Fujita's conjecture on iterated accumulation points of pseudo-effective thresholds
We show that $k$-th iterated accumulation points of pseudo-effective thresholds of $n$-dimensional varieties are bounded by $n-k+1$.
math.AG↗
arXiv subjects
Zhan Li
Publications and source records attributed to Zhan Li.
Efficient parametric frequency conversions in lithium niobate nanophotonic chips
Chip-integrated nonlinear photonics holds the key for advanced optical information processing with superior performance and novel functionalities. Here, we present an optimally mode-matched, periodically poled lithium niobate nanowaveguide for efficient parametric frequency conversions on chip. Using a 4-mm nanowaveguide with subwavelength mode confinement, we demonstrate second harmonic generation with efficiency over $2200\%~W^{-1}cm^{-2}$, and broadband difference frequency generation with similar efficiency over a 4.5-THz spectral span. These allow us to generate correlated photon pairs over multiple frequency channels via spontaneous parametric down conversion, all in their fundamental spatial modes, with a coincidence to accidental ratio as high as 600. The high efficiency and dense integrability of the present chip devices may pave a viable route to scalable nonlinear applications in both classical and quantum domains.
quant-ph↗
Weak Zariski decompositions and log terminal models for generalized polarized pairs
We show that the existence of a birational weak Zariski decomposition for a pseudo-effective generalized polarized lc pair is equivalent to the existence of a generalized polarized log terminal model.
math.AG↗
On Fujita's conjecture for pseudo-effective thresholds
We show Fujita's spectrum conjecture for $ε$-log canonical pairs and Fujita's log spectrum conjecture for log canonical pairs. Then, we generalize the pseudo-effective threshold of a single divisor to multiple divisors and establish the analogous finiteness and the DCC properties.
math.AG↗
OptMark: A Toolkit for Benchmarking Query Optimizers
Query optimizers have long been considered as among the most complex components of a database engine, while the assessment of an optimizer's quality remains a challenging task. Indeed, existing performance benchmarks for database engines (like TPC benchmarks) produce a performance assessment of the query runtime system rather than its query optimizer. To address this challenge, this paper introduces OptMark, a toolkit for evaluating the quality of a query optimizer. OptMark is designed to offer a number of desirable properties. First, it decouples the quality of an optimizer from the quality of its underlying execution engine. Second it evaluates independently both the effectiveness of an optimizer (i.e., quality of the chosen plans) and its efficiency (i.e., optimization time). OptMark includes also a generic benchmarking toolkit that is minimum invasive to the DBMS that wishes to use it. Any DBMS can provide a system-specific implementation of a simple API that allows OptMark to run and generate benchmark scores for the specific system. This paper discusses the metrics we propose for evaluating an optimizer's quality, the benchmark's design and the toolkit's API and functionality. We have implemented OptMark on the open-source MySQL engine as well as two commercial database systems. Using these implementations we are able to assess the quality of the optimizers on these three systems based on the TPC-DS benchmark queries.
cs.DB↗
On the birationality of complete intersections associated to nef-partitions
We prove that generic complete intersections associated to multiple mirror nef-partitions are all birational. This result solves a conjecture by Batyrev and Nill under some mild assumptions.
math.AG↗
On derived equivalence of general Clifford double mirrors
We show that general Clifford double mirrors constructed in "On Clifford double mirrors of toric complete intersections" are derived equivalent.
math.AG↗
On Clifford double mirrors of toric complete intersections
We present a construction of noncommutative double mirrors to complete intersections in toric varieties. This construction unifies existing sporadic examples and explains the underlying combinatorial and physical reasons for their existence.
math.AG↗
Counterexamples of Lefschetz hyperplane type results for movable cones
The main theorem of the paper provides a way to produce examples such that the movable cone of an ample divisor does not coincide with the movable cone of its ambient variety.
math.AG↗
An embryo of protocell membrane: The capsule of graphene oxide
Many signs indicate that the graphene could widely occur on the early Earth. Here, we report a new theory that graphene might be an embryo of protocell membrane, and found several evidences. Firstly, the graphene oxide and phospholipid-graphene oxide composite would curl into capsules in strongly acidic saturated solution of Pb(NO3)2 at low temperature, providing a protective space for biochemical reactions. Secondly, L-animi acids exhibit higher reactivity than D-animi acids for graphene oxides in favor of the formation of left-handed proteins. Thirdly, monolayer graphene with nanopores prepared by unfocused 84Kr25+ has high selectivity for permeation of the monovalent metal ions (Rb+ > K+ > Cs+ > Na+ > Li+), but does not allow Cl- through, which could be attributed to the ion exchange of oxygen-containing groups on the rim of nanopores. It is similar to K+ channels, which would cause efflux of some ions from capsule of graphene oxides with the decrease of pH in the primitive ocean, creating a suitable inner condition for the origin of life. Consequently, the strongly acidic, high salinity and strong radiation as well as temperature changes in the early Earth, regarded as negative factors, would be indispensable for the origin of protocell. In short, graphene bred life, but digested gradually by the evolution.
q-bio.PE↗
On complete intersections with trivial canonical class
We prove birational boundedness results on complete intersections with trivial canonical class of base point free divisors in (some version of) Fano varieties. Our results imply in particular that Batyrev-Borisov toric construction produces only a bounded set of Hodge numbers in any given dimension, even as the codimension is allowed to grow.
math.AG↗
Information Filtering via Implicit Trust-based Network
Based on the user-item bipartite network, collaborative filtering (CF) recommender systems predict users' interests according to their history collections, which is a promising way to solve the information exploration problem. However, CF algorithm encounters cold start and sparsity problems. The trust-based CF algorithm is implemented by collecting the users' trust statements, which is time-consuming and must use users' private friendship information. In this paper, we present a novel measurement to calculate users' implicit trust-based correlation by taking into account their average ratings, rating ranges, and the number of common rated items. By applying the similar idea to the items, a item-based CF algorithm is constructed. The simulation results on three benchmark data sets show that the performances of both user-based and item-based algorithms could be enhanced greatly. Finally, a hybrid algorithm is constructed by integrating the user-based and item-based algorithms, the simulation results indicate that hybrid algorithm outperforms the state-of-the-art methods. Specifically, it can not only provide more accurate recommendations, but also alleviate the cold start problem.
physics.data-an↗