on either the induction or degradation of gonadotropin receptors. Administration of PMSG antiserum, 48 h after PMSG injection, brought about a rapid decline in the induced receptors over the next 24 h, with a rate constant and \iota 1/2 of 0.078 h−1 and 8.9 h for FSH receptors and 0.086 h−1 and 8.0 h for the LH receptors, respectively.

Standardization and validation of an induced ovulation model system in buffalo cows: Characterization of gene expression changes in the periovulatory follicle

In bovines characterization of biochemical and molecular determinants of the dominant follicle before and during different time intervals after gonadotrophin surge requires precise identification of the dominant follicle from a follicular wave. The objectives of the present study were to standardize an experimental model in buffalo cows for accurately identifying the dominant follicle of the first wave of follicular growth and characterize changes in follicular fluid hormone concentrations as well as expression patterns of various genes associated with the process of ovulation. From the day of estrus (day 0), animals were subjected to blood sampling and ultrasonography for monitoring circulating progesterone levels and follicular growth. On day 7 of the cycle, animals were administered a PGF2α analogue (Tiaprost Trometamol, 750 μg i.m.) followed by an injection of hCG (2000 IU i.m.) 36 h later. Circulating progesterone levels progressively increased from day 1 of the cycle to 2.26 ± 0.17 ng/ml on day 7 of the cycle, but declined significantly after PGF2α injection. A progressive increase in the size of the dominant follicle was observed by ultrasonography. The follicular fluid estradiol and progesterone concentrations in the dominant follicle were 600 ± 16.7 and 38 ± 7.6 ng/ml, respectively, before hCG injection and the concentration of estradiol decreased to 125.8 ± 25.26 ng/ml, but concentration of progesterone increased to 195 ± 24.6 ng/ml, 24 h post-hCG injection. Inh-α and Cyp19A1 expressions in granulosa cells were maximal in the dominant follicle and declined in response to hCG treatment. Progesterone receptor, oxytocin and cycloxygenase-2 expressions in granulosa cells, regarded as markers of ovulation, were maximal at 24 h post-hCG. The expressions of genes belonging to the super family of proteases were also examined; Cathepsin L expression decreased, while ADAMTS 3 and 5 expressions increased 24 h post-hCG treatment. The results of the current study indicate that sequential treatments of PGF2α and hCG during early estrous cycle in the buffalo cow leads to follicular growth that culminates in ovulation. The model system reported in the present study would be valuable for examining temporo-spatial changes in the periovulatory follicle immediately before and after the onset of gonadotrophin surge.

Microbial transformation of a fungicide-derived amine, dimethyl-p-phenylene diamine by Alcaligenes DM4

Abstract Microbial transformation of N, N-dimethyl-p-phenylene diamine (DMPDA), a microbial product formed from the fungicide fenaminosulf (p-dimethylaminobenzenediazo sodium sulfonate) was studied by enriching microbes in soils treated with the amine. Microorganisms isolated from DMPDA-treated soil belonged to the genera of Micrococcus, Alcaligenes, and Corynebacterium. Of the various isolates, Alcaligenes DM4 showed maximal growth on DMPDA utilizing it as sources of carbon and nitrogen. When grown in mineral salts basal medium containing 0.05% DMPDA to serve as carbon and nitrogen sources, Alcaligenes DM4 grew exponentially up to 18 h. Even though the characterization of the complete pathway of microbial degradation of DMPDA could not be carried out due to the auto-oxidation of the compound, the initial transformation product of DMPDA by Alcaligenes DM4 has been identified as a dimer. The dimer is generated into the culture medium presumably by the extra-cellular oxidase of Alcaligenes DM4. It is suggested that the risk-benefit evaluation on the use of fenaminosulf is to be made taking into consideration the microbial transformations of the fungicide.