Generalization of form in visual pattern classification.

Human observers were trained to criterion in classifying compound Gabor signals with sym- metry relationships, and were then tested with each of 18 blob-only versions of the learning set. General- ization to dark-only and light-only blob versions of the learning signals, as well as to dark-and-light blob versions was found to be excellent, thus implying virtually perfect generalization of the ability to classify mirror-image signals. The hypothesis that the learning signals are internally represented in terms of a 'blob code' with explicit labelling of contrast polarities was tested by predicting observed generalization behaviour in terms of various types of signal representations (pixelwise, Laplacian pyramid, curvature pyramid, ON/OFF, local maxima of Laplacian and curvature operators) and a minimum-distance rule. Most representations could explain generalization for dark-only and light-only blob patterns but not for the high-thresholded versions thereof. This led to the proposal of a structure-oriented blob-code. Whether such a code could be used in conjunction with simple classifiers or should be transformed into a propo- sitional scheme of representation operated upon by a rule-based classification process remains an open question

Classification of sixth form and further education institutions

"Ninety Three Sixth Form College Corporations, created from 1 April 2010 following the passage of the Apprentice, Skills Children and Learning Act 2009, have been classified as Local Government entities for the purposes of the National Accounts. In the course of the reaching this decision, ONS reviewed the existing classification of other further education institutions in England and Wales using Eurostat’s Manual on Government Deficit and Debt, which has been published since the original classification decision was taken in the late 1990s. ONS has decided that Further Education (FE) Corporations in England and Wales should be reclassified, from Non-Profit Institutions Serving Households (NPISH) to Central Government, from their inception in April 1993. NPISH is often known as the 'third sector'; in National Accounts, NPISH is part of the private sector." - Page 3

Classification of the Entangled states L\times N\times N

We presented a general classification scheme for the tripartite $L\times N\times N$ entangled system under stochastic local operation and classical communication. The whole classification procedure consists of two correlated parts: the simultaneous similarity transformation of a commuting matrix pair into a canonical form and the study of internal symmetry of parameters in the canonical form. Based on this scheme, a concrete example of entanglement classification for a $3\times N\times N$ system is given.Comment: 21 pages; published in Phys. Rev.

Symmetry-Enriched Quantum Spin Liquids in (3+1)d(3+1)d

We use the intrinsic one-form and two-form global symmetries of (3+1)$d$ bosonic field theories to classify quantum phases enriched by ordinary ($0$-form) global symmetry. Different symmetry-enriched phases correspond to different ways of coupling the theory to the background gauge field of the ordinary symmetry. The input of the classification is the higher-form symmetries and a permutation action of the $0$-form symmetry on the lines and surfaces of the theory. From these data we classify the couplings to the background gauge field by the 0-form symmetry defects constructed from the higher-form symmetry defects. For trivial two-form symmetry the classification coincides with the classification for symmetry fractionalizations in $(2+1)d$. We also provide a systematic method to obtain the symmetry protected topological phases that can be absorbed by the coupling, and we give the relative 't Hooft anomaly for different couplings. We discuss several examples including the gapless pure $U(1)$ gauge theory and the gapped Abelian finite group gauge theory. As an application, we discover a tension with a conjectured duality in $(3+1)d$ for $SU(2)$ gauge theory with two adjoint Weyl fermions

Commutative nn-ary superalgebras with an invariant skew-symmetric form

We study $n$-ary commutative superalgebras and $L_{\infty}$-algebras that possess a skew-symmetric invariant form, using the derived bracket formalism. This class of superalgebras includes for instance Lie algebras and their $n$-ary generalizations, commutative associative and Jordan algebras with an invariant form. We give a classification of anti-commutative $m$-dimensional $(m-3)$-ary algebras with an invariant form, and a classification of real simple $m$-dimensional Lie $(m-3)$-algebras with a positive definite invariant form up to isometry. Furthermore, we develop the Hodge Theory for $L_{\infty}$-algebras with a symmetric invariant form, and we describe quasi-Frobenius structures on skew-symmetric $n$-ary algebras.Comment: 27 page

Testing Market Response to Auditor Change Filings: a comparison of machine learning classifiers

The use of textual information contained in company filings with the Securities Exchange Commission (SEC), including annual reports on Form 10-K, quarterly reports on Form 10-Q, and current reports on Form 8-K, has gained the increased attention of finance and accounting researchers. In this paper we use a set of machine learning methods to predict the market response to changes in a firm\u27s auditor as reported in public filings. We vectorize the text of 8-K filings to test whether the resulting feature matrix can explain the sign of the market response to the filing. Specifically, using classification algorithms and a sample consisting of the Item 4.01 text of 8-K documents, which provides information on changes in auditors of companies that are registered with the SEC, we predict the sign of the cumulative abnormal return (CAR) around 8-K filing dates. We report the correct classification performance and time efficiency of the classification algorithms. Our results show some improvement over the naïve classification method