A Lower Bound of 2n2^n Conditional Branches for Boolean Satisfiability on Post Machines

We establish a lower bound of $2^n$ conditional branches for deciding the satisfiability of the conjunction of any two Boolean formulas from a set called a full representation of Boolean functions of $n$ variables - a set containing a Boolean formula to represent each Boolean function of $n$ variables. The contradiction proof first assumes that there exists a Post machine (Post's Formulation 1) that correctly decides the satisfiability of the conjunction of any two Boolean formulas from such a set by following an execution path that includes fewer than $2^n$ conditional branches. By using multiple runs of this Post machine, with one run for each Boolean function of $n$ variables, the proof derives a contradiction by showing that this Post machine is unable to correctly decide the satisfiability of the conjunction of at least one pair of Boolean formulas from a full representation of $n$-variable Boolean functions if the machine executes fewer than $2^n$ conditional branches. This lower bound of $2^n$ conditional branches holds for any full representation of Boolean functions of $n$ variables, even if a full representation consists solely of minimized Boolean formulas derived by a Boolean minimization method. We discuss why the lower bound fails to hold for satisfiability of certain restricted formulas, such as 2CNF satisfiability, XOR-SAT, and HORN-SAT. We also relate the lower bound to 3CNF satisfiability. The lower bound does not depend on sequentiality of access to the boxes in the symbol space and will hold even if a machine is capable of non-sequential access.Comment: This article draws heavily from arXiv:1406.597

Lone Higgs at the LHC

We address the possible scenario that the Large Hadron Collider (LHC) discovers only a Higgs boson after 10 fb^{-1} of operation, and attempt to identify this Higgs boson as that of the Standard Model (SM), the minimal universal extra dimension model (MUED), the littlest Higgs model with T-parity (LHT), or the minimal supersymmetric Standard Model (MSSM), using only the measurement of the product of gluon-fusion production cross section and the di-photon branching ratio. In MUED, by decoupling any new physics sufficiently to evade the discovery reach at the LHC, the deviation of the signal from the SM is not statistically significant. However, in LHT and MSSM, it is possible to have a significant deviation in the signal that is consistent with this "lone Higgs scenario", and, in the case of a very large suppression, we can distinguish MSSM and LHT before the discovery of any new resonances. Starting with the lone Higgs scenario and the deviation in this measurement from the Standard Model prediction (whether or not statistically significant), we offer tests that may discriminate the models and search strategies of discovering new physics signatures with increasing integrated luminosity.Comment: 32 pages, 25 figures, PRD versio

Medial Ganglionic Eminence Progenitors Transplanted into Hippocampus Integrate in a Functional and Subtype-Appropriate Manner.

Medial ganglionic eminence (MGE) transplantation rescues disease phenotypes in various preclinical models with interneuron deficiency or dysfunction, including epilepsy. While underlying mechanism(s) remains unclear to date, a simple explanation is that appropriate synaptic integration of MGE-derived interneurons elevates GABA-mediated inhibition and modifies the firing activity of excitatory neurons in the host brain. However, given the complexity of interneurons and potential for transplant-derived interneurons to integrate or alter the host network in unexpected ways, it remains unexplored whether synaptic connections formed by transplant-derived interneurons safely mirror those associated with endogenous interneurons. Here, we combined optogenetics, interneuron-specific Cre driver mouse lines, and electrophysiology to study synaptic integration of MGE progenitors. We demonstrated that MGE-derived interneurons, when transplanted into the hippocampus of neonatal mice, migrate in the host brain, differentiate to mature inhibitory interneurons, and form appropriate synaptic connections with native pyramidal neurons. Endogenous and transplant-derived MGE progenitors preferentially formed inhibitory synaptic connections onto pyramidal neurons but not endogenous interneurons. These findings demonstrate that transplanted MGE progenitors functionally integrate into the postnatal hippocampal network

Materials Design - Towards a Functionally Graded Electrical Conductor

In this study, we discuss functionally graded (FG) materials as pulsed electrical conductors. These conductors can be designed to be more efficient and longer lasting by applying numerical modeling tools. One focus is on limiting the thermal fatigue damage in conductors caused by very high temperatures that develop during pulse heating. We have quantified the effect of various grading functions on the pulsed Joule heating generated and the peak temperature experienced in the conductors of an electromagnetic launcher by using a 1D numerical code and a state of the art 3D coupled finite element code, EMAP3D. Because FG materials incorporate applications-tailored compositions, structures, and dimensions, smoothly graded properties in lateral and longitudinal cross sections are obtainable. The Solid Freeform Fabrication (SFF) processing approach allows for architectures with a series of important features. These features include the selective use of high efficiency conducting materials in the core, preconditioned conductor/structure interfaces, and built-in features for enhanced cooling where necessary.Mechanical Engineerin

Insights into antibody catalysis: Structure of an oxygenation catalyst at 1.9-Å resolution

The x-ray crystal structures of the sulfide oxidase antibody 28B4 and of antibody 28B4 complexed with hapten have been solved at 2.2-Å and 1.9-Å resolution, respectively. To our knowledge, these structures are the highest resolution catalytic antibody structures to date and provide insight into the molecular mechanism of this antibody-catalyzed monooxygenation reaction. Specifically, the data suggest that entropic restriction plays a fundamental role in catalysis through the precise alignment of the thioether substrate and oxidant. The antibody active site also stabilizes developing charge on both sulfur and periodate in the transition state via cation-pi and electrostatic interactions, respectively. In addition to demonstrating that the active site of antibody 28B4 does indeed reflect the mechanistic information programmed in the aminophosphonic acid hapten, these high-resolution structures provide a basis for enhancing turnover rates through mutagenesis and improved hapten design

Time-of-flight technique for particle identification at energies from 2 to 400 keV/nucleon

The time of flight technique for particle identification was extended to 2 keV/nucleon and the size of the start-time detector was reduced considerably by the use of carbon foils of few micrograms/cm square in thickness combined with microchannel plates for detecting secondary electrons. Time of flight telescopes incorporating this start-time device were used to measure the stopping power of a number of low energy heavy ions in thin carbon foils and the charge states of these ions emerging from such foils. Applications for the detection and identification of low energy interplanetary and magnetospheric particles are suggested

Evaluation of aerothermal modeling computer programs

Various computer programs based upon the SIMPLE or SIMPLER algorithm were studied and compared for numerical accuracy, efficiency, and grid dependency. Four two-dimensional and one three-dimensional code originally developed by a number of research groups were considered. In general, the accuracy and computational efficieny of these TEACH type programs were improved by modifying the differencing schemes and their solvers. A brief description of each program is given. Error reduction, spline flux and second upwind differencing programs are covered