Thermodynamics and quark susceptibilities: a Monte-Carlo approach to the PNJL model

The Monte-Carlo method is applied to the Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model. This leads beyond the saddle-point approximation in a mean-field calculation and introduces fluctuations around the mean fields. We study the impact of fluctuations on the thermodynamics of the model, both in the case of pure gauge theory and including two quark flavors. In the two-flavor case, we calculate the second-order Taylor expansion coefficients of the thermodynamic grand canonical partition function with respect to the quark chemical potential and present a comparison with extrapolations from lattice QCD. We show that the introduction of fluctuations produces only small changes in the behavior of the order parameters for chiral symmetry restoration and the deconfinement transition. On the other hand, we find that fluctuations are necessary in order to reproduce lattice data for the flavor non-diagonal quark susceptibilities. Of particular importance are pion fields, the contribution of which is strictly zero in the saddle point approximation

On the homomorphism order of labeled posets

Partially ordered sets labeled with k labels (k-posets) and their homomorphisms are examined. We give a representation of directed graphs by k-posets; this provides a new proof of the universality of the homomorphism order of k-posets. This universal order is a distributive lattice. We investigate some other properties, namely the infinite distributivity, the computation of infinite suprema and infima, and the complexity of certain decision problems involving the homomorphism order of k-posets. Sublattices are also examined.Comment: 14 page

Algebraic Properties of Valued Constraint Satisfaction Problem

The paper presents an algebraic framework for optimization problems expressible as Valued Constraint Satisfaction Problems. Our results generalize the algebraic framework for the decision version (CSPs) provided by Bulatov et al. [SICOMP 2005]. We introduce the notions of weighted algebras and varieties and use the Galois connection due to Cohen et al. [SICOMP 2013] to link VCSP languages to weighted algebras. We show that the difficulty of VCSP depends only on the weighted variety generated by the associated weighted algebra. Paralleling the results for CSPs we exhibit a reduction to cores and rigid cores which allows us to focus on idempotent weighted varieties. Further, we propose an analogue of the Algebraic CSP Dichotomy Conjecture; prove the hardness direction and verify that it agrees with known results for VCSPs on two-element sets [Cohen et al. 2006], finite-valued VCSPs [Thapper and Zivny 2013] and conservative VCSPs [Kolmogorov and Zivny 2013].Comment: arXiv admin note: text overlap with arXiv:1207.6692 by other author

Constraint Satisfaction with Counting Quantifiers

We initiate the study of constraint satisfaction problems (CSPs) in the presence of counting quantifiers, which may be seen as variants of CSPs in the mould of quantified CSPs (QCSPs). We show that a single counting quantifier strictly between exists^1:=exists and exists^n:=forall (the domain being of size n) already affords the maximal possible complexity of QCSPs (which have both exists and forall), being Pspace-complete for a suitably chosen template. Next, we focus on the complexity of subsets of counting quantifiers on clique and cycle templates. For cycles we give a full trichotomy -- all such problems are in L, NP-complete or Pspace-complete. For cliques we come close to a similar trichotomy, but one case remains outstanding. Afterwards, we consider the generalisation of CSPs in which we augment the extant quantifier exists^1:=exists with the quantifier exists^j (j not 1). Such a CSP is already NP-hard on non-bipartite graph templates. We explore the situation of this generalised CSP on bipartite templates, giving various conditions for both tractability and hardness -- culminating in a classification theorem for general graphs. Finally, we use counting quantifiers to solve the complexity of a concrete QCSP whose complexity was previously open

Measurement of focusing properties for high numerical aperture optics using an automated submicron beamprofiler

The focusing properties of three aspheric lenses with numerical aperture (NA) between 0.53 and 0.68 were directly measured using an interferometrically referenced scanning knife-edge beam profiler with sub-micron resolution. The results obtained for two of the three lenses tested were in agreement with paraxial gaussian beam theory. It was also found that the highest NA aspheric lens which was designed for 830nm was not diffraction limited at 633nm. This process was automated using motorized translation stages and provides a direct method for testing the design specifications of high numerical aperture optics.Comment: 6 pages 4 figure

On the reduction of the CSP dichotomy conjecture to digraphs

It is well known that the constraint satisfaction problem over general relational structures can be reduced in polynomial time to digraphs. We present a simple variant of such a reduction and use it to show that the algebraic dichotomy conjecture is equivalent to its restriction to digraphs and that the polynomial reduction can be made in logspace. We also show that our reduction preserves the bounded width property, i.e., solvability by local consistency methods. We discuss further algorithmic properties that are preserved and related open problems.Comment: 34 pages. Article is to appear in CP2013. This version includes two appendices with proofs of claims omitted from the main articl

Interactions between the NR2B receptor and CaMKII modulate synaptic plasticity and spatial learning.

