Stable Vector Research Articles

Stable Higgs bundles over positive principal elliptic fibrations

Abstract Let M be a compact complex manifold of dimension at least three and Π : M → X a positive principal elliptic fibration, where X is a compact Kähler orbifold. Fix a preferred Hermitian metric on M. In [14], the third author proved that every stable vector bundle on M is of the form L⊕ Π ⃰ B0, where B0 is a stable vector bundle on X, and L is a holomorphic line bundle on M. Here we prove that every stable Higgs bundle on M is of the form (L ⊕ Π ⃰B0, Π ⃰ ɸX), where (B0, ɸX) is a stable Higgs bundle on X and L is a holomorphic line bundle on M.

Moduli space of parabolic vector bundles over hyperelliptic curves

Let X be a smooth projective hyperelliptic curve of arbitrary genus g. In this article, we will classify the rank 2 stable vector bundles with parabolic structure along a reduced divisor of degree 4.

A globally asymptotically stable polynomial vector field with rational coefficients and no local polynomial Lyapunov function

We give an explicit example of a two-dimensional polynomial vector field of degree seven that has rational coefficients, is globally asymptotically stable, but does not admit an analytic Lyapunov function even locally.

Monte Carlo Analysis of Forecast Error Variance Decompositions under Alternative Model Identification Schemes

The goal of the paper is to investigate the estimation precision of forecast error variance decomposition (FEVD) based on stable structural vector autoregressive models identified using short‑run and long‑run restrictions. The analysis is performed by means of Monte Carlo experiments. It is demonstrated that for processes with roots close to one, selected FEVD parameters can be esti­mated more accurately using recursive restrictions on the long‑run multipliers than under recursive restrictions on the impact effects of shocks. This finding contributes to the discussion of pros and cons of using alternative identification schemes by providing counterexamples for the notion that short‑run identifying restrictions lead to smaller estimation errors than long‑run restrictions.

Self-interacting dark matter with a stable vector mediator

Light vector mediators can naturally induce velocity-dependent dark matter self-interactions while at the same time allowing for the correct dark matter relic abundance via thermal freeze-out. If these mediators subsequently decay into Standard Model states such as electrons or photons however, this is robustly excluded by constraints from the Cosmic Microwave Background. We study to what extent this conclusion can be circumvented if the vector mediator is stable and hence contributes to the dark matter density while annihilating into lighter degrees of freedom. We find viable parts of parameter space which lead to the desired self-interaction cross section of dark matter to address the small-scale problems of the collisionless cold dark matter paradigm while being compatible with bounds from the Cosmic Microwave Background and Big Bang Nucleosynthesis observations.

On the stability of flat complex vector bundles over parallelizable manifolds

We investigate the flat holomorphic vector bundles over compact complex parallelizable manifolds G/Γ, where G is a complex connected Lie group and Γ is a cocompact lattice in it. The main result proved here is a structure theorem for flat holomorphic vector bundles Eρ associated with any irreducible representation ρ:Γ⟶GL(r,C). More precisely, we prove that Eρ is holomorphically isomorphic to a vector bundle of the form E⊕n, where E is a stable vector bundle. All the rational Chern classes of E vanish, in particular, its degree is zero.We deduce a stability result for flat holomorphic vector bundles Eρ of rank 2 over G/Γ. If an irreducible representation ρ:Γ⟶GL(2,C) satisfies the condition that the induced homomorphism Γ⟶PGL(2,C) does not extend to a homomorphism from G, then Eρ is proved to be stable.

Structural stability of planar quasi-homogeneous vector fields

In this work, we study the structural stability of planar quasi-homogeneous vector fields under quasi-homogeneous perturbations, and provide a complete classification. This study, which has been the subject of previous works, is only complete in the homogeneous case. The main tool in our analysis is a splitting of planar quasi-homogeneous vector fields into conservative–dissipative parts. Moreover, we describe the topological equivalence classes in the set of the structurally stable planar quasi-homogeneous vector fields. Finally, we include some examples where the equivalence classes are determined.

Establishment and characterization of McA-RH7777 cells using virus-mediated stable overexpression of enhanced green fluorescent protein.

Hepatocellular carcinoma (HCC), the most common primary tumor of the liver, has a poor prognosis, rapid progression. The aim of the current study was to establish a stable lentiviral expression vector for enhanced green fluorescent protein (EGFP) and to evaluate biological characteristics on HCC growth and migration following transfection of HCC cells with EGFP. McA-RH7777 cells were transfected with EGFP overexpression lentiviral vector. Cell activity and mobility were monitored with a Cell-IQ Analyzer. Transwell assays were performed to detect invasiveness and flow cytometry was performed for cell cycle analysis. A subcutaneous tumor rat model was established to analyze the stability of fluorescent protein expression. The result suggested no significant differences between wild-type and EGFP-overexpressing McA-RH7777 cells with regards to cell proliferation, activity, mobility, invasiveness and cell cycle. Green fluorescence was detected over 108 days of culturing. The subcutaneous tumor rat model demonstrated that EGFP expression had no influence on tumor growth and long-term expression was stable. The stable EGFP expression of the HCC transplanted tumor rat model may share biological characteristics with human liver cancer. The model established in the current study may be suitable for various applications, including research focusing on liver cancer metastasis and recurrence, interventional therapy, imaging diagnosis and drug screenings.

