A strong triangle inequality in hyperbolic geometry

For a triangle in the hyperbolic plane, let $\alpha,\beta,\gamma$ denote the angles opposite the sides $a,b,c$, respectively. Also, let $h$ be the height of the altitude to side $c$. Under the assumption that $\alpha,\beta, \gamma$ can be chosen uniformly in the interval $(0,\pi)$ and it is given that $\alpha+\beta+\gamma c + h$ holds approximately 79\% of the time. To accomplish this, we prove a number of theoretical results to make sure that the probability can be computed to an arbitrary precision, and the error can be bounded

Luttinger theorem for the strongly correlated Fermi liquid of composite fermions

While an ordinary Fermi sea is perturbatively robust to interactions, the paradigmatic composite-fermion (CF) Fermi sea arises as a non-perturbative consequence of emergent gauge fields in a system where there was no Fermi sea to begin with. A mean-field picture suggests two Fermi seas, of composite fermions made from electrons or holes in the lowest Landau level, which occupy different areas away from half filling and thus appear to represent distinct states. We show that in the microscopic theory of composite fermions, which satisfies particle-hole symmetry in the lowest Landau level to an excellent degree, the Fermi wave vectors at filling factors $\nu$ and $1-\nu$ are the same, and are generally consistent with the experimental findings of Kamburov {\em et al.} [Phys. Rev. Lett. {\bf 113}, 196801 (2014)]. Our calculations suggest that the area of the CF Fermi sea may slightly violate the Luttinger area rule.Comment: 21 pages, 17 figures including supplemental material, published versio

Comparative analysis of 18S rRNA genes from Myxobolus aeglefini Auerbach, 1906 isolated from cod (Gadus morhua), Plaice (Pleuronectes platessa) and dab (Limanda limanda), using PCR-RFLP

The myxosporean parasite Myxobolus aeglefini is a marine species, which can be found in the cartilage of mainly gadid fish species. The parasite has, however, been recorded in the flatfish plaice (Pleuronectes platessa) and dab (Limanda limanda). It is not clear if isolates from unrelated hosts represent the same species. Therefore a molecular study was conducted to reveal differences at the DNA level between these isolates. PCR was successfully conducted on three different isolates of Myxobolus aeglefini sampled from cod (Gadus morhua), plaice and dab respectively, using 18S rDNA as template. A PCR product of approx. 1600 base pairs was obtained and RFLP (Restriction Fragment Length Polymerase) was conducted on the fragment with the restriction enzymes Hinf I, Msp I and Hae III. No differences between the isolates were found, suggesting that the three isolates represent the same species

Phase Diagram of Fractional Quantum Hall Effect of Composite Fermions in Multi-Component Systems

While the integer quantum Hall effect of composite fermions manifests as the prominent fractional quantum Hall effect (FQHE) of electrons, the FQHE of composite fermions produces further, more delicate states, arising from a weak residual interaction between composite fermions. We study the spin phase diagram of these states, motivated by the recent experimental observation by Liu {\em et al.} \cite{Liu14a,Liu14b} of several spin-polarization transitions at 4/5, 5/7, 6/5, 9/7, 7/9, 8/11 and 10/13 in GaAs systems. We show that the FQHE of composite fermions is much more prevalent in multicomponent systems, and consider the feasibility of such states for systems with ${\cal N}$ components for an SU(${\cal N}$) symmetric interaction. Our results apply to GaAs quantum wells, wherein electrons have two components, to AlAs quantum wells and graphene, wherein electrons have four components (two spins and two valleys), and to an H-terminated Si(111) surface, which can have six components. The aim of this article is to provide a fairly comprehensive list of possible incompressible fractional quantum Hall states of composite fermions, their SU(${\cal N}$) spin content, their energies, and their phase diagram as a function of the generalized "Zeeman" energy. We obtain results at three levels of approximation: from ground state wave functions of the composite fermion theory, from composite fermion diagonalization, and, whenever possible, from exact diagonalization. Effects of finite quantum well thickness and Landau level mixing are neglected in this study. We compare our theoretical results with the experiments of Liu {\em et al.} \cite{Liu14a,Liu14b} as well as of Yeh {\em et al.} \cite{Yeh99} for a two component system.Comment: 29 pages, 6 figure

Phylogeny of Tec Family Kinases: Identification of a Pre-Metazoan Origin of Btk, Bmx, Itk, Tec, Txk and the Btk Regulator SH3BP5

