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Weiyi Zhang

Publications and source records attributed to Weiyi Zhang.

At least 55 records · Page 3Linked to original sources

$J$-holomorphic curves from closed $J$-anti-invariant forms

We study the relation between $J$-anti-invariant $2$-forms and pseudoholomorphic curves in this paper. We show the zero set of a closed $J$-anti-invariant $2$-form on an almost complex $4$-manifold supports a $J$-holomorphic subvariety in the canonical class. This confirms a conjecture of Draghici-Li-Zhang. A higher dimensional analogue is established. We also show the dimension of closed $J$-anti-invariant $2$-forms on an almost complex $4$-manifold is a birational invariant, in the sense that it is invariant under degree one pseudoholomorphic maps.

math.DG↗

Kodaira dimensions of almost complex manifolds I

This is the first of a series of papers, in which we study the plurigenera, the Kodaira dimension and more generally the Iitaka dimension on compact almost complex manifolds. Based on the Hodge theory on almost complex manifolds, we introduce the plurigenera, Kodaira dimension and Iitaka dimension on compact almost complex manifolds. We show that the plurigenera and the Kodaira dimension as well as the irregularity are birational invariants in almost complex category, at least in dimension $4$, where a birational morphism is defined to be a degree one pseudoholomorphic map. However, they are no longer deformation invariants, even in dimension $4$ or under tameness assumption. On the way to establish the birational invariance, we prove the Hartogs extension theorem in the almost complex setting by the foliation-by-disks technique. Some interesting phenomena of these invariants are shown through examples. In particular, we construct non-integrable compact almost complex manifolds with large Kodaira dimensions. Hodge numbers and plurigenera are computed for the standard almost complex structure on the six sphere $S^6$, which are different from the data of a hypothetical complex structure.

math.DG↗

Kodaira dimensions of almost complex manifolds II

This is the second of a series of papers where we study the plurigenera, the Kodaira dimension and the Iitaka dimension on compact almost complex manifolds. By using the pseudoholomorphic pluricanonical map, we define the second version of Kodaira dimension as well as Iitaka dimension on compact almost complex manifolds. We show the almost complex structures with the top Kodaira dimension are integrable. For compact almost complex 4-manifolds with Kodaira dimension one, we obtain elliptic fibration like structural description. Some vanishing theorems in complex geometry are generalized to the almost complex setting. For tamed symplectic $4$-manifolds, we show that the almost Kodaira dimension is bounded above by the symplectic Kodaira dimension, by using a probabilistic combinatorics style argument. The appendix also contains a few results including answering a question of the second author that there is a unique subvariety in exceptional curve classes for irrational symplectic $4$-manifolds, as well as extending Evans-Smith's constraint on symplectic embeddings of certain rational homology balls by removing the assumption on the intersection form.

math.DG↗

Long-term stable poly(ionic liquid)/MWCNTs inks enable enhanced surface modification for electrooxidative detection and quantification of dsDNA

This work demonstrates the use of imidazolium-based poly(ionic liquid)s (PILs) as efficient dispersants of multi-walled carbon nanotubes (MWCNTs). With these polymeric dispersants, highly stable fine dispersions of MWCNTs (inks) can be easily prepared in aqueous media and applied for rather simple but efficient surface modification of screen-printed electrodes (SPEs). Such a modification of SPEs remarkably increases the electroactive surface area and accelerates the electron transfer rate due to synergistic combination of specific features of MWCNTs such as strong adsorptive property and high specific surface with the advantages of PILs like ion conductivity and dispersability. We further show that the PIL/MWCNT-modified SPEs can be beneficially utilized for direct electrochemical analysis of double stranded DNA (dsDNA). Specifically, it is exemplified by the direct electrooxidation of guanine and adenine bases in salmon testes dsDNA chosen as a model system. The linear ranges for the determination of dsDNA correspond to 5-500 microg per mL for the oxidative peak of guanine and 0.5-50 microg per mL for the oxidative peak of adenine. This makes direct electrochemical dsDNA detection with the use of the easy-preparable PIL/MWCNT-modified SPEs strongly competing to currently applied spectral and fluorescent techniques. Furthermore, we show that the developed constructs are capable of sensing a single point mutation in the 12-bases single-stranded DNA fragments. Such detection is of high clinical significance in choosing an adequate anticancer treatment, where the electrochemical identification of the point mutation could offer time and cost benefits.

