A Comparison between the Zero Forcing Number and the Strong Metric Dimension of Graphs

The \emph{zero forcing number}, $Z(G)$, of a graph $G$ is the minimum cardinality of a set $S$ of black vertices (whereas vertices in $V(G)-S$ are colored white) such that $V(G)$ is turned black after finitely many applications of "the color-change rule": a white vertex is converted black if it is the only white neighbor of a black vertex. The \emph{strong metric dimension}, $sdim(G)$, of a graph $G$ is the minimum among cardinalities of all strong resolving sets: $W \subseteq V(G)$ is a \emph{strong resolving set} of $G$ if for any $u, v \in V(G)$, there exists an $x \in W$ such that either $u$ lies on an $x-v$ geodesic or $v$ lies on an $x-u$ geodesic. In this paper, we prove that $Z(G) \le sdim(G)+3r(G)$ for a connected graph $G$, where $r(G)$ is the cycle rank of $G$. Further, we prove the sharp bound $Z(G) \leq sdim(G)$ when $G$ is a tree or a unicyclic graph, and we characterize trees $T$ attaining $Z(T)=sdim(T)$. It is easy to see that $sdim(T+e)-sdim(T)$ can be arbitrarily large for a tree $T$; we prove that $sdim(T+e) \ge sdim(T)-2$ and show that the bound is sharp.Comment: 8 pages, 5 figure

The Maximal U(1)LU(1)_L Inverse Seesaw from d=5d=5 Operator and Oscillating Asymmetric Sneutrino Dark Matter

The maximal $U(1)_L$ supersymmetric inverse seesaw mechanism (M$L$SIS) provides a natural way to relate asymmetric dark matter (ADM) with neutrino physics. In this paper we point out that, M$L$SIS is a natural outcome if one dynamically realizes the inverse seesaw mechanism in the next-to minimal supersymmetric standard model (NMSSM) via the dimension-five operator $(N)^2S^2/M_*$, with $S$ the NMSSM singlet developing TeV scale VEV; it slightly violates lepton number due to the suppression by the fundamental scale $M_*$, thus preserving $U(1)_L$ maximally. The resulting sneutrino is a distinguishable ADM candidate, oscillating and favored to have weak scale mass. A fairly large annihilating cross section of such a heavy ADM is available due to the presence of singlet.Comment: journal versio

Deformation and stress of a composite-metal assembly

Compliant structures, e.g. automobile body panel and airplane wing box are widely used. A compliant structure consists of one or more flexible parts, and these parts share the mating features among them. Because of process-induced deformation and part-to-part variations, external forces are applied during the assembly process and the parts are deformed. As a result, the final assembly is pre-stressed and its geometrical shape may deviate from the designed shape. Therefore, the assembly variation and residual stress need to be analysed in order to evaluate the structure performance. In this study, a new approach based on response surface methodology is developed. A number of organised virtual experiments are conducted with the aid of finite element analysis and regression models are fitted to the resulting data. These regression models relate part variations to assembly variation and residual stress. Monte Carlo simulation can be conveniently done using these simple regression models. The effectiveness of this method was illustrated using a composite–metal assembly. It is shown that the method presented in this paper provides a practical and reliable solution to the analysis of compliant structures

A literature review on surgery for cervical vagal schwannomas

Cervical vagal schwannoma is a benign, slow-growing mass, often asymptomatic, with a very low lifetime risk of malignant transformation in general population, but diagnosis is still a challenge. Surgical resection is the treatment of choice even if its close relationship with nerve fibres, from which it arises, threats vagal nerve preservation. We present a case report and a systematic review of literature. All studies on surgical resection of cervical vagal schwannoma have been reviewed. Papers matching the inclusion criteria (topic on surgical removal of cervical vagal schwannoma, English language, full text available) were selected. Fifty-three patients with vagal neck schwannoma submitted to surgery were identified among 22 studies selected. Female/male ratio was 1.5 and median age 44 years. Median diameter was 5 cm (range 2 to 10). Most schwannoma were asymptomatic (68.2%) and received an intracapsular excision (64.9%). Postoperative symptoms were reported in 22.6% of patients. Cervical vagal schwannoma is a benign pathology requiring surgical excision, but frequently postoperative complications can affect patients lifelong, so, surgical indications should be based carefully on the balance between risks and benefits

On Arrangements of Orthogonal Circles

In this paper, we study arrangements of orthogonal circles, that is, arrangements of circles where every pair of circles must either be disjoint or intersect at a right angle. Using geometric arguments, we show that such arrangements have only a linear number of faces. This implies that orthogonal circle intersection graphs have only a linear number of edges. When we restrict ourselves to orthogonal unit circles, the resulting class of intersection graphs is a subclass of penny graphs (that is, contact graphs of unit circles). We show that, similarly to penny graphs, it is NP-hard to recognize orthogonal unit circle intersection graphs.Comment: Appears in the Proceedings of the 27th International Symposium on Graph Drawing and Network Visualization (GD 2019

Asymmetric Origin for Gravitino Relic Density in the Hybrid Gravity-Gauge Mediated Supersymmetry Breaking