It is generally considered mammals and birds have five Tec family kinases (TFKs): Btk, Bmx (also known as Etk), Itk, Tec, and Txk (also known as Rlk). Here, we discuss the domains and their functions and regulation in TFKs. Over the last few years, a large number of genomes from various phyla have been sequenced making it possible to study evolutionary relationships at the molecular and sequence level. Using bioinformatics tools, we for the first time demonstrate that a TFK ancestor exists in the unicellular choanoflagellate Monosiga brevicollis, which is the closest known relative to metazoans with a sequenced genome. The analysis of the genomes for sponges, insects, hagfish, and frogs suggests that these species encode a single TFK. The insect form has a divergent and unique N-terminal region. Duplications generating the five members took place prior to the emergence of vertebrates. Fishes have two or three forms and the platypus, Ornithorhynchus anatinus, has four (lacks Txk). Thus, not all mammals have all five TFKs. The single identified TFK in frogs is an ortholog of Tec. Bmx seems to be unique to mammals and birds. SH3BP5 is a negative regulator of Btk. It is conserved in choanoflagellates and interestingly exists also in nematodes, which do not express TFKs, suggesting a broader function in addition to Btk regulation. The related SH3BP5-like protein is not found in Nematodes

A Rewriting-Logic-Based Technique for Modeling Thermal Systems

This paper presents a rewriting-logic-based modeling and analysis technique for physical systems, with focus on thermal systems. The contributions of this paper can be summarized as follows: (i) providing a framework for modeling and executing physical systems, where both the physical components and their physical interactions are treated as first-class citizens; (ii) showing how heat transfer problems in thermal systems can be modeled in Real-Time Maude; (iii) giving the implementation in Real-Time Maude of a basic numerical technique for executing continuous behaviors in object-oriented hybrid systems; and (iv) illustrating these techniques with a set of incremental case studies using realistic physical parameters, with examples of simulation and model checking analyses.Comment: In Proceedings RTRTS 2010, arXiv:1009.398

Flavor Alignment via Shining in RS

We present a class of warped extra dimensional models whose flavor violating interactions are much suppressed compared to the usual anarchic case due to flavor alignment. Such suppression can be achieved in models where part of the global flavor symmetry is gauged in the bulk and broken in a controlled manner. We show that the bulk masses can be aligned with the down type Yukawa couplings by an appropriate choice of bulk flavon field representations and TeV brane dynamics. This alignment could reduce the flavor violating effects to levels which allow for a Kaluza-Klein scale as low as 2-3 TeV, making the model observable at the LHC. However, the up-type Yukawa couplings on the IR brane, which are bounded from below by recent bounds on CP violation in the D system, induce flavor misalignment radiatively. Off-diagonal down-type Yukawa couplings and kinetic mixings for the down quarks are both consequences of this effect. These radiative Yukawa corrections can be reduced by raising the flavon VEV on the IR brane (at the price of some moderate tuning), or by extending the Higgs sector. The flavor changing effects from the radiatively induced Yukawa mixing terms are at around the current upper experimental bounds. We also show the generic bounds on UV-brane induced flavor violating effects, and comment on possible additional flavor violations from bulk flavor gauge bosons and the bulk Yukawa scalars.Comment: 28 page

A Flavor Protection for Warped Higgsless Models

We examine various possibilities for realistic 5D higgsless models and construct a full quark sector featuring next-to-minimal flavor violation (with an exact bulk SU(2) protecting the first two generations) satisfying electroweak and flavor constraints. The "new custodially protected representation" is used for the third generation to protect the light quarks from flavor violations induced due to the heavy top. A combination of flavor symmetries, and RS-GIM for the right-handed quarks suppresses flavor-changing neutral currents below experimental bounds, assuming CKM-type mixing on the UV brane. In addition to the usual higgsless RS signals, this model predicts an exotic charge-5/3 quark with mass of about 0.5 TeV which should show up at the LHC very quickly, as well as nonzero flavor-changing neutral currents which could be detected in the next generation of flavor experiments. In the course of our analysis, we also find quantitative estimates for the errors of the fermion zero mode approximation, which are significant for higgsless-type models.Comment: 26 pages, 3 figures. v2: References added, typos fixed, corrected C4 bounds (now less severe), slightly extended discussion of result