Closure operators and projections on involution posets

Investigations of closure operators on an involution poset T lead to a certain type of closure operators (so called c-closure operators) that are closely related to projections on

Closure operators and projections on involution posets

Investigations of closure operators on an involution poset T lead to a certain type of closure operators (so called c-closure operators) that are closely related to projections on T

Relativistic Tunneling Through Two Successive Barriers

We study the relativistic quantum mechanical problem of a Dirac particle tunneling through two successive electrostatic barriers. Our aim is to study the emergence of the so-called \emph{Generalized Hartman Effect}, an effect observed in the context of nonrelativistic tunneling as well as in its electromagnetic counterparts, and which is often associated with the possibility of superluminal velocities in the tunneling process. We discuss the behavior of both the phase (or group) tunneling time and the dwell time, and show that in the limit of opaque barriers the relativistic theory also allows the emergence of the Generalized Hartman Effect. We compare our results with the nonrelativistic ones and discuss their interpretation.Comment: 7 pages, 3 figures. Revised version, with a new appendix added. Slightly changes in the styles and captions of Figures 1 and 2. To appear in Physical Review

AI Solutions for MDS: Artificial Intelligence Techniques for Misuse Detection and Localisation in Telecommunication Environments

This report considers the application of Articial Intelligence (AI) techniques to the problem of misuse detection and misuse localisation within telecommunications environments. A broad survey of techniques is provided, that covers inter alia rule based systems, model-based systems, case based reasoning, pattern matching, clustering and feature extraction, articial neural networks, genetic algorithms, arti cial immune systems, agent based systems, data mining and a variety of hybrid approaches. The report then considers the central issue of event correlation, that is at the heart of many misuse detection and localisation systems. The notion of being able to infer misuse by the correlation of individual temporally distributed events within a multiple data stream environment is explored, and a range of techniques, covering model based approaches, `programmed' AI and machine learning paradigms. It is found that, in general, correlation is best achieved via rule based approaches, but that these suffer from a number of drawbacks, such as the difculty of developing and maintaining an appropriate knowledge base, and the lack of ability to generalise from known misuses to new unseen misuses. Two distinct approaches are evident. One attempts to encode knowledge of known misuses, typically within rules, and use this to screen events. This approach cannot generally detect misuses for which it has not been programmed, i.e. it is prone to issuing false negatives. The other attempts to `learn' the features of event patterns that constitute normal behaviour, and, by observing patterns that do not match expected behaviour, detect when a misuse has occurred. This approach is prone to issuing false positives, i.e. inferring misuse from innocent patterns of behaviour that the system was not trained to recognise. Contemporary approaches are seen to favour hybridisation, often combining detection or localisation mechanisms for both abnormal and normal behaviour, the former to capture known cases of misuse, the latter to capture unknown cases. In some systems, these mechanisms even work together to update each other to increase detection rates and lower false positive rates. It is concluded that hybridisation offers the most promising future direction, but that a rule or state based component is likely to remain, being the most natural approach to the correlation of complex events. The challenge, then, is to mitigate the weaknesses of canonical programmed systems such that learning, generalisation and adaptation are more readily facilitated

Smoothness Properties of the Unit Ball in a JB*-Triple

An element a of norm one in a JB*-triple A is said to be smooth if there exists a unique element x in the unit ball A1* of the dual A* of A at which a attains its norm, and is said to be Fréchet-smooth if, in addition, any sequence (xn) of elements in A1* for which (xn(a)) converges to one necessarily converges in norm to x. The sequence (a2n+1) of odd powers of a converges in the weak*-topology to a tripotent u(a) in the JBW*-envelope A** of A. It is shown that a is smooth if and only if u(a) is a minimal tripotent in A** and a is Fréchet-smooth if and only if, in addition, u(a) lies in

Structural Projections on JBW*-Triples

A linear projection R on a Jordan*-triple A is said to be structural provided that, for all elements a, b and c in A, the equality {Rab Rc} = R{a Rbc} holds. A subtriple B of A is said to be complemented if A = B + Ker(B), where Ker(B) = {a∈A: {B a B} = 0}. It is shown that a subtriple of a JBW*-triple is complemented if and only if it is the range of a structural projection. A weak* closed subspace B of the dual E* of a Banach space E is said to be an N*-ideal if every weak* continuous linear functional on B has a norm preserving extension to a weak* continuous linear functional on E* and the set of elements in E which attain their norm on the unit ball in B is a subspace of E. It is shown that a subtriple of a JBW*-triple A is complemented if and only if it is an N*-ideal, from which it follows that complemented subtriples of A are weak* closed, and structural projections on A are weak* continuous and norm non-increasing. It is also shown that every N*-ideal in A possesses a triple product with respect to which it is a JBW*-triple which is isomorphic to a complemented subtriple of

