Partial mirror symmetry, lattice presentations and algebraic monoids

This is the second in a series of papers that develops the theory of reflection monoids, motivated by the theory of reflection groups. Reflection monoids were first introduced in arXiv:0812.2789. In this paper we study their presentations as abstract monoids. Along the way we also find general presentations for certain join-semilattices (as monoids under join) which we interpret for two special classes of examples: the face lattices of convex polytopes and the geometric lattices, particularly the intersection lattices of hyperplane arrangements. Another spin-off is a general presentation for the Renner monoid of an algebraic monoid, which we illustrate in the special case of the "classical" algebraic monoids.Comment: 41 page

The Southern Extension and Reactivations of the Clarendon-Linden Fault System

Gas seeps located near Pike, New York, on the inferred location of the central fault of the Clarendon-Linden Fault System (CLF), were initiated during, or slightly after, the Saguenay earthquake, 1988. Analyses of the gas show that the gas seeps have a Devonian shale source, and a nearby well suggests that the source may be as deep as 330 m. Thus, CLF fractures extending to depths possibly as great as 300+ m were probably opened as a local response to the Saguenay event, allowing the gas to be vented. Published data show that the CLF extends from Lake Ontario to slightly south of Pike. Previously, there were insufficient data available to enable investigators to determine if the fault system continued farther south. Our soil gas survey and analyses of well logs indicate the CLF continues south into Allegany County, which borders the state of Pennsylvania. Closely-spaced wells suggest that the central fault of the CLF is probably a series of step faults, even in units above the Silurian evaporite section, although a monocline cannot be ruled out. Growth-fault geometries of the CLF suggest that the CLF experienced motion during the Taconic and Acadian orogenies. Isopach maps, coupled with the proposed southward extrapolation of the CLF, suggest that in Late Devonian times the CLF motion history recorded the passage of the Appalachian foreland basin axis across the CLF.Des dégagements gazeux survenus près de Pike (État de New York), à l'emplacement supposé de la faille centrale du réseau de Clarendon-Linden (RCL), se sont produits pendant ou aussitôt après le séisme de 1988, au Saguenay. Les analyses du gaz démontrent que les fuites proviennent d'une source de shale dévonien aussi profonde que 330 m. Les fractures du RCL, atteignant plus de 300 m de profondeur, se sont vraisemblablement ouvertes en réponse au séisme du Saguenay, permettant ainsi au gaz de se dégager. Les données publiées montrent que le RCL s'étend du lac Ontario jusqu'au sud de Pike, mais on n'a pu déterminer jusqu'à maintenant si le réseau se poursuit plus au sud. Les levés sur la détection de gaz dans le sol et les analyses de données des puits indiquent que le RCL se poursuit dans le comté d'Allegany, qui borde la Pennsylvanie. À partir d'indices tirés de puits très rapprochés, on croit que la faille centrale du réseau consiste probablement en une série de failles en gradin, même dans les unités au-dessus de la section d'évaporite du Silurien, bien qu'un monoclinal ne puisse être rejeté. La géométrie de la croissance des failles montre que le RCL s'est déplacé au cours des orogénies laconique et acadienne. Les cartes d'isopaques, ainsi que la trajectoire présumée vers le sud du RCL, indique le RCL a enregistré le passage de l'axe de l'avant-bassin appalachien au cours du Dévonien supérieur.Das Entweichen von Gas in der Nàhe von Pike, New York, an der Stelle, die man fur den zentralen Bruch des Clarendon-Linden Verwerfungssystems halt (CLV), hat I988, wàhrend oder kurz nach dem Erdbeben von Saguenay begonnen. Analysen des Gases zeigen, daB das entwichene Gas aus einer Tonschieferquelle des Devon stammt, und ein nahegelegener Brunnen IaRt vermuten, daB die Quelle 330 m tief sein konnte. So haben sich wohl CLV-Brùche, die môglicherweise bis zu 300+ m tief sind, als lokale Reaktion auf das Saguenay-Ereignis geôffnet und haben so das Gas freigelassen. Die veroffentlichten Daten zeigen, daB das CLV sich vom Ontario-See bis etwas sùdlich von Pike ausdehnt. Zuvor waren nicht genùgend Daten verfùgbar, mit denen die Forscher bestimmen konnten, ob das Verwerfungssystem sich weiter sùdlich ausdehnte. Aus Erhebungen ùber Erdgas und Untersuchungen von Angaben aus Brunnen ergibt sich, daB das CLV sich bis in die Grafschaft Allegany fortsetzt, die an Pennsylvanien grenzt. Dicht aufeinanderfolgende Brunnen lassen darauf schlieBen, daB der zentrale Bruch des CLV wahrscheinlich aus einer Série von abgestuften Verwerfungen besteht, selbst in Einheiten oberhalb des Evaporationsabschnittes aus dem Silur, wenn auch ein Monoklinal nicht ausgeschlossen werden kann. Die Wachstumsgeometrie der Bruche des CLV legt nahe, daB das CLV sich wàhrend der takonischen und akadischen Orogenèse bewegt hat. Isopach-Karten sowie die mutmaBliche Sùdwartsbewegung des CLV zeigen, daB die Bewegungsgeschichte des CLV im spàten Devon den Durchzug der Appalachen-Vorlandbeckenachse durch das CLV aufgezeichent hat