Sensitive and stable vector magnetometer for operation in zero and finite fields.

We report on an optically pumped magnetometer that uses multiple laser beams to pump and probe spin-polarized Cs atoms. The selected sensor geometry allows for operation in finite magnetic fields as well as close to zero field. In finite fields the magnetometer employs free spin precession signals to determine the field modulus and direction as described in a separate publication. This publication focuses on the magnetometer operation close to zero field, which is based on a ground state Hanle resonance. The four laser beams permit the simultaneous measurement of two orthogonal magnetic field components in a differential detection scheme that greatly suppresses technical laser power noise. Sensitivities better than 54 fT/Hz1/2 could be demonstrated simultaneously for both measurement channels in a well shielded environment. A minimum Allan deviation, limited by residual field fluctuations, of better than 40 fT was observed for integration times of 2s. The magnetometer achieves high sensitivity and stability in offset fields as well as close to zero field and is, thus, a universal tool for low frequency magnetic field measurements.

Brill–Noether loci of rank 2 vector bundles on a general $\nu $-gonal curve

In this paper we study the Brill Noether locus of rank 2, (semi)stable vector bundles with at least two sections and of suitable degrees on a general ν-gonal curve. We classify its irreducible components having at least expected dimension. We moreover describe the general member F of such components just in terms of extensions of line bundles with suitable minimality properties, providing information on the birational geometry of such components as well as on the very-ampleness of F.

Internal polarization dynamics of vector dissipative-soliton-resonance pulses in normal dispersion fiber lasers

Internal polarization dynamics of vector dissipative-soliton-resonance (DSR) pulses in a mode-locked fiber laser are investigated. By utilizing a wave plate analyzer configuration to analyze the special structure of a DSR pulse, we find that polarization state is not uniform across a resonant dissipative soliton. Specifically, although the central plane wave of the resonant dissipative soliton acquires nearly a single fixed polarization, the dissipative fronts feature polarization states that are different and spatially varying. This distinct polarization distribution is maintained while the whole soliton extends with increasing gain. Numerical simulation further confirms the experimental observations.

Conformal invariance of (0, 2) sigma models on Calabi-Yau manifolds

Long ago, Nemeschansky and Sen demonstrated that the Ricci-flat metric on a Calabi-Yau manifold could be corrected, order by order in perturbation theory, to produce a conformally invariant (2, 2) nonlinear sigma model. Here we extend this result to (0, 2) sigma models for stable holomorphic vector bundles over Calabi-Yaus.

Very stable bundles and properness of the Hitchin map

Let $X$ be a smooth complex projective curve of genus $g\geq 2$ and let $K$ be its canonical bundle. In this note we show that a stable vector bundle $E$ on $X$ is very stable, i.e. $E$ has no non-zero nilpotent Higgs field, if and only if the restriction of the Hitchin map to the vector space of Higgs fields $H^0(X, \mathrm{End}(E) \otimes K)$ is a proper map.

Characterization of modified mesoporous silica nanoparticles as vectors for siRNA delivery

Gene therapy using siRNA molecules is nowadays considered as a promising approach. For successful therapy, development of a stable and reliable vector for siRNA is crucial. Non-viral and non-organic vectors like mesoporous silica nanoparticles (MSN) are associated with lack of most viral vector drawbacks, such as toxicity, immunogenicity, but also generally a low nucleic acid carrying capacity. To overcome this hurdle, we here modified the pore walls of MSNs with surface-hyperbranching polymerized poly(ethyleneimine) (hbPEI), which provides an abundance of amino-groups for loading of a larger amount of siRNA molecules via electrostatic adsorption. After loading, the particles were covered with a second layer of pre-polymerized PEI to provide better protection of siRNA inside the pores, more effective cellular uptake and endosomal escape. To test the transfection efficiency of PEI covered siRNA/MSNs, MDA-MB 231 breast cancer cells stably expressing GFP were used. We demonstrate that PEI-coated siRNA/MSN complexes provide more effective delivery of siRNAs compared to unmodified MSNs. Thus, it can be concluded that appropriately surface-modified MSNs can be considered as prospective vectors for therapeutic siRNA delivery.

Brauer group of the moduli spaces of stable vector bundles of fixed determinant over a smooth curve

Let X be an irreducible smooth projective curve, defined over an algebraically closed field k, of genus at least three and L a line bundle on X. Let MX(r,L) be the moduli space of stable vector bundles on X of rank r and determinant L with r≥2. We prove that the Brauer group Br(MX(r,L)) is cyclic of order g.c.d.(r,degree(L)). We also prove that Br(MX(r,L)) is generated by the class of the projective bundle obtained by restricting the universal projective bundle. These results were proved earlier in [1] under the assumption that k=C.

