Geometry of Discrete Quantum Computing

Conventional quantum computing entails a geometry based on the description of an n-qubit state using 2^{n} infinite precision complex numbers denoting a vector in a Hilbert space. Such numbers are in general uncomputable using any real-world resources, and, if we have the idea of physical law as some kind of computational algorithm of the universe, we would be compelled to alter our descriptions of physics to be consistent with computable numbers. Our purpose here is to examine the geometric implications of using finite fields Fp and finite complexified fields Fp^2 (based on primes p congruent to 3 mod{4}) as the basis for computations in a theory of discrete quantum computing, which would therefore become a computable theory. Because the states of a discrete n-qubit system are in principle enumerable, we are able to determine the proportions of entangled and unentangled states. In particular, we extend the Hopf fibration that defines the irreducible state space of conventional continuous n-qubit theories (which is the complex projective space CP{2^{n}-1}) to an analogous discrete geometry in which the Hopf circle for any n is found to be a discrete set of p+1 points. The tally of unit-length n-qubit states is given, and reduced via the generalized Hopf fibration to DCP{2^{n}-1}, the discrete analog of the complex projective space, which has p^{2^{n}-1} (p-1)\prod_{k=1}^{n-1} (p^{2^{k}}+1) irreducible states. Using a measure of entanglement, the purity, we explore the entanglement features of discrete quantum states and find that the n-qubit states based on the complexified field Fp^2 have p^{n} (p-1)^{n} unentangled states (the product of the tally for a single qubit) with purity 1, and they have p^{n+1}(p-1)(p+1)^{n-1} maximally entangled states with purity zero.Comment: 24 page

Outcome of Pediatric Cataract Surgeries in a Tertiary Center in Switzerland

Purpose. To determine and to analyze the outcome of pediatric cataract surgery. Methods. A retrospective chart review of individuals aged up to 10 years who underwent cataract surgery between January 1, 2004, and December 31, 2014, at the UniversityHospital Zurich, Switzerland. Results. 63 children (94 affected eyes) with bilateral (68/94) or unilateral (26/94) cataract were identified. Surgery was performed at a median age of 1.5 months (IQR: 1.3–2.6 months) for the aphakic group (45/94) and of 50.7 months (IQR: 38.0–78.4 months) for the IOL group (49/94). At the last follow-up visit (median 31.1 months, IQR: 18.4–50.2 months), visual acuity was better in bilateral than in unilateral cataract cases. Posterior capsular opacification (PCO) was diagnosed in 30.9% of eyes without a significant difference in the IOL and aphakic groups (p=0.12). Aphakic glaucoma was diagnosed in 12/45 eyes at a median of 6.8 months (IQR 2.1–13.3 months) after surgery. Microcornea (5/12) and anterior segment anomalies (8/12) were associated with glaucoma development (p<0.05). Conclusion. Laterality and timing of surgery influence the outcome of pediatric cataract surgery. PCO was the most frequent postoperative complication. Aphakic glaucoma is often associated with ocular developmental abnormalities and a poor visual outcome

Flicker electroretinogram in newborn infants

PURPOSE To develop and validate a flicker electroretinogram (ERG) protocol in term-born neonates as a potential tool for assessing preterm infants at risk of developing retinopathy of prematurity. METHODS A custom flicker ERG protocol was developed for use with the hand-held RETeval® electrophysiology device. Feasibility of measuring flicker ERG through closed eyelids and without mydriasis was established in a pilot study enabling optimisation of the test protocol. Following this, healthy term-born neonates (gestational age 37-42 weeks) were recruited at the Neonatology clinic of the University Hospital Zurich. Flicker ERG recordings were performed using proprietary disposable skin electrodes during the first four days of life when the infants were sleeping. Flicker stimuli were presented at 28.3 Hz for a stimulus series at 3, 6, 12, 30, and 50 cd·s/m$^{2}$, with two measurements at each stimulus level. Results were analysed offline. Flicker ERG peak times and amplitudes were derived from the averaged measurements per stimulus level for each subject. RESULTS 28 term-born neonates were included in the analysis. All infants tolerated the testing procedure well. Flicker ERG recording was achieved in all subjects with reproducible flicker ERG waveforms for 30 and 50 cd·s/m$^{2}$ stimuli. Reproducible ERGs were recorded in the majority of infants for the weaker stimuli (with detectable ERGs in 20/28, 25/28, and 27/28 at 3, 6, and 12 cd·s/m$^{2}$, respectively). Flicker ERG amplitudes increased with increasing stimulus strength, with peak times concurrently decreasing slightly. CONCLUSION Flicker ERG recording is feasible and reliably recorded in sleeping neonates through closed eyelids using skin electrodes and without mydriasis. Flicker ERG amplitude decreases for lower luminance flicker but remains detectable for 3 cd·s/m$^{2}$ flicker in the majority of healthy term-born neonates. These data provide a basis to study retinal function in premature infants using this protocol