We propose the hybrid gravity-gauge mediated supersymmetry breaking where the gravitino mass is about several GeV. The strong constraints on supersymmetry viable parameter space from the CMS and ATLAS experiments at the LHC can be relaxed due to the heavy colored supersymmetric particles, and it is consistent with null results in the dark matter (DM) direct search experiments such as XENON100. In particular, the possible maximal flavor and CP violations from the relatively small gravity mediation may naturally account for the recent LHCb anomaly. In addition, because the gravitino mass is around the asymmetric DM mass, we propose the asymmetric origin of the gravitino relic density and solve the cosmological coincident problem on the DM and baryon densities \Omega_{\rm DM}:\Omega_{B}\approx 5:1. The gravitino relic density arises from asymmetric metastable particle (AMP) late decay. However, we show that there is no AMP candidate in the minimal supersymmetric Standard Model (SM) due to the robust gaugino/Higgsino mediated wash-out effects. Interestingly, AMP can be realized in the well motivated supersymmetric SMs with vector-like particles or continuous U(1)_R symmetry. Especially, the lightest CP-even Higgs boson mass can be lifted in the supersymmetric SMs with vector-like particles.Comment: RevTex4, 21 pages, 1 figure, minor corrections, JHEP versio

Extraction of bodily features for gait recognition and gait attractiveness evaluation

This is the author's accepted manuscript. The final publication is available at Springer via http://dx.doi.org/10.1007/s11042-012-1319-2. Copyright @ 2012 Springer.Although there has been much previous research on which bodily features are most important in gait analysis, the questions of which features should be extracted from gait, and why these features in particular should be extracted, have not been convincingly answered. The primary goal of the study reported here was to take an analytical approach to answering these questions, in the context of identifying the features that are most important for gait recognition and gait attractiveness evaluation. Using precise 3D gait motion data obtained from motion capture, we analyzed the relative motions from different body segments to a root marker (located on the lower back) of 30 males by the fixed root method, and compared them with the original motions without fixing root. Some particular features were obtained by principal component analysis (PCA). The left lower arm, lower legs and hips were identified as important features for gait recognition. For gait attractiveness evaluation, the lower legs were recognized as important features.Dorothy Hodgkin Postgraduate Award and HEFCE

Identification of the protein kinases Pyk3 and Phg2 as regulators of the STATc-mediated response to hyperosmolarity

Cellular adaptation to changes in environmental osmolarity is crucial for cell survival. In Dictyostelium, STATc is a key regulator of the transcriptional response to hyperosmotic stress. Its phosphorylation and consequent activation is controlled by two signaling branches, one cGMP- and the other Ca(2+)-dependent, of which many signaling components have yet to be identified. The STATc stress signalling pathway feeds back on itself by upregulating the expression of STATc and STATc-regulated genes. Based on microarray studies we chose two tyrosine-kinase like proteins, Pyk3 and Phg2, as possible modulators of STATc phosphorylation and generated single and double knock-out mutants to them. Transcriptional regulation of STATc and STATc dependent genes was disturbed in pyk3(-), phg2(-), and pyk3(-)/phg2(-) cells. The absence of Pyk3 and/or Phg2 resulted in diminished or completely abolished increased transcription of STATc dependent genes in response to sorbitol, 8-Br-cGMP and the Ca(2+) liberator BHQ. Also, phospho-STATc levels were significantly reduced in pyk3(-) and phg2(-) cells and even further decreased in pyk3(-)/phg2(-) cells. The reduced phosphorylation was mirrored by a significant delay in nuclear translocation of GFP-STATc. The protein tyrosine phosphatase 3 (PTP3), which dephosphorylates and inhibits STATc, is inhibited by stress-induced phosphorylation on S448 and S747. Use of phosphoserine specific antibodies showed that Phg2 but not Pyk3 is involved in the phosphorylation of PTP3 on S747. In pull-down assays Phg2 and PTP3 interact directly, suggesting that Phg2 phosphorylates PTP3 on S747 in vivo. Phosphorylation of S448 was unchanged in phg2(-) cells. We show that Phg2 and an, as yet unknown, S448 protein kinase are responsible for PTP3 phosphorylation and hence its inhibition, and that Pyk3 is involved in the regulation of STATc by either directly or indirectly activating it. Our results add further complexities to the regulation of STATc, which presumably ensure its optimal activation in response to different environmental cues

Comparing stochastic differential equations and agent-based modelling and simulation for early-stage cancer

There is great potential to be explored regarding the use of agent-based modelling and simulation as an alternative paradigm to investigate early-stage cancer interactions with the immune system. It does not suffer from some limitations of ordinary differential equation models, such as the lack of stochasticity, representation of individual behaviours rather than aggregates and individual memory. In this paper we investigate the potential contribution of agent-based modelling and simulation when contrasted with stochastic versions of ODE models using early-stage cancer examples. We seek answers to the following questions: (1) Does this new stochastic formulation produce similar results to the agent-based version? (2) Can these methods be used interchangeably? (3) Do agent-based models outcomes reveal any benefit when compared to the Gillespie results? To answer these research questions we investigate three well-established mathematical models describing interactions between tumour cells and immune elements. These case studies were re-conceptualised under an agent-based perspective and also converted to the Gillespie algorithm formulation. Our interest in this work, therefore, is to establish a methodological discussion regarding the usability of different simulation approaches, rather than provide further biological insights into the investigated case studies. Our results show that it is possible to obtain equivalent models that implement the same mechanisms; however, the incapacity of the Gillespie algorithm to retain individual memory of past events affects the similarity of some results. Furthermore, the emergent behaviour of ABMS produces extra patters of behaviour in the system, which was not obtained by the Gillespie algorithm