cond-mat.soft↗

Templated synthesis of cyclic poly(ionic liquid)s

Charged cyclic polymers, e.g. cyclic DNAs and polypeptides, play enabling roles in organisms, but their synthesis was challenging due to the well known polyelectrolyte effect. To tackle the challenge, we developed a templated method to synthesize a library of imidazolium and pyridinium based cyclic poly(ionic liquid)s. Cyclic templates, cyclic polyimidazole and poly(2-pyridine), were synthesized first through ring-closure method by light-induced Diels-Alder click reaction. Through quaternization of cyclic templates followed by anion metathesis, the cyclic poly(ionic liquid)s were synthesized, which paired with varied counter anions.

cond-mat.soft↗

Intersection of almost complex submanifolds

We show the intersection of a compact almost complex subvariety of dimension $4$ and a compact almost complex submanifold of codimension $2$ is a $J$-holomorphic curve. This is a generalization of positivity of intersections for $J$-holomorphic curves in almost complex $4$-manifolds to higher dimensions. As an application, we discuss pseudoholomorphic sections of a complex line bundle. We introduce a method to produce $J$-holomorphic curves using the differential geometry of almost Hermitian manifolds. When our main result is applied to pseudoholomorphic maps, we prove the singularity subset of a pseudoholomorphic map between almost complex $4$-manifolds is $J$-holomorphic. Building on this, we show degree one pseudoholomorphic maps between almost complex $4$-manifolds are actually birational morphisms in pseudoholomorphic category.

math.DG↗

Active Learning for Wireless IoT Intrusion Detection

Internet of Things (IoT) is becoming truly ubiquitous in our everyday life, but it also faces unique security challenges. Intrusion detection is critical for the security and safety of a wireless IoT network. This paper discusses the human-in-the-loop active learning approach for wireless intrusion detection. We first present the fundamental challenges against the design of a successful Intrusion Detection System (IDS) for wireless IoT network. We then briefly review the rudimentary concepts of active learning and propose its employment in the diverse applications of wireless intrusion detection. Experimental example is also presented to show the significant performance improvement of the active learning method over traditional supervised learning approach. While machine learning techniques have been widely employed for intrusion detection, the application of human-in-the-loop machine learning that leverages both machine and human intelligence to intrusion detection of IoT is still in its infancy. We hope this article can assist the readers in understanding the key concepts of active learning and spur further research in this area.

cs.CR↗

Experience-driven Networking: A Deep Reinforcement Learning based Approach

Modern communication networks have become very complicated and highly dynamic, which makes them hard to model, predict and control. In this paper, we develop a novel experience-driven approach that can learn to well control a communication network from its own experience rather than an accurate mathematical model, just as a human learns a new skill (such as driving, swimming, etc). Specifically, we, for the first time, propose to leverage emerging Deep Reinforcement Learning (DRL) for enabling model-free control in communication networks; and present a novel and highly effective DRL-based control framework, DRL-TE, for a fundamental networking problem: Traffic Engineering (TE). The proposed framework maximizes a widely-used utility function by jointly learning network environment and its dynamics, and making decisions under the guidance of powerful Deep Neural Networks (DNNs). We propose two new techniques, TE-aware exploration and actor-critic-based prioritized experience replay, to optimize the general DRL framework particularly for TE. To validate and evaluate the proposed framework, we implemented it in ns-3, and tested it comprehensively with both representative and randomly generated network topologies. Extensive packet-level simulation results show that 1) compared to several widely-used baseline methods, DRL-TE significantly reduces end-to-end delay and consistently improves the network utility, while offering better or comparable throughput; 2) DRL-TE is robust to network changes; and 3) DRL-TE consistently outperforms a state-ofthe-art DRL method (for continuous control), Deep Deterministic Policy Gradient (DDPG), which, however, does not offer satisfying performance.

cs.NI↗

The curve cone of almost complex 4-manifolds

In this paper, we study the curve cone of an almost complex $4$-manifold which is tamed by a symplectic form. In particular, we prove the cone theorem as in Mori theory for all such manifolds using the Seiberg-Witten theory. For small rational surfaces and minimal ruled surfaces, we study the configuration of negative curves. We define abstract configuration of negative curves, which records the homological and intersection information of curves. Combinatorial blowdown is the main tool to study these configurations. As an application of our investigation of the curve cone, we prove the Nakai-Moishezon type duality for all almost Kähler structures on $\mathbb CP^2\#k\overline{\mathbb CP^2}$ with $k\le 9$ and minimal ruled surfaces with a negative curve. This is proved using a version of Gram-Schmidt orthogonalization process for the $J$-tamed symplectic inflation.

math.SG↗

Synthesis of Single-crystal-like Nanoporous Carbon Membranes and Their Applications in Overall Water Splitting