Flicker electroretinogram in preterm infants

BACKGROUND Infants born prematurely are at risk of developing retinopathy of prematurity, which is associated with abnormalities in retinal function as measured using electroretinography. The aim of this study was to record non-invasive flicker electroretinograms (ERGs) in preterm infants and compare function of moderate and very or extremely preterm infants. METHODS In this non-randomized, cross-sectional study, 40 moderate preterm (gestational age (GA) 34 0/7 to 36 6/7 weeks, Group A) and 40 very or extremely preterm infants (GA ≤ 31 weeks, Group B) were recruited for flicker ERG recording through closed eyelids using the RETeval® device and skin electrodes. Group A was tested within the first week of life and Group B between 34th and 37th week postmenstrual age. Flicker stimuli were presented at 28.3 Hz with stimulus levels of 3, 6, 12, 30 and 50 cd•s/m$^{2}$. Primary endpoints were peak time (ms) and amplitude (µV). RESULTS Flicker ERGs were recordable in most infants with the highest proportion of reproducible ERGs at 30 cd•s/m$^{2}$. Amplitudes increased with stronger flicker stimulation, while peak times did not differ significantly between stimulus levels nor groups. Amplitudes were significantly greater in Group B at the strongest stimulus level (Mann-Whitney-U-Test=198.00, Z = 4.097, p = <0.001). CONCLUSIONS Feasibility of collecting flicker ERG data in most preterm infants was confirmed. We found no evidence of reduced retinal responses to flicker stimuli associated with extreme prematurity. Higher amplitudes in very and extremely preterm infants could indicate acceleration of retinal development following birth, triggered by visual stimulation

Vitamin A deficiency retinopathy related to medical interventions in a Swiss cohort: a case series

AIMS OF THE STUDY: Vitamin A deficiency retinopathy is a potentially blinding disease. In developed countries, vitamin A deficiency due to malnutrition is rare. However, vitamin A deficiency can be caused by malabsorption resulting from bowel resection or medication. In this retrospective study, we present five cases of vitamin A deficiency retinopathy related to malabsorption secondary to medical interventions. METHODS: Electronic charts over a ten-year period (2012–2022) were screened for vitamin A deficiency retinopathy. Only patients with vitamin A deficiency confirmed by laboratory tests were included. Symptoms, medical history, visual acuity, optical coherence tomography, fundus autofluorescence, electrophysiological examination, and vitamin A levels were reviewed. RESULTS: Five eligible cases were identified. Median age was 44.7 years (range 22.2–88.9), median duration of ocular symptoms prior to diagnosis was 14 months, and median visual acuity was 1.0 (range 0.5–1.0, Snellen, decimal). Three patients had a history of bariatric surgery, one patient had a small bowel resection and was on octreotide treatment, and one patient suffered from cystic fibrosis and had a history of small bowel resection and severe hepatopathy. Optical coherence tomography showed various abnormalities, including a reduced interdigitation zone, subretinal drusenoid deposits, and a thinned outer nuclear layer. Electroretinogram findings ranged from abnormal oscillatory potentials to non-recordable rod responses. CONCLUSIONS: Vitamin A deficiency retinopathy can occur following medical interventions associated with malabsorption. In cases of night blindness, vitamin A levels should be measured