The NR2B subunit of the NMDA receptor interacts with several prominent proteins in the postsynaptic density, including calcium/calmodulin-dependent protein kinase II (CaMKII). To determine the function of these interactions, we derived transgenic mice expressing a ligand-activated carboxy-terminal NR2B fragment (cNR2B) by fusing this fragment to a tamoxifen (TAM)-dependent mutant of the estrogen receptor ligand-binding domain LBD(G521R). Here, we show that induction by TAM allows the transgenic cNR2B fragment to bind to endogenous CaMKII in neurons. Activation of the LBD(G521R)-cNR2B transgenic protein in mice leads to the disruption of CaMKII/NR2B interactions at synapses. The disruption decreases Thr286 phosphorylation of alphaCaMKII, lowers phosphorylation of a key CaMKII substrate in the postsynaptic membrane (AMPA receptor subunit glutamate receptor 1), and produces deficits in hippocampal long-term potentiation and spatial learning. Together our results demonstrate the importance of interactions between CaMKII and NR2B for CaMKII activity, synaptic plasticity, and learning

Cortical actin networks induce spatio-temporal confinement of phospholipids in the plasma membrane – a minimally invasive investigation by STED-FCS

Important discoveries in the last decades have changed our view of the plasma membrane organisation. Specifically, the cortical cytoskeleton has emerged as a key modulator of the lateral diffusion of membrane proteins. Cytoskeleton-dependent compartmentalised lipid diffusion has been proposed, but this concept remains controversial because this phenomenon has thus far only been observed with artefact-prone probes in combination with a single technique: single particle tracking. In this paper, we report the first direct observation of compartmentalised phospholipid diffusion in the plasma membrane of living cells using a minimally invasive, fluorescent dye labelled lipid analogue. These observations were made using optical STED nanoscopy in combination with fluorescence correlation spectroscopy (STED-FCS), a technique which allows the study of membrane dynamics on a sub-millisecond time-scale and with a spatial resolution of down to 40â €‰nm. Specifically, we find that compartmentalised phospholipid diffusion depends on the cortical actin cytoskeleton, and that this constrained diffusion is directly dependent on the F-Actin branching nucleator Arp2/3. These findings provide solid evidence that the Arp2/3-dependent cortical actin cytoskeleton plays a pivotal role in the dynamic organisation of the plasma membrane, potentially regulating fundamental cellular processes.</p

Exhaustive generation of kk-critical H\mathcal H-free graphs

We describe an algorithm for generating all $k$-critical $\mathcal H$-free graphs, based on a method of Ho\`{a}ng et al. Using this algorithm, we prove that there are only finitely many $4$-critical $(P_7,C_k)$-free graphs, for both $k=4$ and $k=5$. We also show that there are only finitely many $4$-critical graphs $(P_8,C_4)$-free graphs. For each case of these cases we also give the complete lists of critical graphs and vertex-critical graphs. These results generalize previous work by Hell and Huang, and yield certifying algorithms for the $3$-colorability problem in the respective classes. Moreover, we prove that for every $t$, the class of 4-critical planar $P_t$-free graphs is finite. We also determine all 27 4-critical planar $(P_7,C_6)$-free graphs. We also prove that every $P_{10}$-free graph of girth at least five is 3-colorable, and determine the smallest 4-chromatic $P_{12}$-free graph of girth five. Moreover, we show that every $P_{13}$-free graph of girth at least six and every $P_{16}$-free graph of girth at least seven is 3-colorable. This strengthens results of Golovach et al.Comment: 17 pages, improved girth results. arXiv admin note: text overlap with arXiv:1504.0697