Quest for molecular graphs with maximal energy: a computer experiment

If lambda(1), lambda(2),..., lambda(n) are the eigenvalues of a graph G, then the energy of G is defined as E(G) = the absolute value of lambda(1) + the absolute value of lambda(2) +.... + the absolute value of lambda(n). If G is a molecular graph, representing a conjugated hydrocarbon, then E(G) is closely related to the respective total pi-electron energy. It is not known which molecular graph with n vertices has maximal energy. With the exception of m = n - 1 and m = n, it is not known which molecular graph with n vertices and m edges has maximal energy. To come closer to the solution of this problem, and continuing an earlier study (J. Chem. Inf. Comput. Sci. 1999, 39, 984-996, ref 7), we performed a Monte Carlo-type construction of molecular (n,m)-graphs, recording those with the largest (not necessarily maximal possible) energy. The results of our search indicate that for even n the maximal-energy molecular graphs might be those possessing as many as possible six-membered cycles; for odd n such graphs seem to prefer both six- and five-membered cycles.

On walks in molecular graphs

Walks in molecular graphs and their counts for a long time have found applications in theoretical chemistry. These are based on the fact that the (i, j)-entry of the kth power of the adjacency matrix is equal to the number of walks starting at vertex i, ending at vertex j, and having length k. In recent papers (refs 13, 18, 19) the numbers of all walks of length k, called molecular walk counts, mwc(k), and their sum from k = 1 to k = n - 1, called total walk count, twc, were proposed as quantities suitable for QSPR studies and capable of measuring the complexity of organic molecules. We now establish a few general properties of mwc's and twc among which are the linear dependence between the mwc's and linear correlations between the mwc's and twc, the spectral decomposition of mwc's, and various connections between the walk counts and the eigenvalues and eigenvectors of the molecular graph. We also characterize the graphs possessing minimal and maximal walk counts.

Relation between distance-based topological indices

The pi-index of the line graph of the molecular graph of an alkane is shown to be related to the pi, Harary, and reciprocal Wiener indices of that alkane. Thus a mathematical relation between several distance-based topological indices is obtained.

An algorithm for the calculation of the hyper-Wiener index of benzenoid hydrocarbons

An algorithm for the calculation of the hyper-Wiener index (WW) of benzenoid hydrocarbons (both cata- and pericondensed) is described, based on the consideration of pairs of elementary cuts of the corresponding benzenoid graph B. A pair of elementary cuts partitions the vertices of B into four classes. WW is expressed as a sum of terms of the form n11n22 + n12n21, each associated with a pair of elementary cuts; nrs, r, s = 1, 2 are the numbers of vertices in the respective four classes. The algorithm proposed enables a relatively easy calculation of WW, finding expressions for WW of homologous series of benzenoid hydrocarbons, and envisaging the relations between WW and molecular structure.

Presumed ocular myasthenia and micropsia. A case report

A 68-year-old woman presented with diplopia. Fluctuations of dysfunction of lateral rectus muscles in both eyes were detected on consecutive examinations. The diagnosis of ocular myasthenia was proposed. After the initiation of therapy, the patient complained of disturbing micropsia. The micropsia and diplopia were relieved by occlusion of one eye or by a base-out prism over one of the patient's eyeglass lenses. Mechanisms of micropsia are discussed.

Optic nerve compression by carotid arteries in low-tension glaucoma

Low-tension glaucoma (LTG) is manifested by glaucomatous optic nerve damage and visual field loss despite normal intraocular pressure (IOP). We describe 62 patients with classical signs of LTG. Computed tomography (CT) was performed in all patients. In 56 of the patients (90.3%), pathology of the intracavernous carotid arteries adjacent to the intracranial opening of the optic canal could be demonstrated. In 28 patients (45.2%) a clear asymmetry of the optic nerve cupping was found and could be correlated with the severity of the carotid artery pathology. A control group of 24 age-matched patients included five (20.8%) with intracavernous carotid artery calcification and only one (4.2%) with intracavernous ectasia. We suggest that calcification, dilatation and ectasia of the carotid artery into the optic canal may play an important role in the pathogenesis of many cases of LTG. The close proximity of the carotid artery to the optic nerve at this location may result in compressive neuropathy with subsequent glaucomatous damage of the optic nerve head.

Suggested mechanism for acute transient myopia after sulfonamide treatment

This report describes the occurrence of acute transient myopia in a patient treated with sulfonamide. We followed this patient by performing A-scan ultrasonographic ocular measurements documenting the anterior chamber depth, lens thickness, and axial length during the acute and convalescent periods. The outstanding feature in this case was the documented ultrasonographically significant reduction of the anterior chamber depth combined with lens thickening. This could be caused by a forward displacement of the lens as a result of allergic ciliary body edema and rotation. These changes could explain the mechanism of drug-induced transient myopia.

Orbital pseudotumor presenting as acute glaucoma with choroidal and retinal detachment

A 68-year-old woman presented with acute visual loss, elevated intraocular pressure (IOP), and a flat anterior chamber combined with retinal and choroidal detachment. The diagnosis of orbital pseudotumor was based on the patient's poor response to conventional therapy and on computerized tomography and ultrasound findings. After treatment with oral corticosteroids, the inflammatory process, elevated IOP, and choroidal and retinal detachment resolved.

