Q2Q_2-free families in the Boolean lattice

For a family $\mathcal{F}$ of subsets of [n]=\{1, 2, ..., n} ordered by inclusion, and a partially ordered set P, we say that $\mathcal{F}$ is P-free if it does not contain a subposet isomorphic to P. Let $ex(n, P)$ be the largest size of a P-free family of subsets of [n]. Let $Q_2$ be the poset with distinct elements a, b, c, d, a<b, c<d; i.e., the 2-dimensional Boolean lattice. We show that $2N -o(N) \leq ex(n, Q_2)\leq 2.283261N +o(N),$ where $N = \binom{n}{\lfloor n/2 \rfloor}$. We also prove that the largest $Q_2$-free family of subsets of [n] having at most three different sizes has at most 2.20711N members.Comment: 18 pages, 2 figure

GALNT2 as a novel modulator of adipogenesis and adipocyte insulin signaling

Background/objectives: A better understanding of adipose tissue biology is crucial to tackle insulin resistance and eventually coronary heart disease and diabetes, leading causes of morbidity and mortality worldwide. GALNT2, a GalNAc-transferase, positively modulates insulin signaling in human liver cells by down-regulating ENPP1, an insulin signaling inhibitor. GALNT2 expression is increased in adipose tissue of obese as compared to that of non-obese individuals. Whether this association is secondary to a GALNT2-insulin sensitizing effect exerted also in adipocytes is unknown. We then investigated in mouse 3T3-L1 adipocytes the GALNT2 effect on adipogenesis, insulin signaling and expression levels of both Enpp1 and 72 adipogenesis-related genes. Methods: Stable over-expressing GALNT2 and GFP preadipocytes (T 0 ) were generated. Adipogenesis was induced with (R+) or without (R−) rosiglitazone and investigated after 15 days (T 15 ). Lipid accumulation (by Oil Red-O staining) and intracellular triglycerides (by fluorimetric assay) were measured. Lipid droplets (LD) measures were analyzed at confocal microscope. Gene expression was assessed by RT-PCR and insulin-induced insulin receptor (IR), IRS1, JNK and AKT phosphorylation by Western blot. Results: Lipid accumulation, triglycerides and LD measures progressively increased from T 0 to T 15 R- and furthermore to T 15 R+. Such increases were significantly higher in GALNT2 than in GFP cells so that, as compared to T 15 R+GFP, T 15 R- GALNT2 cells showed similar (intracellular lipid and triglycerides accumulation) or even higher (LD measures, p &lt; 0.01) values. In GALNT2 preadipocytes, insulin-induced IR, IRS1 and AKT activation was higher than that in GFP cells. GALNT2 effect was totally abolished during adipocyte maturation and completely reversed at late stage maturation. Such GALNT2 effect trajectory was paralleled by coordinated changes in the expression of Enpp1 and adipocyte-maturation key genes. Conclusions: GALNT2 is a novel modulator of adipogenesis and related cellular phenotypes, thus becoming a potential target for tackling the obesity epidemics and its devastating sequelae

A NUMERICAL METHOD FOR SOLVING SYSTEMS OF HYPERSINGULAR INTEGRO-DIFFERENTIAL EQUATIONS

This paper is concerned with a collocation-quadrature method for solving systems of Prandtl's integro-differential equations based on de la Vallee Poussin filtered interpolation at Chebyshev nodes. We prove stability and convergence in Holder-Zygmund spaces of locally continuous functions. Some numerical tests are presented to examine the method's efficacy

Determinants of health sector efficiency: evidence from a two-step analysis on 30 OECD countries

This study aims to assess the efficiency of expenditure on health in 30 OECD countries over the period 2005-2015 by regressing Data Envelopment Analysis (DEA) output efficiency scores on discretionary and non-discretionary variables, with a two-stage DEA/Tobit and bootstrap procedure. We show that health inefficiency in OECD countries is related to per capita GDP, vaccine coverage and tobacco consumption, also controlling for geographical and institutional variables (i.e., bureaucratic red tape and weather temperature)

Ultrasensitive Displacement Noise Measurement of Carbon Nanotube Mechanical Resonators

