The pairwise separability index (SI) has been demonstrated as an effective indicator for capturing crucial phenological differences between two plant species. However, its application to crop types, ...which have more obvious phenological characteristics than natural vegetation, has received less attention, and extending the pairwise SI to multiple crops for feature selection still remains a challenge. This paper presented two SI extension approaches (SI ave and SI min ) to select the optimal spectro-temporal features for multiple crops, and investigated their classification performance using Heilongjiang Province, China, as a study area. Feature interpretability and classification accuracy of different crops were evaluated for the two approaches. The results showed that the SI ave approach generally has relatively high feature interpretability due to its better description of crucial phenological characteristics of different crops. Those crops with high separability are insensitive to the extension approach and have similar classification accuracy for the two approaches, whereas those crops with poor separability show good performance with the SI min method. Due to the higher temporal autocorrelation, the optimal features for crop classification that are selected by the SI ave approach exhibit greater information redundancy across the time domain than those that are selected by the SI min approach, which largely explains the relatively low classification accuracy achieved using the SI ave approach. These comparison results between SI min and SI ave approaches also indicate that time-series images with high temporal resolution do not necessarily produce high classification accuracy, regardless of their ability to describe the seasonal characteristics of crops.
Purpose
For computed tomography (CT) systems in which noise is nonstationary, a local noise power spectrum (NPS) is often needed to characterize its noise property. We have previously developed a ...data‐efficient radial NPS method to estimate the two‐dimensional (2D) local NPS for filtered back projection (FBP)‐reconstructed fan‐beam CT utilizing the polar separability of CT NPS. In this work, we extend this method to estimate three‐dimensional (3D) local NPS for feldkamp‐davis‐kress (FDK)‐reconstructed cone‐beam CT (CBCT) volumes.
Methods
Starting from the 2D polar separability, we analyze the CBCT geometry and FDK image reconstruction process to derive the 3D expression of the polar separability for CBCT local NPS. With the polar separability, the 3D local NPS of CBCT can be decomposed into a 2D radial NPS shape function and a one‐dimensional (1D) angular amplitude function with certain geometrical transforms. The 2D radial NPS shape function is a global function characterizing the noise correlation structure, while the 1D angular amplitude function is a local function reflecting the varying local noise amplitudes. The 3D radial local NPS method is constructed from the polar separability. We evaluate the accuracy of the 3D radial local NPS method using simulated and real CBCT data by comparing the radial local NPS estimates to a reference local NPS in terms of normalized mean squared error (NMSE) and a task‐based performance metric (lesion detectability).
Results
In both simulated and physical CBCT examples, a very small NMSE (<5%) was achieved by the radial local NPS method from as few as two scans, while for the traditional local NPS method, about 20 scans were needed to reach this accuracy. The results also showed that the detectability‐based system performances computed using the local NPS estimated with the NPS method developed in this work from two scans closely reflected the actual system performance.
Conclusions
The polar separability greatly reduces the data dimensionality of the 3D CBCT local NPS. The radial local NPS method developed based on this property is shown to be capable of estimating the 3D local NPS from only two CBCT scans with acceptable accuracy. The minimum data requirement indicates the potential utility of local NPS in CBCT applications even for clinical situations.
Most models of ambiguity aversion satisfy the Anscombe–Aumann monotonicity axiom. Monotonicity implies a weak form of separability of preferences across events that occur with unknown probability. We ...construct a test of weak separability by modifying the Allais paradox, adapting it to the Anscombe–Aumann framework. Three experimental studies are conducted. Study 1 finds frequent, systematic violations of weak separability in the lab. These findings replicate in study 2, where we employ a subject pool of online workers and use a natural rather than an artificial source of uncertainty. Investigating a potential explanation of the violations, study 3 suggests that the certainty effect plays a major role.
Data and the web appendix are available at
https://doi.org/10.1287/mnsc.2017.3010
.
This paper was accepted by Han Bleichrodt, decision analysis.
Let ≽ be a total order on the power set of a finite set
n
. A subset
S
⊂
n
is
separable
when for any
X
,
Y
⊂
S
and any
Z
⊂
n
−
S
, the ordering of
X
and
Y
is the same as the ordering of
X
∪
Z
...and
Y
∪
Z
. The
character
of a preference order is the collection of all separable subsets. Motivated by questions in the theories of voting, marketing and social choice, the
admissibility problem
asks which collections
C
⊂
P
(
n
)
can arise as characters of preference orders. We introduce a linear algebraic technique to construct preference orders. Each vector in our 2
n
-dimensional voter basis induces a simple preference preorder (where ties are allowed) with nice separability properties. Given any collection
C
⊂
P
(
n
)
that contains both
∅
and
n
, and such that all pairs of subsets are either nested or disjoint, we use the voter basis to construct a preference order with character
C
.
