Neural networks with ReLU powers need less depth.

Despite the widespread success of deep learning in various applications, neural network theory has been lagging behind. The choice of the activation function plays a critical role in the expressivity of a neural network but for reasons that are not yet fully understood. While the rectified linear unit (ReLU) is currently one of the most popular activation functions, ReLU squared has only recently been empirically shown to be pivotal in producing consistently superior results for state-of-the-art deep learning tasks (So et al., 2021). To analyze the expressivity of neural networks with ReLU powers, we employ the novel framework of Gribonval et al. (2022) based on the classical concept of approximation spaces. We consider the class of functions for which the approximation error decays at a sufficiently fast rate as network complexity, measured by the number of weights, increases. We show that when approximating sufficiently smooth functions that cannot be represented by sufficiently low-degree polynomials, networks with ReLU powers need less depth than those with ReLU. Moreover, if they have the same depth, networks with ReLU powers can have potentially faster approximation rates. Lastly, our computational experiments on approximating the Rastrigin and Ackley functions with deep neural networks showed that ReLU squared and ReLU cubed networks consistently outperform ReLU networks.

Optimal Selection of COVID-19 Vaccination Sites at the Municipal Level

In this work, we present an approach to determine the optimal location of coronavirus disease (COVID-19) vaccination sites at the municipal level. We assume that each municipality or town is subdivided into smaller administrative units, which we refer to as villages or barangays. The proposed method solves a minimization problem arising from a facility location problem, which is formulated based on the proximity of the vaccination sites to the villages, number of COVID-19 cases, and population densities of the villages. We present a numerical scheme to solve the optimization problem and give a detailed description of the algorithm, which is coded in Python. To make the results reproducible, the codes used in this study are uploaded to a public repository, which also contains complete instructions on how to use them. As an illustration, we apply our method in determining the optimal location of vaccination sites in San Juan, a town in the province of Batangas, in the Philippines. We hope that this study may guide the local government units in coming up with strategic plans for the COVID-19 vaccine rollout.

Low Protein Z levels in patients with plasma cell neoplasms are inversely correlated with IL-6 levels.

Patients with multiple myeloma (MM) have an increased thrombotic risk, but pathogenesis remains uncertain. Low levels of Protein Z (PZ), a vitamin K-dependent plasma protein, are associated with venous as well as arterial thrombosis. The purpose of this study was to analyze PZ levels in patients with plasma cell neoplasms. PATIENTS AND METHODS: The study consisted of 64 plasma cells neoplasm patients and 42 healthy individuals. Clinical investigations included measurement of plasma PZ and IL-6 levels. RESULTS: PZ levels in patients with plasma cell neoplasms were significantly lower compared to healthy controls in the entire cohort (1392±659 vs.2010±603ng/mL, P<0.01), as well as in specific disease subgroups; symptomatic MM (1428±652ng/mL, p<0.01), smoldering MM (1437±883ng/mL, p=0.045) and monoclonal gammopathy of undetermined significance (MGUS) (1247±593ng/mL, p=0.01). PZ was negatively correlated with IL-6 levels in MM patients (r=-0.7, P<0.01). There was no significant difference in PZ levels between patients with or without thrombotic event. CONCLUSION: Plasma cell neoplasm patients have low levels of PZ. This is presumably related to the increased IL-6 production by the bone marrow microenvironment, and could have a potential role in the increased thrombotic tendency in those patients.

[Gases in vitreoretinal surgery]. / Plyny vo vitreoretinálnej chirurgii.

AIM: To evaluate the importance and benefits of using gases in vitreoretinal surgery. MATERIAL AND METHODS: The gases represent a wide group of substances used in eye surgery for more than 100 years. The role of intraocular gases in vitreoretinal surgery is irreplaceable. Their use is still considered to be the "gold standard". An important step in eye surgery was the introduction of expanding gases--sulfur hexafluoride and perfluorocarbons into routine clinical practice. The most common indications for the use of intraocular gases are: retinal detachment, idiopathic macular hole, complications of vitreoretinal surgery and others. RESULTS AND CONCLUSIONS: The introduction of intraocular gases into routine clinical practice, along with other modern surgical techniques resulted in significant improvement of postoperative outcomes in a wide range of eye diseases. Understanding the principles of intraocular gases use brings the benefits to the patient and physician as well. Due to their physical and chemical properties they pose far the best and most appropriate variant of intraocular tamponade. Gases also bring some disadvantages, such as difficulties in detailed fundus examination, visual acuity testing, ultrasonographic examination, difficulties in application of intravitreal drugs or reduced possibility of retina laser treatment. The gases significantly change optical system properties of the eye. The use of gases in vitreoretinal surgery has significantly increased success rate of retinal detachment surgery, complicated posterior segment cases, trauma, surgery of the macula and other diseases.

[Diagnosing of Acanthamoeba keratitis]. / Diagnostika akantamébovej keratitídy.

