The understanding of the functional aspects of objects and tools is of
paramount importance in supporting an intelligent system in navigating around
in the environment and interacting with various objects, structures, and
systems, to help fulfil its goals. A detailed understanding of functionalities
can also lead to design improvements and novel designs that would enhance the
operations of AI and robotic systems on the one hand, and human lives on the
other. This paper demonstrates how a particular object - in this case, a frying
pan - and its participation in the processes it is designed to support - in
this case, the frying process - can be represented in a general function
representational language and framework, that can be used to flesh out the
processes and functionalities involved, leading to a deep conceptual
understanding with explainability of functionalities that allows the system to
answer "why" questions - why is something a good frying pan, say, or why a
certain part on the frying pan is designed in a certain way? Or, why is
something not a good frying pan? This supports the re-design and improvement on
design of objects, artifacts, and tools, as well as the potential for
generating novel designs that are functionally accurate, usable, and
satisfactory.

该论文演示了如何使用通用功能表征语言和框架来表示一个特定对象（煎锅）及其参与的过程（煎食过程），以深入理解其功能，并支持再设计和改良对象、工具和人工智能系统的潜力。

物品功能知识表达与设计理解、改进及生成的工具：以煎锅为例

Why is That a Good or Not a Good Frying Pan? -- Knowledge Representation for Functions of Objects and Tools for Design Understanding, Improvement, and Generation

Graph matching is an important and persistent problem in computer vision and
pattern recognition for finding node-to-node correspondence between
graph-structured data. However, as widely used, graph matching that
incorporates pairwise constraints can be formulated as a quadratic assignment
problem (QAP), which is NP-complete and results in intrinsic computational
difficulties. In this paper, we present a functional representation for graph
matching (FRGM) that aims to provide more geometric insights on the problem and
reduce the space and time complexities of corresponding algorithms. To achieve
these goals, we represent a graph endowed with edge attributes by a linear
function space equipped with a functional such as inner product or metric, that
has an explicit geometric meaning. Consequently, the correspondence between
graphs can be represented as a linear representation map of that functional.
Specifically, we reformulate the linear functional representation map as a new
parameterization for Euclidean graph matching, which is associative with
geometric parameters for graphs under rigid or nonrigid deformations. This
allows us to estimate the correspondence and geometric deformations
simultaneously. The use of the representation of edge attributes rather than
the affinity matrix enables us to reduce the space complexity by two orders of
magnitudes. Furthermore, we propose an efficient optimization strategy with low
time complexity to optimize the objective function. The experimental results on
both synthetic and real-world datasets demonstrate that the proposed FRGM can
achieve state-of-the-art performance.

本研究提出一种新的基于功能表征的图匹配方法，能够降低相关算法的时间和空间复杂度，并且具有比现有方法更准确的匹配性能。

图匹配的函数表示

A Functional Representation for Graph Matching

Heckerman (1993) defined causal independence in terms of a set of temporal
conditional independence statements. These statements formalized certain types
of causal interaction where (1) the effect is independent of the order that
causes are introduced and (2) the impact of a single cause on the effect does
not depend on what other causes have previously been applied. In this paper, we
introduce an equivalent a temporal characterization of causal independence
based on a functional representation of the relationship between causes and the
effect. In this representation, the interaction between causes and effect can
be written as a nested decomposition of functions. Causal independence can be
exploited by representing this decomposition in the belief network, resulting
in representations that are more efficient for inference than general causal
models. We present empirical results showing the benefits of a
causal-independence representation for belief-network inference.

本文介绍了一种基于功能表示的因果独立的时间特征，可以将其应用于信念网络中以实现更高效的推理。

因果独立的新视角

A New Look at Causal Independence

We present a novel sparse modeling approach to non-rigid shape matching using
only the ability to detect repeatable regions. As the input to our algorithm,
we are given only two sets of regions in two shapes; no descriptors are
provided so the correspondence between the regions is not know, nor we know how
many regions correspond in the two shapes. We show that even with such scarce
information, it is possible to establish very accurate correspondence between
the shapes by using methods from the field of sparse modeling, being this, the
first non-trivial use of sparse models in shape correspondence. We formulate
the problem of permuted sparse coding, in which we solve simultaneously for an
unknown permutation ordering the regions on two shapes and for an unknown
correspondence in functional representation. We also propose a robust variant
capable of handling incomplete matches. Numerically, the problem is solved
efficiently by alternating the solution of a linear assignment and a sparse
coding problem. The proposed methods are evaluated qualitatively and
quantitatively on standard benchmarks containing both synthetic and scanned
objects.

我们提出了一种新的基于稀疏建模方法的非刚性形状匹配算法，通过检测可重复区域，建立形状间的精确对应关系，并以非常完美的表现在标准基准数据集上得到了定量和定性的评估。