Mechanical resonators based on a single carbon nanotube are exceptional sensors of mass and force. The force sensitivity in these ultra-light resonators is often limited by the noise in the detection of the vibrations. Here, we report on an ultra-sensitive scheme based on a RLC resonator and a low-temperature amplifier to detect nanotube vibrations. We also show a new fabrication process of electromechanical nanotube resonators to reduce the separation between the suspended nanotube and the gate electrode down to $\sim 150$~nm. These advances in detection and fabrication allow us to reach $0.5~\mathrm{pm}/\sqrt{\mathrm{Hz}}$ displacement sensitivity. Thermal vibrations cooled cryogenically at 300~mK are detected with a signal-to-noise ratio as high as 17~dB. We demonstrate $4.3~\mathrm{zN}/\sqrt{\mathrm{Hz}}$ force sensitivity, which is the best force sensitivity achieved thus far with a mechanical resonator. Our work is an important step towards imaging individual nuclear spins and studying the coupling between mechanical vibrations and electrons in different quantum electron transport regimes.Comment: 9 pages, 5 figure

Neurosurgical implications of the Jugular Vein Nutcracker

In the last ten years, a new variant of Eagle Syndrome is emerging and being described: Styloid Jugular Nutcracker (SJN). In SJN, an elongated or vertically directed styloid process causes jugular vein stenosis by compressing the vein against the arch of C1. The clinical consequences appear to be various and misunderstood, ascribable mainly to venous flow impairment and consequent intracranial hypertension. The aim of this paper is to create an overview of Jugular Vein Nutcracker and to focus on its neurosurgical implications. A PRISMA-based literature search was performed to select the most relevant papers on the topic and to realize a mini-review. Future searches in the neurosurgical field should focus on collecting data about further causes of jugular stenosis compression and the association of SJN with cerebrovascular diseases. It would also be interesting to investigate the potential role of primary and secondary prevention, which is unknown so far

Semiotic Virtual Reality Framework Validation

This paper presents a user study designed for validating the Semiotic VR Framework, a tool that allows to identify the best-suited Virtual Reality (VR) applications to get a specified communication objective, by adopting the appropriate techniques to implement visualization, interaction and modelling of the VR application

Superselectors: Efficient Constructions and Applications

We introduce a new combinatorial structure: the superselector. We show that superselectors subsume several important combinatorial structures used in the past few years to solve problems in group testing, compressed sensing, multi-channel conflict resolution and data security. We prove close upper and lower bounds on the size of superselectors and we provide efficient algorithms for their constructions. Albeit our bounds are very general, when they are instantiated on the combinatorial structures that are particular cases of superselectors (e.g., (p,k,n)-selectors, (d,\ell)-list-disjunct matrices, MUT_k(r)-families, FUT(k, a)-families, etc.) they match the best known bounds in terms of size of the structures (the relevant parameter in the applications). For appropriate values of parameters, our results also provide the first efficient deterministic algorithms for the construction of such structures

Noise-Resilient Group Testing: Limitations and Constructions

We study combinatorial group testing schemes for learning $d$-sparse Boolean vectors using highly unreliable disjunctive measurements. We consider an adversarial noise model that only limits the number of false observations, and show that any noise-resilient scheme in this model can only approximately reconstruct the sparse vector. On the positive side, we take this barrier to our advantage and show that approximate reconstruction (within a satisfactory degree of approximation) allows us to break the information theoretic lower bound of $\tilde{\Omega}(d^2 \log n)$ that is known for exact reconstruction of $d$-sparse vectors of length $n$ via non-adaptive measurements, by a multiplicative factor $\tilde{\Omega}(d)$. Specifically, we give simple randomized constructions of non-adaptive measurement schemes, with $m=O(d \log n)$ measurements, that allow efficient reconstruction of $d$-sparse vectors up to $O(d)$ false positives even in the presence of $\delta m$ false positives and $O(m/d)$ false negatives within the measurement outcomes, for any constant $\delta < 1$. We show that, information theoretically, none of these parameters can be substantially improved without dramatically affecting the others. Furthermore, we obtain several explicit constructions, in particular one matching the randomized trade-off but using $m = O(d^{1+o(1)} \log n)$ measurements. We also obtain explicit constructions that allow fast reconstruction in time \poly(m), which would be sublinear in $n$ for sufficiently sparse vectors. The main tool used in our construction is the list-decoding view of randomness condensers and extractors.Comment: Full version. A preliminary summary of this work appears (under the same title) in proceedings of the 17th International Symposium on Fundamentals of Computation Theory (FCT 2009