Acanthamoeba keratitis is rare corneal disease, its etiology is caused by amoebae of the Acanthamoeba spp. In this paper, the newest findings about the diagnostic and treatment procedures of the disease and epidemiology and preventive issues from the point of public health are presented. The article presents results of the water quality monitoring (according to the Acanthamoeba which is possible to cultivate at 36 degrees C and 44 degrees C) in man-made swimming pools during the period 2004-2008 at the Department of environmental biology of the Regional Public Health Institute in Banská Bystrica, Slovakia, E.U. The examination methods present the techniques of the clinical sampling and taking samples from the environment. The results underline the use of the new effective criteria in controlling of recreational resorts as well as changes of the legal criteria for the water quality used by the public. The results show that the presence of Acanthamoeba spp. in the environment is common, so the water monitoring is perceived as substantial preventive issue to prevent the disease to emerge. The collaboration between the public heath departments and ophthalmologists during the examination of the clinical and environmental samples may help to prevent and diagnose the Acanthamoeba keratitis.

[Lucentis in treatment of the wet-form of age-related macular degeneration--two years experience]. / Lucentis v liecbe vlhkej formy vekom podmienenej degenerácie makuly--dvojrocné skúsenosti.

In a study group of 114 patients (39 males, 75 females) with mean age of 72, 5 years (from 52 to 89 years) with mean follow-up of 8 month we retrospectively studied the effectivity and safety of intravitreal aplication of ranibizumab = Lucentis in the case of wet form of age-related macular degeneration (AMD). All patients met the inclusion criteria. The treatmet was realized on outpatient basis under strict application protocol. In the follow-up period the visual acuity improved in 66 patients (57%), stabilization was achieved in 17 patients (24.9%). In a group of 31 patients (27.2%) the central acuity deteriorated. There were no peroperative complications. In the postoperative period we observed in 22 patients temporary rise of intraocular pressure, in 21 patients suffusion, and in 3 patients there were subretinal haemorrhages found, in 1 case rupture of RPE and in 1 case anterior ischemic opticopathy was observed. Results observed in this study are in full compliance with PRONTO and PIER studies.

[Rhegmatogenous retinal detachment and its treatment]. / Rhegmatogénne odlúpenie sietnice a jeho liecba.

We have analyzed the surgery results of rhegmatogenous retinal detachment (RD) on 73 patients (76 eyes) operated on in 2000. Retinal reattachment was achieved on 59 eyes (77.6%) without silicone oil tamponade (SO) and on 17 eyes (22.4%) with the use of permanent silicone oil tamponade. Visual acuity following the operation was improved on 47 eyes (61.8%). Visual acuity 20/20-20/40 was reached on 16 eyes (21.1%), 20/60-20/120 on 35 eyes (46.0%), 20/200-4/200 on 19 eyes (25.0%), worse than 4/200 on 6 eyes (7.9%). Based on contemporary surgical technique the most important criterion of anatomical and functional success with the retinal detachment treatment is the time between RD onset and the time of the surgery, as well as the presence and extent of proliferative vitreoretinopathy.

[Refractive surgery in Slovakia]. / Refrakcná chirurgia na Slovensku.

Since 1991 the chief specialist evaluates different spheres of ophthalmology based on data provided by all departments in Slovakia. In the submitted article the author summarizes the 10-year period of refractive surgery in Slovakia.

Multicenter study of the Artisan phakic intraocular lens.

PURPOSE: To assess the Artisan intraocular lens to correct myopia in phakic eyes. SETTING: European multicenter study sponsored by Ophtec BV, Groningen, The Netherlands. METHODS: In this prospective multicenter clinical study, the Artisan lens was implanted in 518 eyes between September 1991 and October 1999. The power of the lenses ranged from -5.0 to -20.0 diopters (D). Follow-up examinations were performed at 6 months and 1, 2, and 3 years. Follow-up ranged from 6 months (n = 454) to 3 years (n = 249). The preoperative uncorrected visual acuity (UCVA) was not recorded but was estimated to be worse than 0.1. The preoperative mean best spectacle-corrected visual acuity (BSCVA) was 0.67 +/- 0.26 (SD). Endothelial cell counts were done at 6 months and 1, 2, and 3 years in a subgroup of 129 eyes. RESULTS: A UCVA of 20/40 or better was observed in 76.8% of eyes regardless of the postoperative goal. A BSCVA of 20/40 or better was observed in 93.9% of eyes and remained stable throughout the follow-up. Of the eyes with extremely high myopia (>-15.0 D), 63.3% gained 2 or more lines of BSCVA; of those with moderate myopia (-5.0 to -10.0 D), 23.5% gained 2 or more lines. The mean endothelial cell density change was 4.8% at 6 months, 2.4% at 1 year, 1.7% at 2 years, and 0.7% at 3 years. The incidence of persistent adverse events at 3 years was relatively low. Secondary surgical interventions included repositioning of the lens because of poor initial placement and lens exchange because of preoperative power calculation errors. Glare and halo effects during night driving were noted and were related to large pupils in young patients. CONCLUSION: The Artisan lens is a safe, stable, efficacious, and predictable method to correct -5.0 to -20.0 D of myopia. This study suggests that the corneal endothelial cell loss is stabilized to the physiologically normal level after 3 years.

