Binocular summation improves performance to defocus-induced blur

PURPOSE. To assess whether there are any advantages of binocular over monocular vision under blur conditions. METHODS. We measured the effect of defocus, induced by positive lenses, on the pattern reversal Visual Evoked Potential (VEP) and on visual acuity (VA). Monocular (dominant eye) and binocular VEPs were recorded from thirteen volunteers (average age: 28±5 years, average spherical equivalent: -0.25±0.73 D) for defocus up to 2.00 D using positive powered lenses. VEPs were elicited using reversing 10 arcmin checks at a rate of 4 reversals/second. The stimulus subtended a circular field of 7 degrees with 100% contrast and mean luminance 30 cd/m2. VA was measured under the same conditions using ETDRS charts. All measurements were performed at 1m viewing distance with best spectacle sphero-cylindrical correction and natural pupils. RESULTS. With binocular stimulation, amplitudes and implicit times of the P100 component of the VEPs were greater and shorter, respectively, in all cases than for monocular stimulation. Mean binocular enhancement ratio in the P100 amplitude was 2.1 in-focus, increasing linearly with defocus to be 3.1 at +2.00 D defocus. Mean peak latency was 2.9 ms shorter in-focus with binocular than for monocular stimulation, with the difference increasing with defocus to 8.8 ms at +2.00 D. As for the VEP amplitude, VA was always better with binocular than with monocular vision, with the difference being greater for higher retinal blur. CONCLUSIONS. Both subjective and electrophysiological results show that binocular vision ameliorates the effect of defocus. The increased binocular facilitation observed with retinal blur may be due to the activation of a larger population of neurons at close-to-threshold detection under binocular stimulation.

Temporal summation of intrinsically photosensitive retinal ganglion cell (ipRGC) contributions to the human pupil.

Purpose: IpRGCs mediate non-image forming functions including photoentrainment and the pupil light reflex (PLR). Temporal summation increases visual sensitivity and decreases temporal resolution for image forming vision, but the summation properties of nonimage forming vision are unknown. We investigated the temporal summation of inner (ipRGC) and outer (rod/cone) retinal inputs to the PLR. Method: The consensual PLR of the left eye was measured in six participants with normal vision using a Maxwellian view infrared pupillometer. Temporal summation was investigated using a double-pulse protocol (100 ms stimulus pairs; 0–1024 ms inter-stimulus interval, ISI) presented to the dilated fellow right eye (Tropicamide 1%). Stimulus lights (blue λmax = 460 nm; red λmax = 638 nm) biased activity to inneror outer retinal inputs to non-image forming vision. Temporal summation was measured suprathreshold (15.2 log photons.cm−2.s−1 at the cornea) and subthreshold (11.4 log photons.cm−2.s−1 at the cornea). Results: RM-ANOVAs showed the suprathreshold and subthreshold 6 second post illumination pupil response (PIPR: expressed as percentage baseline diameter) did not significantly vary for red or blue stimuli (p > .05). The PIPR for a subthreshold red 16 ms double-pulse control condition did not significantly differ with ISI (p > .05). The maximum constriction amplitude for red and blue 100 ms double- pulse stimuli did not significantly vary with ISI (p > .05). Conclusion: The non-significant changes in suprathreshold PIPR and subthreshold maximum pupil constriction indicate that inner retinal ipRGC inputs and outer retinal photoreceptor inputs to the PLR do not show temporal summation. The results suggest a fundamental difference between the temporal summation characteristics of image forming and non-image forming vision.

Revisiting Polya's summation techniques using a spreadsheet : from addition tables to Bernoulli polynomials

Recurrence relations in mathematics form a very powerful and compact way of looking at a wide range of relationships. Traditionally, the concept of recurrence has often been a difficult one for the secondary teacher to convey to students. Closely related to the powerful proof technique of mathematical induction, recurrences are able to capture many relationships in formulas much simpler than so-called direct or closed formulas. In computer science, recursive coding often has a similar compactness property, and, perhaps not surprisingly, suffers from similar problems in the classroom as recurrences: the students often find both the basic concepts and practicalities elusive. Using models designed to illuminate the relevant principles for the students, we offer a range of examples which use the modern spreadsheet environment to powerfully illustrate the great expressive and computational power of recurrences.

Calculating the bound spectrum by path summation in action-angle variables

The density of states n(E) is calculated for a bound system whose classical motion is integrable, starting from an expression in terms of the trace of the time-dependent Green function. The novel feature is the use of action-angle variables. This has the advantages that the trace operation reduces to a trivial multiplication and the dependence of n(E) on all classical closed orbits with different topologies appears naturally. The method is contrasted with another, not applicable to integrable systems except in special cases, in which quantization arises from a single closed orbit which is assumed isolated and the trace taken by the method of stationary phase.