Compact tripotents in bi-dual JB*-triples

The set consisting of the partially ordered set of tripotents in a JBW*-triple C with a greatest element adjoined forms a complete lattice. This paper is mainly concerned with the situation in which C is the second dual A** of a complex Banach space A and, more particularly, when A is itself a JB*-triple. A subset of consisting of the set of tripotents compact relative to A (denned in Section 4) with a greatest element adjoined is studied. It is shown to be an atomic complete lattice with the properties that the infimum of an arbitrary family of elements of is the same whether taken in or in and that every decreasing net of non-zero elements of has a non-zero infimum. The relationship between the complete lattice and the complete lattice where B is a Banach space such that B** is a weak*-closed subtriple of A** is also investigated. When applied to the special case in which A is a C*-algebra the results provide information about the set of compact partial isometries relative to A and are closely related to those recently obtained by Akemann and Pedersen. In particular it is shown that a partial isometry is compact relative to A if and only if, in their terminology, it belongs locally to A. The main results are applied to this and other example

Distal ventriculoperitoneal shunt failure secondary to Clostridium Difficile Colitis

Journal ArticleDistal ventriculoperitoneal shunt obstruction is typically associated with cerebrospinal fluid (CSF) infection, fluid pseudocysts, bowel obstruction, bowel perforation, or improper shunt placement in the abdomen. We describe a unique etiology for distal shunt obstruction secondary to Clostridium difficile pancolitis that occurred because of inflammation and ascites, which led to incomplete drainage and absorption of CSF. This case illustrates the importance of considering distal shunt obstruction in a patient with signs of abdominal pathology in the setting of mental status changes, and the effective treatment of this patient initially with distal catheter externalization followed by internalization of a new distal catheter after resolution of the pancoliti

Comparison of radiosurgery and conventional surgery for the treatment of glomus jugulare tumors

Journal ArticleObject. The optimal management of glomus jugulare tumors remains controversial. Available treatments were once associated with poor outcomes and significant complication rates. Advances in skull base surgery and the delivery of radiation therapy by stereotactic radiosurgery have improved the results obtained using these treatment options. The authors summarize and compare the contemporary outcomes and complications for these therapies. Methods. Papers published between 1994 and 2004 that detailed the use of radiosurgery or surgery to treat glomus jugulare tumors were reviewed. Eight radiosurgery series including 142 patients and seven surgical studies including 374 patients were evaluated for neurological outcome, change in tumor size (radiosurgery) or percent of total resection (surgery), recurrences, tumor control, need for further treatment, and complications. The mean age at treatment for patients who underwent surgery and radiosurgery was 47.3 and 56.7 years, respectively. The mean follow-up duration was 49.2 and 39.4 months, respectively. The surgical control rate was 92.1%, with 88.2% of tumors totally resected in the initial surgery. A cerebrospinal fluid leak occurred in 8.3% of patients who underwent surgery and recurrences were found in 3.1%; the mortality rate was 1.3%. Among patients who underwent radiosurgery, tumors diminished in 36.5%, whereas 61.3% had no change in tumor size, and subjective or objective improvements occurred in 39%. Despite the presence of residual tumor in 100% of radiosurgically treated patients, recurrences were found in only 2.1%, the morbidity rate was 8.5%, and there were no deaths. Conclusions. Death and recurrences after these treatments are infrequent, and therefore both treatments are considered to be safe and efficacious. Although surgery is associated with higher morbidity rates, it immediately and totally eliminates the tumor. The radiosurgery results are very promising, although the incidence of late recurrence (after 10-20 years) is unknown

Trigeminal amyloidoma: case report and review of the literature

ManuscriptThe authors present a case of amyloid infiltration involving the trigeminal nerve that mimicked a malignant cavernous sinus tumor with perineural tumor infiltration. A 64-year-old man presented with trigeminal nerve numbness. Imaging revealed a plaque-like enhancing lesion along the right lateral cavernous sinus extending anteriorly into Meckel's cave and involving the proximal V2 and V3 trigeminal nerves. The patient underwent extradural frontotemporal craniotomy with middle fossa exposure of the cavernous sinus to diagnose and treat the presumed malignant cavernous sinus tumor. A reddish mass involving the lateral dural wall of the cavernous sinus was resected. There was also enlargement of the gasserian ganglion and second and third divisions of the trigeminal nerve, the latter of which was biopsied. Permanent histopathological studies demonstrated microscopic eosinophilic, amorphous material, which stained positive for Congo red, and absence of neoplastic cells. The final diagnosis was amyloidoma. Thus, amyloidomas may occur from the trigeminal nerve or ganglia and should be considered in the differential diagnosis of a cavernous sinus lesion mimicking a tumor. The few reports of trigeminal amyloidomas are reviewed and the presentation, imaging, and management of this skull base lesion are discussed. Overall, patients may have symptomatic improvement of trigeminal neuropathy with resection of the amyloidoma outside of the nerve capsule that is compressing the nerve, while resection of the lesion from within the capsule may result in permanent trigeminal nerve dysfunction