Nanoporous graphitic carbon membranes with defined chemical composition and pore architecture are novel nanomaterials that are actively pursued. Compared to easy-to-make porous carbon powders that dominate the porous carbon research and applications in energy generation/conversion and environmental remediation, porous carbon membranes are synthetically more challenging though rather appealing from an application perspective due to their structural integrity, interconnectivity and purity. Here we report a simple bottom-up approach to fabricate large-size, freestanding, porous carbon membranes that feature an unusual single-crystal-like graphitic order and hierarchical pore architecture plus favorable nitrogen doping. When loaded with cobalt nanoparticles, such carbon membranes serve as high-performance carbon-based non-noble metal electrocatalyst for overall water splitting.

cond-mat.mtrl-sci↗

Poly(1-vinyl-1,2,4-triazolium) poly(ionic liquid)s: synthesis and the unique behavior in loading metal ions

Herein we report the synthesis of a series of poly(4-alkyl-1-vinyl-1,2,4-triazolium) poly(ionic liquid)s either via straightforward free radical polymerization of their corresponding ionic liquid monomers, or via anion metathesis of the polymer precursors bearing halide as counter anion. The ionic liquid monomers were first prepared via N-alkylation reaction of commercially available 1-vinyl-1,2,4-triazole with alkyl iodides, followed by anion metathesis with targeted fluorinated anions. The thermal properties and solubilities of these poly(ionic liquid)s have been systematically investigated. Interestingly, it was found that the poly(4-ethyl-1-vinyl-1,2,4-triazolium) poly(ionic liquid) exhibited an improved loading capacity of transition metal ions in comparison with its imidazolium counterpart.

cond-mat.mtrl-sci↗

The fundamental group of symplectic $4$-manifolds with $b^+=1$

In this article we apply the technique of Luttinger surgery to study the complexity of the fundamental group of symplectic $4$-manifolds with holomorphic Euler number $χ_h=1$. We discuss the topology of symplectic $4$-manifolds with $b^+=1$ and provide various constructions of symplectic $4$-manifolds with $b^+=1$ and prescribed $c_1^2$.

math.GT↗

Almost Kahler forms on rational 4-manifolds

We study Nakai-Moishezon type question and Donaldson's "tamed to compatible" question for almost complex structures on rational four manifolds. By extending Taubes' subvarieties--current--form technique to $J-$nef genus $0$ classes, we give affirmative answers of these two questions for all tamed almost complex structures on $S^2$ bundles over $S^2$ as well as for many geometrically interesting tamed almost complex structures on other rational four manifolds, including the del Pezzo ones.

math.SG↗

J-holomorphic curves in a nef class

Taubes established fundamental properties of $J-$holomorphic subvarieties in dimension 4 in \cite{T1}. In this paper, we further investigate properties of reducible $J-$holomorphic subvarieties. We offer an upper bound of the total genus of a subvariety when the class of the subvariety is $J-$nef. For a spherical class, it has particularly strong consequences. It is shown that, for any tamed $J$, each irreducible component is a smooth rational curve. We also completely classify configurations of maximal dimension. To prove these results we treat subvarieties as weighted graphs and introduce several combinatorial moves.

math.SG↗

Geometric structures, Gromov norm and Kodaira dimensions

We define the Kodaira dimension for $3$-dimensional manifolds through Thurston's eight geometries, along with a classification in terms of this Kodaira dimension. We show this is compatible with other existing Kodaira dimensions and the partial order defined by non-zero degree maps. For higher dimensions, we explore the relations of geometric structures and mapping orders with various Kodaira dimensions and other invariants. Especially, we show that a closed geometric $4$-manifold has nonvanishing Gromov norm if and only if it has geometry $\mathbb H^2\times \mathbb H^2$, $\mathbb H^2(\mathbb C)$ or $\mathbb H^4$.

math.GT↗

On Cohomological Decomposability of Almost-Kähler Structures

We study the J-invariant and J-anti-invariant cohomological subgroups of the de Rham cohomology of a compact manifold M endowed with an almost-Kähler structure (J, ω, g). In particular, almost-Kähler manifolds satisfying a Lefschetz type property, and solvmanifolds endowed with left-invariant almost-complex structures are investigated.

math.DG↗

A note on exact forms on almost complex manifolds

Reformulations of Donaldson's "tamed to compatible" question are obtained in terms of spaces of exact forms on a compact almost complex manifold $(M^{2n},J)$. In dimension 4, we show that $J$ admits a compatible symplectic form if and only if $J$ admits tamed symplectic forms with arbitrarily given $J$-anti-invariant parts. Some observations about the cohomology of $J$-modified de Rham complexes are also made.

math.SG↗