Perturbative expansion of the QCD Adler function improved by renormalization-group summation and analytic continuation in the Borel plane

We examine the large-order behavior of a recently proposed renormalization-group-improved expansion of the Adler function in perturbative QCD, which sums in an analytically closed form the leading logarithms accessible from renormalization-group invariance. The expansion is first written as an effective series in powers of the one-loop coupling, and its leading singularities in the Borel plane are shown to be identical to those of the standard ``contour-improved'' expansion. Applying the technique of conformal mappings for the analytic continuation in the Borel plane, we define a class of improved expansions, which implement both the renormalization-group invariance and the knowledge about the large-order behavior of the series. Detailed numerical studies of specific models for the Adler function indicate that the new expansions have remarkable convergence properties up to high orders. Using these expansions for the determination of the strong coupling from the hadronic width of the tau lepton we obtain, with a conservative estimate of the uncertainty due to the nonperturbative corrections, alpha(s)(M-tau(2)) = 0.3189(-0.0151)(+0.0173), which translates to alpha(s)(M-Z(2)) = 0.1184(-0.0018)(+0.0021). DOI: 10.1103/PhysRevD.87.014008

Dirac spectra, summation formulae, and the spectral action

Noncommutative geometry is a source of particle physics models with matter Lagrangians coupled to gravity. One may associate to any noncommutative space (A, H, D) its spectral action, which is defined in terms of the Dirac spectrum of its Dirac operator D. When viewing a spin manifold as a noncommutative space, D is the usual Dirac operator. In this paper, we give nonperturbative computations of the spectral action for quotients of SU(2), Bieberbach manifolds, and SU(3) equipped with a variety of geometries. Along the way we will compute several Dirac spectra and refer to applications of this computation.

A study of threshold and loudness summation in listeners with sensorineural hearing impairments

This paper investigates loudness summation in a group of listeners with moderate to severe hearing losses and the applicability of this information to hearing aid fittings.

A study of threshold and loudness summation in normal-hearing listeners

This paper presents some normative data on the relation between the perceived loudness of third-octave bands of noise and that of broad-band noise. The study used normally-hearing listeners and was used as a control study for a parallel study done with hearing impaired listeners.

Monaural and binaural loudness summation of speech

This paper reviews a study to determine optimum hearing aid settings based on loudness.

Estimate of the cutoff errors in the Ewald summation for dipolar systems

Theoretical estimates for the cutoff errors in the Ewald summation method for dipolar systems are derived. Absolute errors in the total energy, forces and torques, both for the real and reciprocal space parts, are considered. The applicability of the estimates is tested and confirmed in several numerical examples. We demonstrate that these estimates can be used easily in determining the optimal parameters of the dipolar Ewald summation in the sense that they minimize the computation time for a predefined, user set, accuracy.

Comparison of the effects of the alpha-2 agonists detomidine, romifidine and xylazine on nociceptive withdrawal reflex and temporal summation in horses

OBJECTIVE: To evaluate and compare the antinociceptive effects of the three alpha-2 agonists, detomidine, romifidine and xylazine at doses considered equipotent for sedation, using the nociceptive withdrawal reflex (NWR) and temporal summation model in standing horses. STUDY DESIGN: Prospective, blinded, randomized cross-over study. ANIMALS: Ten healthy adult horses weighing 527-645 kg and aged 11-21 years old. METHODS: Electrical stimulation was applied to the digital nerves to evoke NWR and temporal summation in the left thoracic limb and pelvic limb of each horse. Electromyographic reflex activity was recorded from the common digital extensor and the cranial tibial muscles. After baseline measurements a single bolus dose of detomidine, 0.02 mg kg(-1), romifidine 0.08 mg kg(-1), or xylazine, 1 mg kg(-1), was administered intravenously (IV). Determinations of NWR and temporal summation thresholds were repeated at 10, 20, 30, 40, 60, 70, 90, 100, 120 and 130 minutes after test-drug administration alternating the thoracic limb and the pelvic limb. Depth of sedation was assessed before measurements at each time point. Behavioural reaction was observed and recorded following each stimulation. RESULTS: The administration of detomidine, romifidine and xylazine significantly increased the current intensities necessary to evoke NWR and temporal summation in thoracic limbs and pelvic limbs of all horses compared with baseline. Xylazine increased NWR thresholds over baseline values for 60 minutes, while detomidine and romifidine increased NWR thresholds over baseline for 100 and 120 minutes, respectively. Temporal summation thresholds were significantly increased for 40, 70 and 130 minutes after xylazine, detomidine and romifidine, respectively. CONCLUSIONS AND CLINICAL RELEVANCE: Detomidine, romifidine and xylazine, administered IV at doses considered equipotent for sedation, significantly increased NWR and temporal summation thresholds, used as a measure of antinociceptive activity. The extent of maximal increase of NWR and temporal summation thresholds was comparable, while the duration of action was drug-specific.

