Abstract:
This paper aims to study the efficiency of two short-term progestagen (FGA vs. MAP) + eCG treatments in estrus synchronization and artificial insemination (AI) with fresh or chilled semen in Assaf ewes fertility rate. All ewes received a subcutaneous implant of exogenous melatonin 45 days before been treated with short-term progestagens + eCG. By June 1^{st}, ewes were divided in two groups: half was treated with an intravaginal sponge impregnated with 20 mg of FGA and the other half with an intravaginal sponge impregnated with 60 mg of MAP. Progestagen treatments lasted for 6 days. At sponge withdraw, all ewes were injected with 750 IU of eCG. Ovarian activity was assessed by plasmatic progesterone levels before and after progestagens + eCG treatment. Semen was collected by electro ejaculation and extended with Andromed^{？} or OviXcell^{？}. AI was performed 55 hours after eCG administration with fresh or chilled semen. During AI several factors were assessed: vagina mucosa color and lubrication, external cervical Os type, cervical mucous viscosity, semen deposition place and seminal cervix outflow. Semen was deposited as deep as possible without distress or trauma cervix mucosa. All Assaf ewes presented cyclic activity before progestagen + eCG treatments (2^{nd} fortnight of May). Short-term progestagen + eCG treatments were equally efficient (100.0%). About 76.5% of Assaf ewes were pregnant 41 days after AI. Fertility rate was influenced by external Os type, semen deposition place and seminal cervix outflow. However, this rate was not conditioned by vaginal color or lubrication, cervical mucus viscosity, semen preservation technic and semen extender.

Abstract:
In Systems Biology there is a growing interest in the question, whether or not a given mathematical model can admit more than one steady state. As parameter values are often unknown or subject to a very high uncertainty, one is often interested in the question, whether or not a given mathematical model can, for some conceivable parameter vector, exhibit multistationarity at all. A partial answer to this question is given in Feinberg's deficiency one algorithm. This algorithm can decide about multistationarity by analyzing systems of linear inequalities that are independent of parameter values. However, the deficiency one algorithm is limited to what its author calls regular deficiency one networks. Many realistic networks have a deficiency higher than one, thus the algorithm cannot be applied directly. In a previous publication it was suggested to analyze certain well defined subnetworks that are guaranteed to be of deficiency one. Realistic reaction networks, however, often lead to subnetworks that are irregular, especially if metabolic networks are considered. Here the special structure of the subnetworks is used to derive conditions for multistationarity. These conditions are independent of the regularity conditions required by the deficiency one algorithm. Thus, in particular, these conditions are applicable to irregular subnetworks.

Abstract:
The Wheeler-DeWitt equation for a class of Kantowski-Sachs like models is completely solved. The generalized models include the Kantowski-Sachs model with cosmological constant and pressureless dust. Likewise contained is a joined model which consists of a Kantowski-Sachs cylinder inserted between two FRW half--spheres. The (second order) WKB approximation is exact for the wave functions of the complete set and this facilitates the product structure of the wave function for the joined model. In spite of the product structure the wave function can not be interpreted as admitting no correlations between the different regions. This problem is due to the joining procedure and may therefore be present for all joined models. Finally, the {s}ymmetric {i}nitial {c}ondition (SIC) for the wave function is analyzed and compared with the ``no bouindary'' condition. The consequences of the different boundary conditions for the arrow of time are briefly mentioned.

Abstract:
The meaning of `tunneling' in a timeless theory such as quantum cosmology is discussed. A recent suggestion of `tunneling' of the macroscopic universe at the classical turning point is analyzed in an anisotropic and inhomogeneous toy model. This `inhomogeneous tunneling' is a local process which cannot be interpreted as a tunneling of the universe.

Abstract:
Biochemical mechanisms with mass action kinetics are often modeled by systems of polynomial differential equations (DE). Determining directly if the DE system has multiple equilibria (multistationarity) is difficult for realistic systems, since they are large, nonlinear and contain many unknown parameters. Mass action biochemical mechanisms can be represented by a directed bipartite graph with species and reaction nodes. Graph-theoretic methods can then be used to assess the potential of a given biochemical mechanism for multistationarity by identifying structures in the bipartite graph referred to as critical fragments. In this article we present a graph-theoretic method for conservative biochemical mechanisms characterized by bounded species concentrations, which makes the use of degree theory arguments possible. We illustrate the results with an example of a MAPK network.