The interaction of multiple parts with each other within a system according to certain intrinsic rules is a crucial natural phenomenon. The notion of entanglement and its decomposition of ...high-dimensional arrays is particularly intriguing since it opens a new way of thinking in data processing and communication, of which the applications will be broad and significant. Depending on how the internal parts engage with each other, there are different types of entanglements with distinct characteristics. This paper concerns the approximation over a multipartite system whose subsystems consist of symmetric rank-1 matrices that are entangled via the Kronecker tensor product. Such a structure resembles that arising in quantum mechanics where a mixed state is to be approximated by its nearest separable state, except that the discussion in this paper is limited to real-valued matrices. Unlike the conventional low-rank tensor approximations, the added twist due to the involvement of the Kronecker product destroys the multi-linearity, which makes the problem harder. As a first step, this paper explores the rank-1 multipartite approximation only. Reformulated as a nonlinear eigenvalue problem and a nonlinear singular value problem, respectively, the problem can be tackled numerically by power-like iterative methods and SVD-like iterative methods. The iteration in both classes of methods can be implemented cyclically or acyclically. Motivations, schemes, and convergence theory are discussed in this paper. Preliminary numerical experiments suggest these methods are effective and efficient when compared with some general-purpose optimization packages.
Despite the fact that the Arbitration building has been consolidated on the foundations of the unequivocal expression of consent, for years the institution of Arbitration has been subject to a regime ...that has not been able to establish the differential line between contract and arbitration consent, to such an extent that both terms are taken as synonyms in most studies on the matter. Hence, the observations and analyzes made on issues related to the aptitude and material validity of consent in Arbitration are scarce, confusing, and problematic. For such considerations, the present academic essay aims to propose a rereading of the feld of action of the arbitration consent, in order to purge it of the semantic faults inherited by the Arbitration Doctrine, highly influenced by the General Theory of Obligations. Finally it aims to highlight in an exclusive way the material product of the interrelation between violence, economy, and arbitration consensus, together with its jurisdictional consequences.
We analyze the metric properties of conditioned quantum state spaces These spaces are the convex sets of density matrices that, when partially traced over m degrees of freedom, respectively yield the ...given n × n density matrix . For the case n = 2, the volume of equipped with the Hilbert-Schmidt measure can be conjectured to be a simple polynomial of the radius of in the Bloch-ball. Remarkably, for we find numerically that the probability to find a separable state in is independent of (except for pure). For , the same holds for , the probability to find a state with a positive partial transpose in . These results are proven analytically for the case of the family of 4 × 4 X-states, and thoroughly numerically investigated for the general case. The important implications of these findings for the clarification of open problems in quantum theory are pointed out and discussed.
Let k be a nonperfect field of characteristic 2. Let G be a k-split simple algebraic group of type E6 (or G2) defined over k. In this paper, we present the first examples of nonabelian ...non-G-completely reducible k-subgroups of G which are G-completely reducible over k. Our construction is based on that of subgroups of G acting non-separably on the unipotent radical of a proper parabolic subgroup of G in our previous work. We also present examples with the same property for a non-connected reductive group G. Along the way, several general results concerning complete reducibility over nonperfect fields are proved using the recently proved Tits center conjecture for spherical buildings. In particular, we show that under mild conditions a connected k-subgroup of G is pseudo-reductive if it is G-completely reducible over k.
Although nonnegative matrix factorization (NMF) is NP-hard in general, it has been shown very recently that it is tractable under the assumption that the input nonnegative data matrix is close to ...being separable. (Separability requires that all columns of the input matrix belong to the cone spanned by a small subset of these columns.) Since then, several algorithms have been designed to handle this subclass of NMF problems. In particular, Bittorf et al. Adv. Neural Inform. Process. Syst., 25 (2012), pp. 1223--1231 proposed a linear programming model, referred to as Hottopixx. In this paper, we provide a new and more general robustness analysis of their method. In particular, we design a provably more robust variant using a postprocessing strategy which allows us to deal with duplicates and near duplicates in the data set. PUBLICATION ABSTRACT
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