The Stable Roommates problem with short lists

We consider two variants of the classical Stable Roommates problem with Incomplete (but strictly ordered) preference lists SRI that are degree constrained, i.e., preference lists are of bounded length. The first variant, EGAL d-SRI, involves finding an egalitarian stable matching in solvable instances of SRI with preference lists of length at most d. We show that this problem is NP-hard even if d=3. On the positive side we give a (2d+3)/7-approximation algorithm for d={3,4,5} which improves on the known bound of 2 for the unbounded preference list case. In the second variant of SRI, called d-SRTI, preference lists can include ties and are of length at most d. We show that the problem of deciding whether an instance of d-SRTI admits a stable matching is NP-complete even if d=3. We also consider the "most stable" version of this problem and prove a strong inapproximability bound for the d=3 case. However for d=2 we show that the latter problem can be solved in polynomial time.Comment: short version appeared at SAGT 201

Magnetic Properties of a Superconductor with no Inversion Symmetry

We study the magnetic properties of a superconductor in a crystal without $z \to -z$ symmetry, in particular how the lack of this symmetry exhibits itself. We show that, though the penetration depth itself shows no such effect, for suitable orientation of magnetic field, there is a magnetic field discontinuity at the interface which shows this absence of symmetry. The magnetic field profile of a vortex in the $x-y$ plane is shown to be identical to that of an ordinary anisotropic superconductor except for a shift in the $-z$ direction by ${\tilde \kappa} \lambda_x$ (see errata). For a vortex along $z$, there is an induced magnetization along the radial direction.Comment: J. Low Temp. Physics, 140, 67 (2005); with Errat

Infrared fixed point in quantum Einstein gravity

We performed the renormalization group analysis of the quantum Einstein gravity in the deep infrared regime for different types of extensions of the model. It is shown that an attractive infrared point exists in the broken symmetric phase of the model. It is also shown that due to the Gaussian fixed point the IR critical exponent $\nu$ of the correlation length is 1/2. However, there exists a certain extension of the model which gives finite correlation length in the broken symmetric phase. It typically appears in case of models possessing a first order phase transitions as is demonstrated on the example of the scalar field theory with a Coleman-Weinberg potential.Comment: 9 pages, 7 figures, final version, to appear in JHE

Non-Melanoma Skin Cancer: news from microbiota research

Recently, research has been deeply focusing on the role of the microbiota in numerous diseases, either affecting the skin or other organs. What it is well established is that its dysregulation promotes several cutaneous disorders (i.e. psoriasis and atopic dermatitis). To date, little is known about its composition, mediators and role in the genesis, progression and response to therapy of Non-Melanoma Skin Cancer (NMSC). Starting from a bibliographic study, we classified the selected articles into four sections: i) normal skin microbiota; ii) in vitro study models; iii) microbiota and NMSC and iv) probiotics, antibiotics and NMSC. What has emerged is how skin microflora changes, mainly represented by increases of Staphylococcus aureus, Streptococcus pyogenes and Pseudomonas aeruginosa strains, modifications in the mutual quantity of \u3b2-Human papillomavirus genotypes, of Epstein Barr Virus and Malassezia or candidiasis, may contribute to the induction of a state of chronic self-maintaining inflammation, leading to cancer. In this context, the role of S. aureus and that of specific antimicrobial peptides look to be prominent. Moreover, although antibiotics may contribute to carcinogenesis, due to their ability to influence the microbiota balance, specific probiotics, such as Lacticaseibacillus rhamnosus GG, Lactobacillus johnsonii NCC 533 and Bifidobacteria spp., may be protective

A Variant in a MicroRNA complementary site in the 3' UTR of the KIT oncogene increases risk of acral melanoma.

