Counting proofs in propositional logic

We give a procedure for counting the number of different proofs of a formula in various sorts of propositional logic. This number is either an integer (that may be 0 if the formula is not provable) or infinite

Stochastic modeling of cargo transport by teams of molecular motors

Many different types of cellular cargos are transported bidirectionally along microtubules by teams of molecular motors. The motion of this cargo-motors system has been experimentally characterized in vivo as processive with rather persistent directionality. Different theoretical approaches have been suggested in order to explore the origin of this kind of motion. An effective theoretical approach, introduced by M\"uller et al., describes the cargo dynamics as a tug-of-war between different kinds of motors. An alternative approach has been suggested recently by Kunwar et al., who considered the coupling between motor and cargo in more detail. Based on this framework we introduce a model considering single motor positions which we propagate in continuous time. Furthermore, we analyze the possible influence of the discrete time update schemes used in previous publications on the system's dynamic.Comment: Cenference proceedings - Traffic and Granular Flow 1

Dicke-Type Energy Level Crossings in Cavity-Induced Atom Cooling: Another Superradiant Cooling

This paper is devoted to energy-spectral analysis for the system of a two-level atom coupled with photons in a cavity. It is shown that the Dicke-type energy level crossings take place when the atom-cavity interaction of the system undergoes changes between the weak coupling regime and the strong one. Using the phenomenon of the crossings we develop the idea of cavity-induced atom cooling proposed by the group of Ritsch, and we lay mathematical foundations of a possible mechanism for another superradiant cooling in addition to that proposed by Domokos and Ritsch. The process of our superradiant cooling can function well by cavity decay and by control of the position of the atom, at least in (mathematical) theory, even if there is neither atomic absorption nor atomic emission of photons.Comment: 15 pages; 8 figure

Guardians Ad Litem as Surrogate Parents: Implication for Role Definition and Confidentiality

SALMON (Scalable Ab-initio Light–Mattersimulator for Optics and Nanoscience, http://salmon-tddft.jp) is a software package for the simulation of electron dynamics and optical properties of molecules, nanostructures, and crystalline solids based on first-principles time-dependent density functional theory. The core part of the software is the real-time, real-space calculation of the electron dynamics induced in molecules and solids by an external electric field solving the time-dependent Kohn–Sham equation. Using a weak instantaneous perturbing field, linear response properties such as polarizabilities and photoabsorptions in isolated systems and dielectric functions in periodic systems are determined. Using an optical laser pulse, the ultrafast electronic response that may be highly nonlinear in the field strength is investigated in time domain. The propagation of the laser pulse in bulk solids and thin films can also be included in the simulation via coupling the electron dynamics in many microscopic unit cells using Maxwell’s equations describing the time evolution of the electromagnetic fields. The code is efficiently parallelized so that it may describe the electron dynamics in large systems including up to a few thousand atoms. The present paper provides an overview of the capabilities of the software package showing several sample calculations. Program summary Program Title: SALMON: Scalable Ab-initio Light–Matter simulator for Optics and Nanoscience Program Files doi:http://dx.doi.org/10.17632/8pm5znxtsb.1 Licensing provisions: Apache-2.0 Programming language: Fortran 2003 Nature of problem: Electron dynamics in molecules, nanostructures, and crystalline solids induced by an external electric field is calculated based on first-principles time-dependent density functional theory. Using a weak impulsive field, linear optical properties such as polarizabilities, photoabsorptions, and dielectric functions are extracted. Using an optical laser pulse, the ultrafast electronic response that may be highly nonlinear with respect to the exciting field strength is described as well. The propagation of the laser pulse in bulk solids and thin films is considered by coupling the electron dynamics in many microscopic unit cells using Maxwell’s equations describing the time evolution of the electromagnetic field. Solution method: Electron dynamics is calculated by solving the time-dependent Kohn–Sham equation in real time and real space. For this, the electronic orbitals are discretized on a uniform Cartesian grid in three dimensions. Norm-conserving pseudopotentials are used to account for the interactions between the valence electrons and the ionic cores. Grid spacings in real space and time, typically 0.02 nm and 1 as respectively, determine the spatial and temporal resolutions of the simulation results. In most calculations, the ground state is first calculated by solving the static Kohn–Sham equation, in order to prepare the initial conditions. The orbitals are evolved in time with an explicit integration algorithm such as a truncated Taylor expansion of the evolution operator, together with a predictor–corrector step when necessary. For the propagation of the laser pulse in a bulk solid, Maxwell’s equations are solved using a finite-difference scheme. By this, the electric field of the laser pulse and the electron dynamics in many microscopic unit cells of the crystalline solid are coupled in a multiscale framework

Complexity Bounds for Ordinal-Based Termination

`What more than its truth do we know if we have a proof of a theorem in a given formal system?' We examine Kreisel's question in the particular context of program termination proofs, with an eye to deriving complexity bounds on program running times. Our main tool for this are length function theorems, which provide complexity bounds on the use of well quasi orders. We illustrate how to prove such theorems in the simple yet until now untreated case of ordinals. We show how to apply this new theorem to derive complexity bounds on programs when they are proven to terminate thanks to a ranking function into some ordinal.Comment: Invited talk at the 8th International Workshop on Reachability Problems (RP 2014, 22-24 September 2014, Oxford

Essential Microenvironment for Thymopoiesis is Preserved in Human Adult and Aged Thymus

Normal human thymuses at various ages were immunohistologically examined in order to determine whether adult or aged thymus maintained the microenvironment for the T cell development and thymopoiesis was really ongoing. To analyze the thymic microenvironment, two monoclonal antibodies (MoAb) were employed. One is MoAb to IL-1 receptor (IL-1R) recognizing medullary and subcapsular cortical epithelial cells of normal infant human thymus. The other is UH-1 MoAb recognizing thymic epithelial cells within the cortex, which are negative with IL-1R-MoAb. Thymus of subjects over 20 years of age was split into many fragments and dispersed in the fatty tissue. However, the microenvironment of each fragment was composed of both IL-1R positive and UH-1 positive epithelial cells, and the UH-1 positive portion was populated with lymphocytes showing a follicle-like appearance. Lymphocytes in these follicle-like portions were mostly CD4+CD8+ double positive cells and contained many proliferating cells as well as apoptotic cells. Thus these follicle-like portions in adult and aged thymus were considered to be functioning as cortex as in infant thymus. Proliferative activity of thymocytes in the thymic cortex and the follicle-like portions definitely declined with advance of age, while incidence of apoptotic thymocytes increased with aging

Cilia at the node of mouse embryos sense fluid flow for left-right determination via Pkd2

Unidirectional fluid flow plays an essential role in the breaking of left-right (L-R) symmetry in mouse embryos, but it has remained unclear how the flow is sensed by the embryo. We report that the Ca2+ channel Polycystin-2 (Pkd2) is required specifically in the perinodal crown cells for sensing the nodal flow. Examination of mutant forms of Pkd2 shows that the ciliary localization of Pkd2 is essential for correct L-R patterning. Whereas Kif3a mutant embryos, which lack all cilia, failed to respond to an artificial flow, restoration of primary cilia in crown cells rescued the response to the flow. Our results thus suggest that nodal flow is sensed in a manner dependent on Pkd2 by the cilia of crown cells located at the edge of the node.CREST of the Japan Science and Technology Corporation; NIH [P30 DK090744]; Human Frontier Science Program [ST00246/2003C]; Deutsche Forschungsgemeinschaft [PE 853/2]; Japan Society for the Promotion of Science; American Heart Association [R10682]info:eu-repo/semantics/publishedVersio