33 research outputs found
Relationship between Nichols braided Lie algebras and Nichols algebras
We establish the relationship among Nichols algebras, Nichols braided Lie
algebras and Nichols Lie algebras. We prove two results: (i) Nichols algebra
is finite-dimensional if and only if Nichols braided Lie
algebra is finite-dimensional if there does not exist any
-infinity element in ; (ii) Nichols Lie algebra is infinite dimensional if is infinite. We give the sufficient
conditions for Nichols braided Lie algebra to be a homomorphic
image of a braided Lie algebra generated by with defining relations.Comment: LeTex 18 pages, need JOLT-macros to compile. To appear in Journal of
Lie Theor
On Nichols (braided) Lie algebras
We prove {\rm (i)} Nichols algebra of vector space is
finite-dimensional if and only if Nichols braided Lie algebra
is finite-dimensional; {\rm (ii)} If the rank of connected is and
is an arithmetic root system, then and {\rm (iii)} if is an arithmetic
root system and there does not exist any -infinity element with for any , then if and
only if there exists , which is twisting equivalent to , such that Furthermore we give an estimation of
dimensions of Nichols Lie algebras and two examples of Lie algebras which do
not have maximal solvable ideals.Comment: 29 Pages; Substantially revised version; To appear in International
Journal of Mathematic
Structures of Nichols (braided) Lie algebras of diagonal type
Let be a braided vector space of diagonal type. Let ,
and be the Nichols algebra, Nichols Lie
algebra and Nichols braided Lie algebra over , respectively. We show that a
monomial belongs to if and only if that this monomial is
connected. We obtain the basis for of arithmetic root systems
and the dimension for of finite Cartan type. We give the
sufficient and necessary conditions for and . We obtain an explicit basis of
over quantum linear space with .Comment: 23 pages. Version to appear in Journal of Lie Theor
Time To Live: Temporal Management of Large-Scale RFID Applications
In coming years, there will be billions of RFID tags living in the world tagging almost everything for tracking and identification purposes. This phenomenon will impose a new challenge not only to the network capacity but also to the scalability of event processing of RFID applications. Since most RFID applications are time sensitive, we propose a notion of Time To Live (TTL), representing the period of time that an RFID event can legally live in an RFID data management system, to manage various temporal event patterns. TTL is critical in the "Internet of Things" for handling a tremendous amount of partial event-tracking results. Also, TTL can be used to provide prompt responses to time-critical events so that the RFID data streams can be handled timely. We divide TTL into four categories according to the general event-handling patterns. Moreover, to extract event sequence from an unordered event stream correctly and handle TTL constrained event sequence effectively, we design a new data structure, namely Double Level Sequence Instance List (DLSIList), to record intermediate stages of event sequences. On the basis of this, an RFID data management system, namely Temporal Management System over RFID data streams (TMS-RFID), has been developed. This system can be constructed as a stand-alone middleware component to manage temporal event patterns. We demonstrate the effectiveness of TMS-RFID on extracting complex temporal event patterns through a detailed performance study using a range of high-speed data streams and various queries. The results show that TMS-RFID has a very high throughout, namely 170,000 - 870,000 events per second for different highly complex continuous queries. Moreover, the experiments also show that the main structure to record the intermediate stages in TMS-RFID does not increase exponentially with the number of events. These illustrate that TMS-RFID not only has a high processing speed, but also has a good scalability
3D Instances as 1D Kernels
We introduce a 3D instance representation, termed instance kernels, where
instances are represented by one-dimensional vectors that encode the semantic,
positional, and shape information of 3D instances. We show that instance
kernels enable easy mask inference by simply scanning kernels over the entire
scenes, avoiding the heavy reliance on proposals or heuristic clustering
algorithms in standard 3D instance segmentation pipelines. The idea of instance
kernel is inspired by recent success of dynamic convolutions in 2D/3D instance
segmentation. However, we find it non-trivial to represent 3D instances due to
the disordered and unstructured nature of point cloud data, e.g., poor instance
localization can significantly degrade instance representation. To remedy this,
we construct a novel 3D instance encoding paradigm. First, potential instance
centroids are localized as candidates. Then, a candidate merging scheme is
devised to simultaneously aggregate duplicated candidates and collect context
around the merged centroids to form the instance kernels. Once instance kernels
are available, instance masks can be reconstructed via dynamic convolutions
whose weights are conditioned on instance kernels. The whole pipeline is
instantiated with a dynamic kernel network (DKNet). Results show that DKNet
outperforms the state of the arts on both ScanNetV2 and S3DIS datasets with
better instance localization. Code is available:
https://github.com/W1zheng/DKNet.Comment: Appearing in ECCV, 202
DoF-NeRF: Depth-of-Field Meets Neural Radiance Fields
Neural Radiance Field (NeRF) and its variants have exhibited great success on
representing 3D scenes and synthesizing photo-realistic novel views. However,
they are generally based on the pinhole camera model and assume all-in-focus
inputs. This limits their applicability as images captured from the real world
often have finite depth-of-field (DoF). To mitigate this issue, we introduce
DoF-NeRF, a novel neural rendering approach that can deal with shallow DoF
inputs and can simulate DoF effect. In particular, it extends NeRF to simulate
the aperture of lens following the principles of geometric optics. Such a
physical guarantee allows DoF-NeRF to operate views with different focus
configurations. Benefiting from explicit aperture modeling, DoF-NeRF also
enables direct manipulation of DoF effect by adjusting virtual aperture and
focus parameters. It is plug-and-play and can be inserted into NeRF-based
frameworks. Experiments on synthetic and real-world datasets show that,
DoF-NeRF not only performs comparably with NeRF in the all-in-focus setting,
but also can synthesize all-in-focus novel views conditioned on shallow DoF
inputs. An interesting application of DoF-NeRF to DoF rendering is also
demonstrated. The source code will be made available at
https://github.com/zijinwuzijin/DoF-NeRF.Comment: Accepted by ACMMM 202
SMCB-E-03172004-0141.R2 1 A Multiagent Evolutionary Algorithm for Constraint Satisfaction Problems
Abstract—With the intrinsic properties of constraint satisfaction problems (CSPs) in mind, we divide CSPs into two types, namely, permutation CSPs and non-permutation CSPs. According to their characteristics, several behaviors are designed for agents by making use of the ability of agents to sense and act on the environment. These behaviors are controlled by means of evolution, so that the multiagent evolutionary algorithm for constraint satisfaction problems (MAEA-CSPs) results. To overcome the disadvantages of the general encoding methods, the minimum conflict encoding is also proposed. Theoretical analyses show that MAEA-CSPs has a linear space complexity and converges to the global optimum. The first part of the experiments uses 250 benchmark binary CSPs and 79 graph coloring problems from the DIMACS challenge to test the performance of MAEA-CSPs for non-permutation CSPs. MAEA-CSPs is compared with six well-defined algorithms and the effect of the parameters is analyzed systematically. The second part of the experiments uses a classical CSP, n-queen problems, and a more practical case, job-shop scheduling problems (JSPs), to test the performance of MAEA-CSPs for permutation CSPs. The scalability of MAEA-CSPs along n for n-queen problems is studied with great care. The results show that MAEA-CSPs achieves good performance when n increases from 10 4 to 10 7, and has a linear time complexity. Even for 10 7-queen problems, MAEA-CSPs finds the solutions by only 150 seconds. For JSPs, 59 benchmark problems are used, and good performance is also obtained. Index Terms—Constraint satisfaction problems, evolutionary algorithms, graph coloring problems, job-shop schedulin