Integrating geometries of ReLU feedforward neural networks

This paper investigates the integration of multiple geometries present within a ReLU-based neural network. A ReLU neural network determines a piecewise affine linear continuous map, M, from an input space ℝm to an output space ℝn. The piecewise behavior corresponds to a polyhedral decomposition of ℝm. Each polyhedron in the decomposition can be labeled with a binary vector (whose length equals the number of ReLU nodes in the network) and with an affine linear function (which agrees with M when restricted to points in the polyhedron). We develop a toolbox that calculates the binary vector for a polyhedra containing a given data point with respect to a given ReLU FFNN. We utilize this binary vector to derive bounding facets for the corresponding polyhedron, extraction of "active" bits within the binary vector, enumeration of neighboring binary vectors, and visualization of the polyhedral decomposition (Python code is available at https://github.com/cglrtrgy/GoL_Toolbox). Polyhedra in the polyhedral decomposition of ℝm are neighbors if they share a facet. Binary vectors for neighboring polyhedra differ in exactly 1 bit. Using the toolbox, we analyze the Hamming distance between the binary vectors for polyhedra containing points from adversarial/nonadversarial datasets revealing distinct geometric properties. A bisection method is employed to identify sample points with a Hamming distance of 1 along the shortest Euclidean distance path, facilitating the analysis of local geometric interplay between Euclidean geometry and the polyhedral decomposition along the path. Additionally, we study the distribution of Chebyshev centers and related radii across different polyhedra, shedding light on the polyhedral shape, size, clustering, and aiding in the understanding of decision boundaries.

High plasma D-dimer level is associated with decreased survival in patients with lung cancer

AIMS

An elevated plasma D-dimer level indicates the activation of coagulation and fibrinolysis. In the present study, we investigated the association of pre-treatment haemostatic parameters (D-dimer, fibrinogen and prothrombin fragment 1+2) with clinicopathological parameters and outcome in patients with lung cancer.

MATERIALS AND METHODS

Plasma levels of D-dimer and other parameters were measured in 78 evaluable patients with lung cancer (60 non-small cell lung cancers, 18 small cell lung cancers). At diagnosis, 35 patients (44.9%) were locally advanced stage (IIIA/B) and 43 patients (55.1%) had metastatic disease (IV). Multivariate statistical analysis was carried out using Cox's proportional hazards model. The receiver operating characteristic curve was used to determine the cut-off values for D-dimer, fibrinogen and prothrombin fragment 1+2.

RESULTS

The median survival for all patients was 264 days (95% confidence interval 200-328 days). A significant association between the plasma levels of D-dimer and the response to chemotherapy was observed (P=0.03). With the univariate analysis, tumour stage, pre-treatment plasma levels of D-dimer, fibrinogen, platelet count, lactate dehydrogenase concentration and Karnofsky performance status were predictive for survival. With the multivariate analysis (P< or =0.1), the plasma level of D-dimer (P<0.001), tumour stage (P=0.01) and Karnofsky performance status (P=0.02) were identified as independent predictive factors. The median survival times were 405 days (95% confidence interval 165-644 days) and 207 days (95% confidence interval 146-267 days, P<0.001), respectively, for patients with a low D-dimer level (< or =0.65 microg/ml) and a high D-dimer level (>0.65 microg/ml).

CONCLUSIONS

Elevated plasma levels of D-dimer in patients with lung cancer are associated with decreased survival and a poor response to treatment. Pre-treatment for the D-dimer level may be useful in the prediction of survival and the response to treatment.

Laparoscopic versus open cholecystectomy: effect on pulmonary function tests

BACKGROUND/AIMS

Operations often cause impairment in respiration due to pain. This study was designed to compare the changes in pulmonary function tests after open and laparoscopic cholecystectomy.

METHODOLOGY

Two groups of 35 patients were randomly set up. Each patient had 3 pulmonary function tests performed and 2 postero-anterior grid chest roentgenograms taken. All of these data were evaluated by the same group of investigators.

RESULTS

After taking into consideration the difference between pulmonary function tests, values were not significant (P < or = 0.05). All pulmonary function test values decreased significantly on the 1st postoperative day (P < or = 0.05). When postero-anterior chest roentgenograms were compared no clinically evident atelectasis except 3 lineary was seen in the laparoscopic cholecystectomy group, whereas 5 lineary, 7 focal, and 3 segmentary atelectasia were encountered in the open cholecystectomy group (P < or = 0.05).

CONCLUSIONS

We believe that laparoscopic cholecystectomy has more advantages when speaking of postoperative pulmonary function tests and atelectasia.

Patellar metastasis from a lung epidermoid carcinoma

Patellar metastases are very rare. There have been approximately 20 cases reported in the literature. We have also noted two other reports of patellar metastasis from lung carcinoma as the first manifestation of lung cancer in our literature review. We present a case of patellar metastasis as the first manifestation of lung epidermoid carcinoma in a patient who was a smoker for 33 years.

The prevalence of allergic diseases in primary school children in Edirne, Turkey

BACKGROUND

Allergic diseases present a major health burden for children as shown by the rising morbidity and increased mortality from asthma. Information on the prevalences of allergic disorders and contributing factors as well will help to establish feasible measures to change this trend, and more efficient assignment of the limited health resources.

