Status of the differential transformation method

Further to a recent controversy on whether the differential transformation method (DTM) for solving a differential equation is purely and solely the traditional Taylor series method, it is emphasized that the DTM is currently used, often only, as a technique for (analytically) calculating the power series of the solution (in terms of the initial value parameters). Sometimes, a piecewise analytic continuation process is implemented either in a numerical routine (e.g., within a shooting method) or in a semi-analytical procedure (e.g., to solve a boundary value problem). Emphasized also is the fact that, at the time of its invention, the currently-used basic ingredients of the DTM (that transform a differential equation into a difference equation of same order that is iteratively solvable) were already known for a long time by the "traditional"-Taylor-method users (notably in the elaboration of software packages --numerical routines-- for automatically solving ordinary differential equations). At now, the defenders of the DTM still ignore the, though much better developed, studies of the "traditional"-Taylor-method users who, in turn, seem to ignore similarly the existence of the DTM. The DTM has been given an apparent strong formalization (set on the same footing as the Fourier, Laplace or Mellin transformations). Though often used trivially, it is easily attainable and easily adaptable to different kinds of differentiation procedures. That has made it very attractive. Hence applications to various problems of the Taylor method, and more generally of the power series method (including noninteger powers) has been sketched. It seems that its potential has not been exploited as it could be. After a discussion on the reasons of the "misunderstandings" which have caused the controversy, the preceding topics are concretely illustrated.Comment: To appear in Applied Mathematics and Computation, 29 pages, references and further considerations adde

Laser-Assisted In Vitro Fertilization Facilitates Fertilization of Vitrified-Warmed C57BL/6 Mouse Oocytes with Fresh and Frozen-Thawed Spermatozoa, Producing Live Pups

The utility of cryopreserved mouse gametes for reproduction of transgenic mice depends on development of assisted reproductive technologies, including vitrification of unfertilized mouse oocytes. Due to hardening of the zona pellucida, spermatozoa are often unable to penetrate vitrified-warmed (V-W) oocytes. Laser-assisted in vitro fertilization (LAIVF) facilitates fertilization by allowing easier penetration of spermatozoa through a perforation in the zona. We investigated the efficiency of V-W C57BL/6NTac oocytes drilled by the XYClone laser, compared to fresh oocytes. By using DAP213 for cryoprotection, 83% (1,470/1,762) of vitrified oocytes were recovered after warming and 78% were viable. Four groups were evaluated for two-cell embryo and live offspring efficiency: 1) LAIVF using V-W oocytes, 2) LAIVF using fresh oocytes, 3) conventional IVF using V-W oocytes and 4) conventional IVF using fresh oocytes. First, the groups were tested using fresh C57BL/6NTac spermatozoa (74% motile, 15 million/ml). LAIVF markedly improved the two-cell embryo efficiency using both V-W (76%, 229/298) and fresh oocytes (69%, 135/197), compared to conventional IVF (7%, 12/182; 6%, 14/235, respectively). Then, frozen-thawed C57BL/6NTac spermatozoa (35% motile, 15 million/ml) were used and LAIVF was again found to enhance fertilization efficiency, with two-cell embryo rates of 87% (298/343) using V-W oocytes (P<0.05, compared to fresh spermatozoa), and 73% (195/266) using fresh oocytes. Conventional IVF with frozen-thawed spermatozoa using V-W (6%, 10/168) and fresh (5%, 15/323) oocytes produced few two-cell embryos. Although live offspring efficiency following embryo transfer was greater with conventional IVF (35%, 18/51; LAIVF: 6%, 50/784), advantage was seen with LAIVF in live offspring obtained from total oocytes (5%, 50/1,010; conventional IVF: 2%, 18/908). Our results demonstrated that zona-drilled V-W mouse oocytes can be used for IVF procedures using both fresh and frozen-thawed spermatozoa, producing live pups. The ability to cryopreserve mouse gametes for LAIVF may facilitate management of large-scale transgenic mouse production facilities.National Institutes of Health (U.S.) (NIH National Research Service Award (T32-RR070036))National Institutes of Health (U.S.) (NIH National Cancer Institute Program Project (P01CA10451)

Parallel Computational Subunits in Dentate Granule Cells Generate Multiple Place Fields

A fundamental question in understanding neuronal computations is how dendritic events influence the output of the neuron. Different forms of integration of neighbouring and distributed synaptic inputs, isolated dendritic spikes and local regulation of synaptic efficacy suggest that individual dendritic branches may function as independent computational subunits. In the present paper, we study how these local computations influence the output of the neuron. Using a simple cascade model, we demonstrate that triggering somatic firing by a relatively small dendritic branch requires the amplification of local events by dendritic spiking and synaptic plasticity. The moderately branching dendritic tree of granule cells seems optimal for this computation since larger dendritic trees favor local plasticity by isolating dendritic compartments, while reliable detection of individual dendritic spikes in the soma requires a low branch number. Finally, we demonstrate that these parallel dendritic computations could contribute to the generation of multiple independent place fields of hippocampal granule cells

Sframe: An Efficient System for Detailed DC Simulation of Bipolar Analog Integrated Circuits Using Continuation Methods

In this paper we describe an experimental system called sframe which is being incorporated into the design for manufacturability initiative at the Reading Works of AT&T Bell Laboratories. Our system is able to perform detailed and accurate DC analyses of integrated circuits containing several hundred transistors to be fabricated in a relatively complex junction isolated complementary technology

Effects of acute and chronic temperature changes on the functional responses of the dogfish Scyliorhinus canicula (Linnaeus, 1758) towards amphipod prey Echinogammarus marinus (Leach, 1815)

Predation is a strong driver of population dynamics and community structure and it is essential to reliably quantify and predict predation impacts on prey populations in a changing thermal landscape. Here, we used comparative functional response analyses to assess how predator-prey interactions between dogfish and invertebrate prey change under different warming scenarios. The Functional Response Type, attack rate, handling time and maximum feeding rate estimates were calculated for Scyliorhinus canicula preying upon Echinogammarus marinus under temperatures of 11.3 °C and 16.3 °C, which represent both the potential daily variation and predicted higher summer temperatures within Strangford Lough, N. Ireland. A two x two design of “Predator Acclimated”, “Prey Acclimated”, “Both Acclimated”, and “Both Unacclimated” was implemented to test functional responses to temperature rise. Attack rate was higher at 11.3 °C than at 16.3 °C, but handling time was lower and maximum feeding rates were higher at 16.3 °C. Non-acclimated predators had similar maximum feeding rate towards non-acclimated and acclimated prey, whereas acclimated predators had significantly higher maximum feeding rates towards acclimated prey as compared to non-acclimated prey. Results suggests that the predator attack rate is decreased by increasing temperature but when both predator and prey are acclimated the shorter handling times considerably increase predator impact. The functional response of the fish changed from Type II to Type III with an increase in temperature, except when only the prey were acclimated. This change from population destabilizing Type II to more stabilizing Type III could confer protection to prey at low densities but increase the maximum feeding rate by Scyliorhinus canicula in the future. However, predator movement between different thermal regimes may maintain a Type II response, albeit with a lower maximum feeding rate. This has implications for the way the increasing population Scyliorhinus canicula in the Irish Sea may exploit valuable fisheries stocks in the future