Functional and Morphological Characteristics of the Retina of Patients with Drusen-like Deposits and Systemic Lupus Erythematosus Treated with Hydroxychloroquine: A Retrospective Study

Purpose: To evaluate the impact of drusen-like deposits (DLD) on retinal layer integrity and retinal function by optical coherence tomography (OCT) and multifocal electroretinography (mfERG) in patients with systemic lupus erythematosus (SLE). Methods: We identified 66 eyes of 33 SLE patients treated with hydroxychloroquine (HCQ) that were categorized into two groups according to whether DLDs were present (34 eyes, Group One) or absent (32 eyes, Group Two). The groups were matched for age, sex, HCQ treatment duration, daily, and cumulative dosage. OCT (retinal layer thicknesses, central retinal thickness, CRT) and mfERG concentric ring analysis were analyzed and compared. Results: CRT was significantly thicker in Group One compared to Group Two (273.21 ± 3.96 vs. 254.5 ± 7.62) (p = 0.023). Group One also demonstrated an overall thicker retinal pigment epithelium compared to Group Two; however, the other outer retinal layers, outer nuclear layer, and photoreceptor layer were found to be significantly thinner in Group One compared to Group Two. We found no differences in mfERG parameters between the two groups. Conclusions: DLDs in SLE patients lead to abnormal central retinal layer thickness, which has no measurable impact on cone-mediated retinal function assessed by mfERG

A three-year longitudinal study of retinal function and structure in patients with multiple sclerosis

BACKGROUND Researchers have in recent years begun to investigate ophthalmological manifestations of multiple sclerosis (MS) other than optic neuritis (ON), and it is now clear that changes to retinal function (measured using the electroretinogram, ERG) and structure (measured using optical coherence tomography, OCT) are found in MS patients irrespective of prior ON episodes. ERG results are consistent with dysfunctional bipolar cells, as in other autoimmune diseases. To date, studies have presented only cross-sectional data regarding ERG and OCT. We, therefore, studied the longitudinal course of ERG and OCT in patients with MS, as well as the effect of disability changes and non-ON clinical relapses on these functional and structural measures. METHODS MS patients (n = 23) participating in an ongoing longitudinal observational study were invited to take part in a 3-year ophthalmological substudy. ERG and OCT were performed, and measures of MS-related disability and relapse history were obtained. Study visits were repeated annually. ERG peak times, rod b-wave amplitude, mixed rod/cone and cone b-/a-wave amplitude ratios, thickness of the peripapillary retinal nerve fibre layer, and volumes of the segmented retinal layers/complexes were analysed. Using generalised estimating equation models adjusted for age, ON, and MS treatment status, we assessed changes to ERG and OCT over the study duration, the effect of changes in disability and recent non-ON MS relapses on ERG and OCT, and the effect of selected OCT parameters on corresponding ERG parameters. RESULTS At the group level, small fluctuations of several ERG peak times were recorded, with OCT values remaining stable. Increased disability between visits was associated with significant prolongation of mixed rod-cone ERG b-wave peak times. No evidence of associations between OCT and ERG parameters was observed. CONCLUSIONS Retinal bipolar cell function may be affected by changes in disability in patients with MS; however, recent non-ON MS clinical relapses appear not to affect ERG or OCT results. As ERG changes in MS patients over 3 years are likely to be small and of uncertain clinical relevance, longitudinal studies of retinal function in MS should be planned over an extended period

The effect of high-dose erythropoietin perinatally on retinal function in school-aged children born extremely or very preterm