[Microsurgery of cataracts in glaucoma]. / Mikrochirurgia katarakty pri glaukóme.

In a group of 205 implantations of artificial intraocular lenses in 172 patients with glaucoma the authors demonstrate that microsurgery of cataract with implantation, in particular of posterior chamber lenses, has also a permanent hypotonic effect. 155 eyes (75.6%) with primary glaucoma were operated and 50 eyes (24.4%) with secondary glaucoma, 198 times (96.6%) primary implantation was used and 7 times (3.4%) secondary implantation. The highest ratio in the group was formed by extracapsular extractions in 95.0%, intracapsular extractions in 3% and phacoemulsification in 2%. One of the greatest obstacles of microsurgery of cataract in eyes affected with glaucoma is the narrow pupil. The authors give an account of possible solutions of this problem. Vision of 5/10 or better with correction was achieved in 68.8%. The most frequent cause of reduced vision of less than 5/50 was atrophy of the TZN in 11.25% Permanent compensation of intraocular pressure without further treatment was observed in 64.4% during a mean follow-up period of 66.7 months.

[10,000 implants of artificial intraocular lenses at the Ophthalmology Department of the Regional Hospital in Banská Bystrica]. / 10,000 implantácií umelých vnútroocných sosoviek na ocnom oddelení KNsP v Banskej Bystrici.

Since December 6, 1979 till October 31, 1995 at the Ophthalmological Department of the Regional hospital (now F.D. Roosevelt's Eye Clinic) in Banská Bystrica 10,000 artificial intraocular lenses were implanted. The author reminds in a historical review of the initial pioneer work and implantations implemented by Vanýsek et al. in 1951-1960. After 20 years the author took up the tradition and implanted on December 6, 1979 the first iris clip Fjodorov-Zacharov lens. Since 1979 every year the number of implantations in the department rises. Since 1985 almost only various models of posterior chamber intraocular lenses are implanted. As to unconventional materials hydrogel and silicone lenses were implanted, first after extracapsular cataract extraction and later in the folded state after phacoemulsification. At present modern surgery of cataract and implantation of artificial intraocular lenses in made as a matter of routine in the majority of departments in the Czech and Slovak Republic.

[Extraction of a clear lens-cataract as refractive surgery in severe myopia]. / Extrakcia círej sosovky--kararakty ako refrakcná operácia pri t'azkej krátkozrakosti.

Fukals operation (extraction of a transparent lens in severe myopia) was of a long time considered risky in particular because of possible retinal complications. Based on ten years experience (1985 - 1994) the authors provide evidence that modern microsurgical methods, in particular phacoemulsification make it possible to perform this operation at a qualitatively higher level, much more safety and with a lower rate of complications. In a group of 284 operated eyes with myopia (15.96 diopters) were 4.57% transparent lenses, 37.68% with mild partial turbidity and 57.75% with dense or complete turbidity. Corrected vision 5/5 - 5/10 was achieved in 44.37%. Peroperative prolapse of the vitreous body occurred in 5.28%. The most frequent late complication was secondary cataract (26.76%). During the mean follow-up period of 37.57 months there was no case of cystoid oedema of the macula or detachment of the retina. Extraction of a transparent lens or incipient cataract in severe myopia is becoming an alternative method of other refractive operations.

[An increasing trend in cataract surgery in Slovakia (1990-1993)]. / Narastajúci trend chirurgie katarakty na Slovensku (1990-1993).

The authors present data obtained in an enquiry from all Ophthalmological Clinics and departments in Slovakia which were concerned with surgery of cataract in 1990-1993. They evaluate the number of cataracts, implanted artificial intraocular lenses, the applied surgical methods and types of implanted lenses. During the period of investigation the number of operated cataracts increased by 66%, the number of implanted lenses increased from 29% to 66.8% of the total number of operated cataracts. The number of departments which implant artificial lenses increased from 38.7% to 81.8%. The EKEK method is already used in 85%. Slowly also the number of phacoemulsifications is rising from 1.9% to 6.2%.

[Development of cataract surgery and implantation of artificial intraocular lenses in Czecho-Slovakia 1988-1992]. / Vývoj chirurgie katarakty a implantácie umelých vnútorných sosoviek v Cesko-Slovensku v rokoch 1988-1992.

After a brief introduction on the history of implantations of synthetic intraocular lenses in Czechoslovakia the authors present an analysis of surgery of cataract and implantation of artificial intraocular lenses during the past five years in Czechoslovakia. The number of operations of cataract increases every year, a substantial increase was recorded in particular in 1992. During the other years there is also a change from intracapsular to extracapsular extraction of cataract and a slow onset of phacoemulsification. The number of departments where artificial lenses are implanted is increasing as well as the ratio of implantations in relation to the total of cataract surgery. In particular during the remaining three years a marked rise of implantation of posterior chamber lenses was recorded and a decline in implantations of iris-clip lenses. Almost 95% of implantations of posterior chamber lenses is considered satisfactory, while less than 60% implantations from the total number of cataract surgery is still insufficient.