Evaluation of binomial double sums involving absolute values

We show that double sums of the form $$\sum_{i,j=-n} ^{n} |i^sj^t(i^k-j^k)^\beta| \binom {2n} {n+i} \binom {2n} {n+j}$$ can always be expressed in terms of a linear combination of just four functions, namely $\binom {4n}{2n}$, ${\binom {2n}n}^2$, $4^n\binom {2n}n$, and $16^n$, with coefficients that are rational in $n$. We provide two different proofs: one is algorithmic and uses the second author's computer algebra package Sigma; the second is based on complex contour integrals. In many instances, these results are extended to double sums of the above form where $\binom {2n}{n+j}$ is replaced by $\binom {2m}{m+j}$ with independent parameter $m$.Comment: AmS-LaTeX, 42 pages; substantial revision: several additional and more general results, see Proposition 11 and Theorems 15-1

Snapping Graph Drawings to the Grid Optimally

In geographic information systems and in the production of digital maps for small devices with restricted computational resources one often wants to round coordinates to a rougher grid. This removes unnecessary detail and reduces space consumption as well as computation time. This process is called snapping to the grid and has been investigated thoroughly from a computational-geometry perspective. In this paper we investigate the same problem for given drawings of planar graphs under the restriction that their combinatorial embedding must be kept and edges are drawn straight-line. We show that the problem is NP-hard for several objectives and provide an integer linear programming formulation. Given a plane graph G and a positive integer w, our ILP can also be used to draw G straight-line on a grid of width w and minimum height (if possible).Comment: Appears in the Proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD 2016

Spike propagation through the dorsal root ganglia in an unmyelinated sensory neuron: a modeling study

Unmyelinated C-fibers are a major type of sensory neurons conveying pain information. Action potential conduction is regulated by the bifurcation (T-junction) of sensory neuron axons within the dorsal root ganglia (DRG). Understanding how C-fiber signaling is influenced by the morphology of the T-junction and the local expression of ion channels is important for understanding pain signaling. In this study we used biophysical computer modeling to investigate the influence of axon morphology within the DRG and various membrane conductances on the reliability of spike propagation. As expected, calculated input impedance and the amplitude of propagating action potentials were both lowest at the T-junction. Propagation reliability for single spikes was highly sensitive to the diameter of the stem axon and the density of voltage-gated Na+ channels. A model containing only fast voltage-gated Na+ and delayed-rectifier K+ channels conducted trains of spikes up to frequencies of 110 Hz. The addition of slowly activating KCNQ channels (i.e., KV7 or M-channels) to the model reduced the following frequency to 30 Hz. Hyperpolarization produced by addition of a much slower conductance, such as a Ca²+-dependent K+ current, was needed to reduce the following frequency to 6 Hz. Attenuation of driving force due to ion accumulation or hyperpolarization produced by a Na+-K+ pump had no effect on following frequency but could influence the reliability of spike propagation mutually with the voltage shift generated by a Ca²+-dependent K+ current. These simulations suggest how specific ion channels within the DRG may contribute toward therapeutic treatments for chronic pain

Higgs Mass from D-Terms: a Litmus Test

We explore supersymmetric theories in which the Higgs mass is boosted by the non-decoupling D-terms of an extended $U(1)_X$ gauge symmetry, defined here to be a general linear combination of hypercharge, baryon number, and lepton number. Crucially, the gauge coupling, $g_X$, is bounded from below to accommodate the Higgs mass, while the quarks and leptons are required by gauge invariance to carry non-zero charge under $U(1)_X$. This induces an irreducible rate, $\sigma$BR, for $pp \rightarrow X \rightarrow \ell\ell$ relevant to existing and future resonance searches, and gives rise to higher dimension operators that are stringently constrained by precision electroweak measurements. Combined, these bounds define a maximally allowed region in the space of observables, ($\sigma$BR, $m_X$), outside of which is excluded by naturalness and experimental limits. If natural supersymmetry utilizes non-decoupling D-terms, then the associated $X$ boson can only be observed within this window, providing a model independent `litmus test' for this broad class of scenarios at the LHC. Comparing limits, we find that current LHC results only exclude regions in parameter space which were already disfavored by precision electroweak data.Comment: 7 pages, 9 figure