MicroRNAs (miRNAs) are small ∼22nt single stranded RNAs that negatively regulate protein expression by binding to partially complementary sequences in the 3' untranslated region (3' UTRs) of target gene messenger RNAs (mRNA). Recently, mutations have been identified in both miRNAs and target genes that disrupt regulatory relationships, contribute to oncogenesis and serve as biomarkers for cancer risk. KIT, an established oncogene with a multifaceted role in melanogenesis and melanoma pathogenesis, has recently been shown to be upregulated in some melanomas, and is also a target of the miRNA miR-221. Here, we describe a genetic variant in the 3' UTR of the KIT oncogene that correlates with a greater than fourfold increased risk of acral melanoma. This KIT variant results in a mismatch in the seed region of a miR-221 complementary site and reporter data suggests that this mismatch can result in increased expression of the KIT oncogene. Consistent with the hypothesis that this is a functional variant, KIT mRNA and protein levels are both increased in the majority of samples harboring the KIT variant. This work identifies a novel genetic marker for increased heritable risk of melanoma

Realization of GHZ States and the GHZ Test via Cavity QED

In this article we discuss the realization of atomic GHZ states involving three-level atoms and we show explicitly how to use this state to perform the GHZ test in which it is possible to decide between local realism theories and quantum mechanics. The experimental realizations proposed makes use of the interaction of Rydberg atoms with a cavity prepared in a coherent state.Comment: 16 pages and 3 figures. submitted to J. Mod. Op

Moment-based parameter estimation in binomial random intersection graph models

Binomial random intersection graphs can be used as parsimonious statistical models of large and sparse networks, with one parameter for the average degree and another for transitivity, the tendency of neighbours of a node to be connected. This paper discusses the estimation of these parameters from a single observed instance of the graph, using moment estimators based on observed degrees and frequencies of 2-stars and triangles. The observed data set is assumed to be a subgraph induced by a set of $n_0$ nodes sampled from the full set of $n$ nodes. We prove the consistency of the proposed estimators by showing that the relative estimation error is small with high probability for $n_0 \gg n^{2/3} \gg 1$. As a byproduct, our analysis confirms that the empirical transitivity coefficient of the graph is with high probability close to the theoretical clustering coefficient of the model.Comment: 15 pages, 6 figure

Sequential Deliberation for Social Choice

In large scale collective decision making, social choice is a normative study of how one ought to design a protocol for reaching consensus. However, in instances where the underlying decision space is too large or complex for ordinal voting, standard voting methods of social choice may be impractical. How then can we design a mechanism - preferably decentralized, simple, scalable, and not requiring any special knowledge of the decision space - to reach consensus? We propose sequential deliberation as a natural solution to this problem. In this iterative method, successive pairs of agents bargain over the decision space using the previous decision as a disagreement alternative. We describe the general method and analyze the quality of its outcome when the space of preferences define a median graph. We show that sequential deliberation finds a 1.208- approximation to the optimal social cost on such graphs, coming very close to this value with only a small constant number of agents sampled from the population. We also show lower bounds on simpler classes of mechanisms to justify our design choices. We further show that sequential deliberation is ex-post Pareto efficient and has truthful reporting as an equilibrium of the induced extensive form game. We finally show that for general metric spaces, the second moment of of the distribution of social cost of the outcomes produced by sequential deliberation is also bounded

Charge 4e4e superconductivity from pair density wave order in certain high temperature superconductors

A number of spectacular experimental anomalies\cite{li-2007,fujita-2005} have recently been discovered in certain cuprates, notably {\LBCO} and {\LNSCO}, which exhibit unidirectional spin and charge order (known as ``stripe order''). We have recently proposed to interpret these observations as evidence for a novel ``striped superconducting'' state, in which the superconducting order parameter is modulated in space, such that its average is precisely zero. Here, we show that thermal melting of the striped superconducting state can lead to a number of unusual phases, of which the most novel is a charge $4e$ superconducting state, with a corresponding fractional flux quantum $hc/4e$. These are never-before observed states of matter, and ones, moreover, that cannot arise from the conventional Bardeen-Cooper-Schrieffer (BCS) mechanism. Thus, direct confirmation of their existence, even in a small subset of the cuprates, could have much broader implications for our understanding of high temperature superconductivity. We propose experiments to observe fractional flux quantization, which thereby could confirm the existence of these states.Comment: 5 pages, 2 figures; new version in Nature Physics format with a discussion of the effective Josephson coupling J2 and minor changes. Mildly edited abstract. v3: corrected versio

Renormalization of QCD_2

The low energy infrared scaling of the multi-color 2-dimensional quantum chromodynamics is determined in the framework of its bosonized model by using the functional renormalization group method with gliding sharp cut-off k in momentum space in the local potential approximation. The model exhibits a single phase with a superuniversal effective potential.Comment: 15 pages, 3 figures, final versio