We isolate here a wide class of well founded orders called tame orders, and show that each such order of cardinality at most κ can be realized as the Mitchell order on a measurable cardinal κ, from a consistency assumption weaker than o(κ) = κ+.

We address the question regarding the structure of the Mitchell order on normal measures. We show that every well founded order can be realized as the Mitchell order on a measurable cardinal κ, from some large cardinal assumption.

Structure information is ubiquitous in natural scene images and it plays an important role in scene representation. In this paper, third order structure statistics (TOSS) and fourth order structure statistics (FOSS) are exploited to encode higher order structure information. Afterwards, based on the radial and normal slice of TOSS and FOSS, we propose the high order structure feature: third ord...

We propose a general method for finding pointwise correspondence between 2-D shapes based on the concept of order structure and using geometric hashing. The problem of finding correspondence and the problem of establishing shape equivalence can be considered as one and the same problem. Given shape equivalence, we can in general find pointwise correspondence and the existence of a unambiguous c...

The quotient operation is a standard feature of set theory, where a set is partitioned into subsets by an equivalence relation. We reinterpret this idea for higher order logic, where types are divided by an equivalence relation to create new types, called quotient types. We present a design to mechanically construct quotient types as new types in the logic, and to support the automatic lifting ...

Characterization of 2 nd order local image structure by a 6-D vector (or jet) of Gaussian derivative measurements is considered. We consider the affect on jets of a group of transformations – affine intensity-scaling, image rotation and reflection, and their compositions – that preserve intrinsic image structure. We show how this group stratifies the jet space into a system of orbits. Consideri...

In Order and Structure I have two main goals. First, I argue that the grammar should be viewed as an incremental left-to-right structure building system, and that this solves a number of problems in constituent structure. Second, I reassess the relationship between linguistic knowledge and language processing, and argue that mental systems for grammar and processing can be viewed as identical. ...

We consider constraint-based methods for causal structure learning, such as the PC-, FCI-, RFCIand CCDalgorithms (Spirtes et al. (2000, 1993), Richardson (1996), Colombo et al. (2012), Claassen et al. (2013)). The first step of all these algorithms consists of the PCalgorithm. This algorithm is known to be order-dependent, in the sense that the output can depend on the order in which the variab...

From observations on the partial disintegration of isolated human metaphase chromosomes we propose that human metaphase chromatids have a rather simple organization based on the folding and coiling of a long, regular, hollow cylindrical structure with a diameter of about 4000 A. This cylindrical structure, the unit fiber, is postulated to be a super-solenoid formed by the coiling of a 300 A sol...

In this paper, we study the orders obtained by the generalized dynamics of the sand piles model (SPM). We show that these orders are suborders of LB, lattice of integer partitions introduced in Brylawski (Discrete Math. 6 (1973) 201), and we deduce from that a characterization of their 4xed point. We prove that these orders form an increasing sequence of lattices from SPM to LB. We then charact...