OBJECTIVE

To assess the prevalences of asthma and other allergic diseases and the contribution of various risk factors in primary school children in Edirne, Turkey.

METHODS

Children aged 7 to 12 in primary schools in the municipality and 24 villages of Edirne were surveyed via a questionnaire completed by the parents. The cumulative (lifetime) and current (last 12 months) prevalences of allergic diseases and the presence of passive smoking, atopic family history, animal contact and breast-feeding in infancy were determined.

RESULTS

A total of 5412 children (70.1% from the metropolitan and 29.9% from the rural area) were enrolled. The cumulative and current prevalences of all allergic diseases were 24.6% and 9.9% respectively. The cumulative (lifetime) prevalences of bronchial asthma, wheezing, allergic rhinitis and atopic dermatitis were 16.4%, 18.9%, 12.3% and 2.2%, and the current (last 12 months) prevalences were 5.6%, 5.8%, 4.5% and 0.9% respectively. Three-fourths of the children were exposed to tobacco smoke at home. Atopic heredity appeared the most prominent risk factor for any allergic disorder. Neither age, breast-feeding nor place of habitation affected the occurrence of allergic disorders. Animal contact was a significant risk factor for asthma and wheezing (adjusted odd ratios (OR) and 95% confidence intervals (CI) for current prevalences are 1.38 (CI = 1.04-1.83) and 1.35 (CI = 1.02-1.78) respectively), exposure to indoor tobacco smoke for wheezing (OR = 1.52, CI = 1.10-2.09), and male gender for asthma (OR = 1.50, CI = 1.16-1.93). Current prevalences for all allergic diseases were significantly lower than those previously reported in Ankara, Turkey.

CONCLUSIONS

Allergic diseases are a major health burden for primary school children in Edirne, Turkey. Although atopic heredity appears to be the foremost important risk factor, reduction of exposure to indoor tobacco smoke and animal contact, especially for those with atopic family history, are important preventive measures. The impact of environmental exposures on distinguishing prevalences of allergic diseases in Ankara and Edirne should be further investigated.

Malignant degeneration of mature cystic teratomas

Malignant transformation of benign cystic teratoma is rare and the most common malignancy is squamous cell carcinoma. The diagnosis is rarely made preoperatively and the prognosis is usually poor. We report 4 cases with dermoid cysts showing malignant transformation, 3 with squamous carcinoma and 1 with adenocarcinoma. The patients were within the reproductive age and underwent surgical intervention with intraoperative evaluation. Frozen section identified 2 cases with malignant transformation and staging laparotomy was performed at the initial laparotomy. One of the remaining underwent reoperation following a pregnancy termination and the other refused further surgery. None had metastases and/or capsule invasion. One had tumour rupture during excision and received combined chemotherapy following surgery. Three of the patients remain well and 1 is lost to follow-up.

Chronic pelvic pain in adolescent women. Diagnostic laparoscopy and ultrasonography

OBJECTIVE

To evaluate the correlation of preoperative pelvic examination and ultrasonography with the laparoscopic findings in 45 adolescent women with chronic pelvic pain.

STUDY DESIGN

Between January 1, 1989, and December 31, 1992, 45 adolescent women underwent diagnostic laparoscopy following a detailed clinical workup for evaluation of chronic pelvic pain.

RESULTS

Thirty-five of 45 pelvic examination findings correlated with the laparoscopic findings. The predictive values of normal and abnormal findings at pelvic examination were 42.8% and 93.5%, respectively. Ultrasonography (US) correlated with laparoscopy in 39 of 45 cases. The predictive value of normal findings at US was 60%, and that of abnormal findings was 94.2%. When both pelvic examination and US were normal, 50% of cases were abnormal at laparoscopy. However, laparoscopy revealed abnormality in 100% of patients with abnormal pelvic examinations and abnormal US findings.

CONCLUSION

Clinical evaluation of chronic pelvic pain, when combined with US, is highly predictive but needs confirmation, best provided by laparoscopy.

How does negative clinical evaluation of ovarian carcinoma after full course of chemotherapy correlate with second-look laparotomy findings?

Surgical reexploration was performed in 46 patients with epithelial nonmucinous ovarian adenocarcinoma requiring adjuvant chemotherapy whose initial therapy consisted of optimum debulking and surgical staging. All patients were placed on CAP (cisplatinum, Adriamycin, cyclophosphamide) chemotherapy for at least six courses until proved to be clinically disease free (mainly CA-125 below 35 U/ml and normal ultrasonography or computerized tomography). All women underwent second-look laparotomy (SLL) after completion of adjuvant therapy. We classified SLL findings in five categories, namely, no evidence of disease, cytological evidence of disease, histological evidence of disease, macroscopic evidence of disease (< 2 cm), and bulky tumor (> 2 cm). SLL demonstrated 14 (30%) patients with disease. Of these, five cases had histological evidence of disease and nine had macroscopic disease; however, we found no patient with persistent disease larger than 1.5 cm. No patient in stage I demonstrated disease at SLL. All cases with macroscopic disease and three cases with histological disease were initially in stage III. We found that about one third of cases who were clinically free of disease had persistent disease at the completion of chemotherapy. Hence, we conclude that routine SLL is still of importance in the management of patients with epithelial ovarian adenocarcinoma except those with stage I disease.