The influence of a continuous rate infusion of dexmedetomidine on the nociceptive withdrawal reflex and temporal summation during isoflurane anaesthesia in dogs

Objective To examine the influence of a low dose dexmedetomidine infusion on the nociceptive withdrawal reflex and temporal summation in dogs during isoflurane anaesthesia. Study design Prospective experimental blinded cross-over study. Animals Eight healthy mixed breed dogs, body weight Mean +/- SD 26.5 +/- 8.4 kg and age 25 +/- 16 months. Methods Anaesthesia was induced with propofol and maintained with isoflurane (Fe'ISO 1.3%) delivered in oxygen and air. After stabilization, baseline recordings (time 0) were obtained, then a dexmedetomidine bolus (1 mug kg(-1) IV) followed by a continuous rate infusion (1 mug kg(-1) hour(-1) ) or saline placebo were administered. At times 10, 30 and 60 minutes after the initial bolus, electrical stimulations of increasing intensity were applied over the lateral plantar digital nerve, and administered both as single and as repeated stimuli. The resulting reflex responses were recorded using electromyography. Data were analysed using a multivariable linear regression model and a Kruskal Wallis test for single stimulation data, and repeated measures anova and paired t-test for repeated stimulation data. Results The AUC for the stimulus-response curves after single stimulation were similar for both treatments at time 0. At times 10, 30 and 60 the AUCs for the stimulus-response curves were significantly lower with dexmedetomidine treatment than with placebo. Temporal summation was evident in both treatments at times 0, 10, 30 and 60 starting from a stimulation intensity of 10 mA. The magnitude of temporal summation was smaller in dexmedetomidine than in placebo treated dogs at time 10, 30 and 60, but not at time 0. Conclusions During isoflurane anaesthesia, low dose dexmedetomidine suppresses the nociceptive reflex responses after single and repeated electrical stimulation. Clinical relevance This experimental study confirms previous reports on its peri-operative efficacy under clinical conditions, and further indicates that dexmedetomidine might reduce the risk of post-operative chronic pain development.

Repeated electrical stimulations as a tool to evoke temporal summation of nociceptive inputs in healthy, non-medicated experimental sheep.

The nociceptive withdrawal reflex (NWR) model is used in animal pain research to quantify nociception. The aim of this study was to evaluate the NWR evoked by repeated stimulations in healthy, non-medicated standing sheep. Repeated electrical stimulations were applied at 5Hz for 2s to the digital nerves of the right thoracic and the pelvic limbs of 25 standing sheep. The stimulation intensities applied were fractions (0.5, 0.6, 0.7, 0.8, 0.9 and 1) of the individual previously determined nociceptive threshold (It) after single stimulation. Surface-electromyographic activity (EMG) was recorded from the deltoid, the femoral biceps or the peroneus tertius muscles. The repeated stimulation threshold (RS It) was reached if at least one stimulus in the train was followed by a reflex with a minimal root-mean-square-amplitude (RMSA) of 20μV. The behavioural reaction following each series of stimulations was scored on a scale from 0 (no reaction) to 5 (vigorous whole-body reaction). For the deltoid muscle, RS It was 2.3mA (1.6-3mA) with a reaction score of 2 (1-2) and at a fraction of 0.6 (0.5-0.8)×It. For the biceps femoris muscle, RS It was 2.9mA (2.6-4mA) with a reaction score of 1 (1-2) at a fraction of and 0.55 (0.4-0.7)×It while for the peroneus tertius muscle RS It was 3mA (2.8-3.5mA) with a reaction score of 1 (1-2) and at a fraction of 0.8 (0.8-0.95)×It. Both, RMSA and reaction scores increased significantly with increasing stimulation intensities in all muscles (p<0.001). The repeated application of electrical stimuli led to temporal summation of nociceptive inputs and therefore a reduction of the stimulus intensity evoking a withdrawal reaction in healthy, standing sheep. Data achieved in this study can now serve as reference for further clinical or experimental applications of the model in this species.

The elements of the true arithmetic of infinites : In which all the propositions in the arithmetic of infinites invented by Dr. Wallis, relative to the summation of infinite series : and, also, the principles of the doctrine of fluxions are demonstrated to be false : and the nature of infinitesimals is unfolded /

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