Malignant prolactinoma

Malignant prolactinoma is a rare entity and only a few cases have been published. The diagnostic criteria and the clinical course remain unclear. We present a case of malignant prolactinoma in a woman with a 30-year duration of the disease. In the terminal stage of the disease the prolactinoma metastasized to the left eye, the prolactin level reaching 196000 mU/l. Bromocriptine in high doses was not effective. The response to pergolide was good in the first two years of treatment; thereafter an escape effect was observed. The patient died in a comatose state. A review of previously published cases follows.

Lumbar spine dimensions in paraparetic patients: a 10 year follow up study

Lumbar spinal AP radiographs of 13 C3-T11 paraparetic patients taken at about a 10 year interval were compared. The height (H) and maximum width (W) of the interapophysolaminar spaces (IALS), the width of the vertebral bodies at their waist (V) and the relationship between them showed minimal change over the follow up period. The difference between the late and early mean IALS height values increased caudally but was statistically significant only below L5. Subjective evaluation of the consecutive x-ray films revealed few new degenerative abnormalities. It is concluded that the normal aging process, which includes horizontal spreading of the lumbar vertebral bodies and narrowing of the lumbar spinal canal, is not accelerated by paraparesis and may even be retarded by relative immobilization.

Nd:YAG laser trabeculopuncture in angle-recession glaucoma

Nd:YAG laser trabeculopuncture (YLT) was performed in 12 eyes of 12 patients with angle-recession glaucoma. Confluent, 1-clock-hour trabeculotomy was attempted in all eyes. The calculated average laser energy was 181 +/- 86 mJ. Where possible, the midtrabecular meshwork was treated, preferably at the superior half. After a mean follow up of 12.0 +/- 5.6 months, intraocular pressure (IOP) was controlled (less than or equal to 19 mm Hg) in five eyes (41.7%). YLT was associated with blood reflux during or after treatment in all successfully treated eyes. In eyes that failed, blood reflux could be detected in only two of seven eyes (28.6%). YLT failed to control IOP in all five eyes that had angle-recession for 360 degrees. Following YLT, IOP rose in two eyes (16.6%), minimal hyphema occurred in one eye, and temporary flare and cells developed in the anterior chamber in all eyes. Six eyes (50%) required glaucoma surgery (four had trabeculectomy and two had Molteno implant surgery). We recommend YLT only for selected cases of uncontrolled angle-recession glaucoma in which at least part of the trabecular meshwork by gonioscopy appears to maintain its anatomical structure, permitting penetration into Schlemm's canal.

The Range of the Wiener Index and Its Mean Isomer Degeneracy

Sharp lower and upper bounds for the Wiener index (W) of a connected (n, m)-graph are reported; n = number of vertices, m = number of edges. The mean isomer degeneracy of W is estimated and is shown to unboundedly increase with increasing n. Thus the isomer-discriminating power of W is confirmed to be very low in the case of large molecules.

Identification, prevention, and treatment of silicone oil pupillary block after an inferior iridectomy

We treated two patients in whom silicone oil pupillary block developed despite a patent inferior iridectomy. The clinical characteristics of this complication were a deep anterior chamber, specular reflexes from the iris surface, identification by biomicroscopy of aqueous trapped inferiorly in the vitreous cavity, and no convection currents in the anterior chamber. This complication may be prevented by early face-down positioning of the patient after the operation, and the avoidance of large, centrally located, inferior iridectomies. We recommend that the iridectomy be placed peripherally no larger than 2 mm and propose a new technique for breaking the silicone oil block, which was clearly successful in one of the patients.

Postoperative complications after Molteno implant surgery

We performed Molteno implant surgery in one eye each of 41 patients with uncontrolled glaucoma. Intraocular pressure was controlled (intraocular pressure less than or equal to 18 mm Hg) in 32 eyes (78%). The mean preoperative intraocular pressure was 40 +/- 13.2 mm Hg, whereas the mean postoperative intraocular pressure was 16 +/- 6.6 mm Hg. Patients were followed up for an average of 16 months after the operation. Visual acuity was unchanged in 23 eyes (56%), improved in nine eyes (22%), and poorer in nine eyes (22%). The major complications included shallow anterior chamber and hypotony in six eyes (14.6%), vitreous hemorrhage in two eyes (4.9%), retinal detachment in one eye (2.4%), and malignant glaucoma in two eyes (4.9%). Less grave complications included hyphema in four eyes (9.8%), peripheral choroidal effusion in 15 eyes (36.6%), obstruction of the tube in six eyes (14.6%), recession of the tube into the angle in two eyes (4.9%), erosion of the tube in one eye (2.4%), and Tenon's cyst formation in three eyes (7.3%).

Metastatic thyroid carcinoma masquerading as lacrimal gland tumor

A 56-year-old woman presented with orbital signs and symptoms suggestive of lacrimal gland tumor. An excised biopsy specimen was obtained and showed glandular tissue, which could be confused with lacrimal gland acini. Closer microscopic examination and immunohistochemical studies revealed a metastatic tumor of thyroid gland origin. Initially, there was no identifiable nodule in the thyroid, but 3 months later a thyroid nodule was found by ultrasound and radioisotope scan. The histopathologic appearance of the thyroid nodule was similar to that found in the orbit. This case demonstrates the usefulness of immunohistochemistry in establishing a diagnosis when the microscopic appearance is inconclusive.