Embedding of a compactified Jacobian and theta divisors

Using a general stable vector bundle, we give an embedding $$\alpha _Y$$ of the compactified Jacobian $$\bar{J}(Y)$$ of an integral nodal curve Y into the moduli space $$U_Y(r,d)$$ of semistable torsion free sheaves of rank r and degree d on Y. We also give an embedding of the normalisation $$\tilde{J}(Y)$$ of $$\bar{J}(Y)$$ in the normalisation P(r, d) of $$U_Y(r,d)$$ . We determine a relation between the restriction of the theta line bundle on P(r, d) to $$\tilde{J}(Y)$$ and the theta line bundle on $$\tilde{J}(Y)$$ . We show that the restriction of the Picard bundle $$E_{r,d}$$ on $$U_Y(r,d)$$ to $$\bar{J}(Y)$$ is stable with respect to any theta divisor $$\theta _{\bar{J}(Y)}$$ on $$\bar{J}(Y)$$ if $$d > r(2g-1)$$ and it is semistable if $$d= r(2g-1)$$ . Finally we prove some results on natural cohomology.

Fire and collapse: Untangling the formation of destruction layers using archaeomagnetism

AbstractHistorical events are sometimes expressed in destruction layers. We present here a study in which aspects of construction, destruction, and chronostratigraphy of fired mud bricks were explored using archaeomagnetism, infrared spectroscopy, and micromorphology. We measured 88 oriented samples mostly collected from one stratum, datedca. 1000 B.C.E., representing a destroyed late Canaanite (late Iron Age I) city in Tel Megiddo, Israel. Firing temperatures, evaluated from infrared spectroscopy, micromorphology, and high‐temperature magnetic susceptibility cycles, range between 300°C and 800°C. Samples studied in one archaeomagnetic site yield a single stable magnetization vector in demagnetization experiments. Archaeomagnetic site means of three standing walls are grouped near the expected direction of the ancient geomagnetic field. We propose that walls in the destruction layer were constructed from sun‐dried mud bricks that later burned during the destruction. Collapsed bricks and tilted walls show variable directions, diagnostic for the relative timing of collapse and cooling of bricks, during and following the destruction event. In addition, we attempt to assign stratigraphic affiliation based on archaeomagnetic considerations to standing walls, which are spatially disconnected from the studied destruction layer. Altogether, this study demonstrates the usefulness of archaeomagnetism to understanding site formation processes related to fire and destruction.

On modulated ergodic theorems

Let $T$ be a weakly almost periodic (WAP) linear operator on a Banach space $X$. A sequence of scalars $(a_n)_{n\ge 1}$ {\it modulates} $T$ on $Y \subset X$ if $\frac1n\sum_{k=1}^n a_kT^k x$ converges in norm for every $x \in Y$. We obtain a sufficient condition for $(a_n)$ to modulate every WAP operator on the space of its flight vectors, a necessary and sufficient condition for (weakly) modulating every WAP operator $T$ on the space of its (weakly) stable vectors, and sufficient conditions for modulating every contraction on a Hilbert space on the space of its weakly stable vectors. We study as an example modulation by the modified von Mangoldt function $\Lambda'(n):=\log n1_\mathbb P(n)$ (where $\mathbb P =(p_k)_{k\ge 1}$ is the sequence of primes), and show that, as in the scalar case, convergence of the corresponding modulated averages is equivalent to convergence of the averages along the primes $\frac1n\sum_{k=1}^n T^{p_k}x$. We then prove that for any contraction $T$ on a Hilbert space $H$ and $x \in H$, and also for every invertible $T$ with $\sup_{n \in \mathbb Z} \|T^n\| <\infty$ on $L^r(\Omega,\mu)$ ($1<r< \infty$) and $f \in L^r$, the averages along the primes converge.

Summarization of Scientific Paper Through Reinforcement Ranking on Semantic Link Network

The semantic link network is a semantics modeling method for effective information services. This paper proposes a new text summarization approach that extracts semantic link network from scientific paper consisting of language units of different granularities as nodes and semantic links between the nodes, and then ranks the nodes to select Top-k sentences to compose summary. A set of assumptions for reinforcing representative nodes is set to reflect the core of paper. Then, semantic link networks with different types of node and links are constructed with different combinations of the assumptions. Finally, an iterative ranking algorithm is designed for calculating the weight vectors of the nodes in a converged iteration process. The iteration approximately approaches a stable weight vector of sentence nodes, which is ranked to select Top-k high-rank nodes for composing summary. We designed six types of ranking models on semantic link networks for evaluation. Both objective assessment and intuitive assessment show that ranking semantic link network of language units can significantly help identify the representative sentences. This paper not only provides a new approach to summarizing text based on the extraction of semantic links from text but also verifies the effectiveness of adopting the semantic link network in rendering the core of text. The proposed approach can be applied to implementing other summarization applications such as generating an extended abstract, the mind map, and the bulletin points for making the slides of a given paper. It can be easily extended by incorporating more semantic links to improve text summarization and other information services.

Irreducibility of the moduli space of stable vector bundles of rank two and odd degree on a very general quintic surface

The moduli space $M(c_2)$, of stable rank two vector bundles of degree one on a very general quintic surface $X\subset {\mathbb P}^3$, is irreducible for all $c_2\geq 4$ and empty otherwise.