PURPOSE: To investigate the long-term effects of high-dose recombinant human erythropoietin (rhEPO) administered during the perinatal period on retinal and visual function in children born extremely or very preterm. DESIGN: Randomized, double-blind clinical trial follow-up plus cohort study. METHODS: Setting: Department of Ophthalmology, University Hospital Zurich, Zurich, Switzerland. Study population: extremely or very preterm-born children aged 7-15 years, previously randomized to receive either high-dose rhEPO or placebo in the perinatal period. Inclusion criteria: participation in an ongoing neuropediatric study (EpoKids), written informed consent (IC). Exclusion criteria: previous ocular trauma or surgery; retinal or developmental disease unrelated to prematurity. Healthy control (HC) children of comparable age were recruited. Inclusion criteria: term birth, IC. Exclusion criteria: any ocular/visual abnormality, high refractive error. Intervention status (rhEPO/placebo) was unknown to examiners and subjects at examination, with examiners unblinded only after completion of all analyses. Observation procedures: Electroretinography (ERG) was performed with the RETeval device (LKC Technologies, Inc., Gaithersburg MD). Ophthalmological and orthoptic examinations excluded comorbidity in the prematurely born cohort and ocular diseases in the HC group. Main outcome measures: Scotopic and photopic ERG response amplitudes and peak times (6 amplitudes; 6 peak times). Secondary outcomes were habitual visual acuity and color discrimination performance (for descriptive summary only). RESULTS: No differences in ERG parameters between EPO (n=52; 104 eyes) and placebo (n=35; 70 eyes) subgroups were observed (all corrected p>0.05). Two cone system-mediated peak times were slightly slower in the placebo than HC (n=52; 104 eyes) subgroup (coefficient/95% confidence interval (CI) = 0.53/0.21 to 0.85 and 0.36/0.13 to 0.60; p = 0.012 and 0.022); a predominantly rod system-mediated peak time was slightly faster in the EPO than the HC subgroup (coefficient/95% CI = -4.33/-6.88 to -1.78; p = 0.011). Secondary outcomes were comparable across subgroups. CONCLUSIONS: Administration of high-dose rhEPO to infants born extremely or very preterm during the perinatal period has no measurable effects on retinal function in childhood compared to placebo. Premature birth may cause small, likely clinically insignificant effects on retinal function in childhood, which may be partially mitigated by administration of rhEPO during the perinatal period

A Hot DQ White Dwarf in the Open Star Cluster M35

We report the discovery of a hot DQ white dwarf, NGC 2168:LAWDS 28, that is a likely member of the 150-Myr old cluster NGC 2168 (Messier 35). The spectrum of the white dwarf is dominated by CII features. The effective temperature is difficult to estimate but likely > 20,000 K based on the temperatures of hot DQs with similar spectra. NGC2168:LAWDS 28 provides further evidence that hot DQs may be the ``missing'' high-mass helium-atmosphere white dwarfs. Based on published studies, we find that the DBA WD LP 475-242 is likely a member of the Hyades open cluster, as often assumed. These two white dwarfs are the entire sample of known He-atmosphere white dwarfs in open clusters with turnoff masses >2 solar masses. Based on the number of known cluster DA white dwarfs and a redetermination of the H-atmosphere:He-atmosphere ratio, commonly known as the DA:DB ratio, we re-examine the hypothesis that the H- to He-atmosphere ratio in open clusters is the same as the ratio in the field. Under this hypothesis, we calculate that five He-atmosphere WDs are expected to have been discovered, with a probability of finding fewer than three He-atmosphere white dwarfs of 0.08, or at the ~ 2-sigma level.Comment: 9 pages with 2 figures, uses LaTeX/AASTeX 5.2. Accepted for publications in ApJ Letter

Audiovisual time perception is spatially specific

Our sensory systems face a daily barrage of auditory and visual signals whose arrival times form a wide range of audiovisual asynchronies. These temporal relationships constitute an important metric for the nervous system when surmising which signals originate from common external events. Internal consistency is known to be aided by sensory adaptation: repeated exposure to consistent asynchrony brings perceived arrival times closer to simultaneity. However, given the diverse nature of our audiovisual environment, functionally useful adaptation would need to be constrained to signals that were generated together. In the current study, we investigate the role of two potential constraining factors: spatial and contextual correspondence. By employing an experimental design that allows independent control of both factors, we show that observers are able to simultaneously adapt to two opposing temporal relationships, provided they are segregated in space. No such recalibration was observed when spatial segregation was replaced by contextual stimulus features (in this case, pitch and spatial frequency). These effects provide support for dedicated asynchrony mechanisms that interact with spatially selective mechanisms early in visual and auditory sensory pathways