Abstract:
Multisite phosphorylation plays an important role in intracellular signaling. There has been much recent work aimed at understanding the dynamics of such systems when the phosphorylation/dephosphorylation mechanism is distributive, that is, when the binding of a substrate and an enzyme molecule results in addition or removal of a single phosphate group and repeated binding therefore is required for multisite phosphorylation. In particular, such systems admit bistability. Here we analyze a different class of multisite systems, in which the binding of a substrate and an enzyme molecule results in addition or removal of phosphate groups at all phosphorylation sites. That is, we consider systems in which the mechanism is processive, rather than distributive. We show that in contrast with distributive systems, processive systems modeled with mass-action kinetics do not admit bistability and, moreover, exhibit rigid dynamics: each invariant set contains a unique equilibrium, which is a global attractor. Additionally, we obtain a monomial parametrization of the steady states. Our proofs rely on a technique of Johnston for using "translated" networks to study systems with "toric steady states", recently given sign conditions for injectivity of polynomial maps, and a result from monotone systems theory due to Angeli and Sontag.

Abstract:
Binomial ideals are special polynomial ideals with many algorithmically and theoretically nice properties. We discuss the problem of deciding if a given polynomial ideal is binomial. While the methods are general, our main motivation and source of examples is the simplification of steady state equations of chemical reaction networks. For homogeneous ideals we give an efficient, Gr\"obner-free algorithm for binomiality detection, based on linear algebra only. On inhomogeneous input the algorithm can only give a sufficient condition for binomiality. As a remedy we construct a heuristic toolbox that can lead to simplifications even if the given ideal is not binomial.

Abstract:
Many biochemical processes can successfully be described by dynamical systems allowing some form of switching when, depending on their initial conditions, solutions of the dynamical system end up in different regions of state space (associated with different biochemical functions). Switching is often realized by a bistable system (i.e. a dynamical system allowing two stable steady state solutions) and, in the majority of cases, bistability is established numerically. In our point of view this approach is too restrictive, as, one the one hand, due to predominant parameter uncertainty numerical methods are generally difficult to apply to realistic models originating in Systems Biology. And on the other hand switching already arises with the occurrence of a saddle type steady state (characterized by a Jacobian where exactly one Eigenvalue is positive and the remaining eigenvalues have negative real part). Consequently we derive conditions based on linear inequalities that allow the analytic computation of states and parameters where the Jacobian derived from a mass action network has a defective zero eigenvalue so that -- under certain genericity conditions -- a saddle-node bifurcation occurs. Our conditions are applicable to general mass action networks involving at least one conservation relation, however, they are only sufficient (as infeasibility of linear inequalities does not exclude defective zero eigenvalues).

Abstract:
A numerical technique is proposed for an efficient numerical determination of the average phase factor of the fermionic determinant continued to imaginary values of the chemical potential. The method is tested in QCD with eight flavors of dynamical staggered fermions. A direct check of the validity of analytic continuation is made on small lattices and a study of the scaling with the lattice volume is performed.

Abstract:
Multisite protein phosphorylation plays a prominent role in intracellular processes like signal transduction, cell-cycle control and nuclear signal integration. Many proteins are phosphorylated in a sequential and distributive way at more than one phosphorylation site. Mathematical models of $n$-site sequential distributive phosphorylation are therefore studied frequently. In particular, in {\em Wang and Sontag, 2008,} it is shown that models of $n$-site sequential distributive phosphorylation admit at most $2n-1$ steady states. Wang and Sontag furthermore conjecture that for odd $n$, there are at most $n$ and that, for even $n$, there are at most $n+1$ steady states. This, however, is not true: building on earlier work in {\em Holstein et.al., 2013}, we present a scalar determining equation for multistationarity which will lead to parameter values where a $3$-site system has $5$ steady states and parameter values where a $4$-site system has $7$ steady states. Our results therefore are counterexamples to the conjecture of Wang and Sontag. We furthermore study the inherent geometric properties of multistationarity in $n$-site sequential distributive phosphorylation: the complete vector of steady state ratios is determined by the steady state ratios of free enzymes and unphosphorylated protein and there exists a linear relationship between steady state ratios of phosphorylated protein.