Ultrasmall radio frequency driven microhollow cathode discharge

We have operated 25-100 mu m diameter radio frequency microhollow cathode discharges stably, for many hours, in neon and in argon. Electrical and spectroscopic measurements were used to explore three possible electron heating modes and obtain detail regarding the electron energy distribution. Analysis points to the possibility of pendular electron heating at low voltages. (c) 2008 American Institute of Physics

Limits of minimal models and continuous orbifolds

The lambda=0 't Hooft limit of the 2d W_N minimal models is shown to be equivalent to the singlet sector of a free boson theory, thus paralleling exactly the structure of the free theory in the Klebanov-Polyakov proposal. In 2d, the singlet sector does not describe a consistent theory by itself since the corresponding partition function is not modular invariant. However, it can be interpreted as the untwisted sector of a continuous orbifold, and this point of view suggests that it can be made consistent by adding in the appropriate twisted sectors. We show that these twisted sectors account for the `light states' that were not included in the original 't Hooft limit. We also show that, for the Virasoro minimal models (N=2), the twisted sector of our orbifold agrees precisely with the limit theory of Runkel & Watts. In particular, this implies that our construction satisfies crossing symmetry.Comment: 33 pages; v2: minor improvements and references added, published versio

Evolution of oesophageal adenocarcinoma from metaplastic columnar epithelium without goblet cells in Barrett's oesophagus

Supported by the Dutch Cancer Society (KWF) and Cancer Research UK (CR-UK). This work was supported by Cancer Research UK (grant number A14895

Identification and validation of oncologic miRNA biomarkers for Luminal A-like breast cancer

Introduction: Breast cancer is a common disease with distinct tumor subtypes phenotypically characterized by ER and HER2/neu receptor status. MiRNAs play regulatory roles in tumor initiation and progression, and altered miRNA expression has been demonstrated in a variety of cancer states presenting the potential for exploitation as cancer biomarkers. Blood provides an excellent medium for biomarker discovery. This study investigated systemic miRNAs differentially expressed in Luminal A-like (ER+PR+HER2/neu-) breast cancer and their effectiveness as oncologic biomarkers in the clinical setting. Methods: Blood samples were prospectively collected from patients with Luminal A-like breast cancer (n=54) and controls (n=56). RNA was extracted, reverse transcribed and subjected to microarray analysis (n=10 Luminal A-like; n=10 Control). Differentially expressed miRNAs were identified by artificial neural network (ANN) data-mining algorithms. Expression of specific miRNAs was validated by RQ-PCR (n=44 Luminal A; n=46 Control) and potential relationships between circulating miRNA levels and clinicopathological features of breast cancer were investigated. Results: Microarray analysis identified 76 differentially expressed miRNAs. ANN revealed 10 miRNAs for further analysis ( miR-19b, miR-29a, miR-93, miR-181a, miR-182, miR-223, miR-301a, miR-423-5p, miR-486-5 and miR-652 ). The biomarker potential of 4 miRNAs ( miR-29a, miR-181a , miR-223 and miR-652 ) was confirmed by RQ-PCR, with significantly reduced expression in blood of women with Luminal A-like breast tumors compared to healthy controls (p=0.001, 0.004, 0.009 and 0.004 respectively). Binary logistic regression confirmed that combination of 3 of these miRNAs ( miR-29a, miR-181a and miR-652 ) could reliably differentiate between cancers and controls with an AUC of 0.80. Conclusion: This study provides insight into the underlying molecular portrait of Luminal A-like breast cancer subtype. From an initial 76 miRNAs, 4 were validated with altered expression in the blood of women with Luminal A-like breast cancer. The expression profiles of these 3 miRNAs, in combination with mammography, has potential to facilitate accurate subtype- specific breast tumor detection

The generalised NMSSM at one loop: fine tuning and phenomenology

We determine the degree of fine tuning needed in a generalised version of the NMSSM that follows from an underlying Z4 or Z8 R symmetry. We find that it is significantly less than is found in the MSSM or NMSSM and extends the range of Higgs mass that have acceptable fine tuning up to Higgs masses of mh ~ 130 GeV. For universal boundary conditions analogous to the CMSSM the phenomenology is rather MSSM like with the singlet states typically rather heavy. For more general boundary conditions the singlet states can be light, leading to interesting signatures at the LHC and direct detection experiments.Comment: 20 pages, 9 figures, matches published versio