Estimating Subjective Probabilities

Subjective probabilities play a role in many economic decisions. There is a large theoretical literature on the elicitation of subjective probabilities, and an equally large empirical literature. However, there is a gulf between the two. The theoretical literature proposes a range of procedures that can be used to recover subjective probabilities, but stresses the need to make strong auxiliary assumptions or "calibrating adjustments" to elicited reports in order to recover the latent probability. With some notable exceptions, the empirical literature seems intent on either making those strong assumptions or ignoring the need for calibration. We illustrate how the joint estimation of risk attitudes and subjective probabilities using structural maximum likelihood methods can provide the calibration adjustments that theory calls for. This allows the observer to make inferences about the latent subjective probability, calibrating for virtually any well-specified model of choice under uncertainty. We demonstrate our procedures with experiments in which we elicit subjective probabilities. We calibrate the estimates of subjective beliefs assuming that choices are made consistently with expected utility theory or rank-dependent utility theory. Inferred subjective probabilities are significantly different when calibrated according to either theory, thus showing the importance of undertaking such exercises. Our findings also have implications for the interpretation of probabilities inferred from prediction markets.

Automatic Recognition of Light Microscope Pollen Images

This paper is a progress report on a project aimed at the realization of a low-cost, automatic, trainable system "AutoStage" for recognition and counting of pollen. Previous work on image feature selection and classification has been extended by design and integration of an XY stage to allow slides to be scanned, an auto focus system, and segmentation software. The results of a series of classification tests are reported, and verified by comparison with classification performance by expert palynologists. A number of technical issues are addressed, including pollen slide preparation and slide sampling protocols

Inferring Beliefs as Subjectively Uncertain Probabilities

We propose a method for estimating subjective beliefs, viewed as a subjective probability distribution. The key insight is to characterize beliefs as a parameter to be estimated from observed choices in a well-defined experimental task, and to estimate that parameter as a random coefficient. The experimental task consists of a series of standard lottery choices in which the subject is assumed to use conventional risk attitudes to select one lottery or the other, and then a series of betting choices in which the subject is presented with a range of bookies offering odds on the outcome of some event that the subject has a belief over. Knowledge of the risk attitudes of subjects conditions the inferences about subjective beliefs. Maximum simulated likelihood methods are used to estimate a structural model in which subjects employ subjective beliefs to make bets. We present evidence that some subjective probabilities are indeed best characterized as probability distributions with non-zero variance.

ANTI-NMDA ENCEPHALITIS IN THE ACUTE SETTING

Background: Encephalitis associated with antibodies targeted against the N-methyl-D-aspartate (NMDA) receptor is increasingly recognised as a major cause of an acute presentation of organic psychosis. Misdiagnosis and subsequent inappropriate referral to psychiatric services is common and avoidable. This review focuses on addressing this issue in the acute setting. Methods: The authors present a review of existing literature relating to the pathophysiology and presentation of anti-NMDA receptor encephalitis, prior to proposing a management pathway avoiding delays to treatment incurred through misdiagnosis or inappropriate referral. Conclusions: Acute care physicians should have a low threshold for suspecting anti-NMDA receptor encephalitis in any patient presenting with acute psychosis in the context of non-specific coryzal and constitutional symptoms in whom infective causes have been excluded. The presence of pleocytosis and reduced protein in routine CSF analysis should further raise suspicion, and samples should be sent for immunohistochemical testing. Availability and efficiency of this testing is currently suboptimal