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The effect of blue light filters on the anomaloscopic examination was analyzed. Thirty subjects (18–43 y, 20 female, 10 male) without color vision disorders were examined in 4 filter conditions: no filter (F-0), Blue Control Hoya (F-BC), Med-1 JZO (F-Med1) and 450 Eschenbach (F-450). Both Rayleigh test (red–green axis) and Moreland test (blue–green axis) were performed. Application of F-BC filter shows negligible effect on color vision perception in both tests. Contrary to this, the application of strong F-450 filter causes significant shift in Moreland test towards tritanopy and the decrease in correlations of Moreland parameters with Rayleigh test parameters. The application of medium strong F-Med1 filter causes the slight shift in Moreland test towards the center of the Moreland scale and increases the Spearman correlations between Moreland and Rayleigh test parameters. This observation suggests that the about 15–40% reduction of blue diode intensity in the Moreland test may be beneficial in detecting mild changes in color vision perception in the blue-green axis and may improve its usefulness in evaluating the color vision perception disorders accompanying different illnesses, such as diabetes, glaucoma, neuritis optica, or cataract. The discussion concerning the modifications of Moreland test construction is also presented.
Krzysztof Michalak; Jacek Zabel; Jan Olszewski; Paulina Wojtyła-Buciora; Anna Przekoracka-Krawczyk. Application of Blue Filters Increases the Usefulness of Moreland Test in Anomaloscopic Color Vision Assessment for Blue–Green Color Range. International Journal of Environmental Research and Public Health 2021, 18, 7654 .
AMA StyleKrzysztof Michalak, Jacek Zabel, Jan Olszewski, Paulina Wojtyła-Buciora, Anna Przekoracka-Krawczyk. Application of Blue Filters Increases the Usefulness of Moreland Test in Anomaloscopic Color Vision Assessment for Blue–Green Color Range. International Journal of Environmental Research and Public Health. 2021; 18 (14):7654.
Chicago/Turabian StyleKrzysztof Michalak; Jacek Zabel; Jan Olszewski; Paulina Wojtyła-Buciora; Anna Przekoracka-Krawczyk. 2021. "Application of Blue Filters Increases the Usefulness of Moreland Test in Anomaloscopic Color Vision Assessment for Blue–Green Color Range." International Journal of Environmental Research and Public Health 18, no. 14: 7654.
Aim To validate the reference ranges proposed by the manufacturer of the Oculus HMC Anomaloscope MR for Rayleigh and Moreland tests in healthy young adults. Method The manual Rayleigh (red-green) and the Moreland (blue-green) anomaloscope tests were performed on 90 healthy subjects (54 female, 36 male, 178 eyes) residing in Poland, aged between 18–45 years, and without color vision disorders (assessed with HRR test). The analyzed parameters for both the Rayleigh and the Moreland tests were as follows: the lower (R1/M1) and the upper (R2/M2) limits; the center (RC/MC) and the width (RW/MW) of the matching ranges. Results The results of the Rayleigh test were similar to the values proposed in the anomaloscope user’s manual, however, with a small shift of RC and R2 towards the red color. The double-peak distribution of R2 with a small second peak (approximately at R2 = 52) was mainly due to the measurements in male subjects (nmale = 8, nfemale = 2), which suggests that this group might be diagnosed with subtle protanomaly. The results of the Moreland test showed a high MW which did not correspond to the reference range described in the anomaloscope user’s manual. The observed significant correlations between R1 and M1 suggest that the M1 parameter seems to be the best indicator of blue vision quality. Conclusions Oculus HMC Anomaloscope MR is a sensitive tool for detection of prot-deuteranomalies but the reference ranges for young adults require a certain adjustment towards the red color. The parameters obtained for the Moreland test varied significantly between the subjects and therefore the test should not be used as is to diagnose color vision deficits in the green-blue area (tritanomaly).
Jacek Zabel; Anna Przekoracka-Krawczyk; Jan Olszewski; Krzysztof Piotr Michalak. Variability of Rayleigh and Moreland test results using anomaloscope in young adults without color vision disorders. PLOS ONE 2021, 16, e0251903 .
AMA StyleJacek Zabel, Anna Przekoracka-Krawczyk, Jan Olszewski, Krzysztof Piotr Michalak. Variability of Rayleigh and Moreland test results using anomaloscope in young adults without color vision disorders. PLOS ONE. 2021; 16 (5):e0251903.
Chicago/Turabian StyleJacek Zabel; Anna Przekoracka-Krawczyk; Jan Olszewski; Krzysztof Piotr Michalak. 2021. "Variability of Rayleigh and Moreland test results using anomaloscope in young adults without color vision disorders." PLOS ONE 16, no. 5: e0251903.
To measure body balance using computerised dynamic posturography in young adults wearing multifocal contact lenses (MFCL) with high addition powers designed for myopia control. Twenty-four young adults (mean age: 24 years) wearing distance-centred soft MFCL (SwissLens Orbis Relax) with two different central zones (3 and 4.5 mm), two addition powers (+2 D, +4 D) and single vision control lenses. Body balance was measured on a moving platform under three viewing conditions: (1) eyes open when fixating on letters at 3 m or (2) at 40 cm, as well as (3) with the eyes closed. Parameters of body stabilisation were analysed: the rate of body stabilisation (τrelax ), the stabilisation time (Tmax ) and the number of oscillations (Nosc ). The MFCLs did not produce a significant difference in the mean values of the analysed parameters (p > 0.05 for τrelax, Tmax, Nosc ). However, a positive correlation was found between pupil size and Nosc and Tmax (p < 0.01), suggesting an effect of the +4 D add with the 3 mm central zone on the posturographic parameters. As was expected, dynamic body stabilisation was better with eyes open versus eyes closed (p < 0.005). Distance-centred MFCLs with a medium addition (+2 D) do not disturb body stabilisation in young adults. However, high additions (+4 D) with a small central zone may affect body balance control in subjects with large pupil size.
Katarzyna Przekoracka; Krzysztof Piotr Michalak; Jan Olszewski; Andrzej Michalski; Anna Przekoracka‐Krawczyk. Computerised dynamic posturography for postural control assessment in subjects wearing multifocal contact lenses dedicated for myopia control. Ophthalmic and Physiological Optics 2021, 41, 486 -495.
AMA StyleKatarzyna Przekoracka, Krzysztof Piotr Michalak, Jan Olszewski, Andrzej Michalski, Anna Przekoracka‐Krawczyk. Computerised dynamic posturography for postural control assessment in subjects wearing multifocal contact lenses dedicated for myopia control. Ophthalmic and Physiological Optics. 2021; 41 (3):486-495.
Chicago/Turabian StyleKatarzyna Przekoracka; Krzysztof Piotr Michalak; Jan Olszewski; Andrzej Michalski; Anna Przekoracka‐Krawczyk. 2021. "Computerised dynamic posturography for postural control assessment in subjects wearing multifocal contact lenses dedicated for myopia control." Ophthalmic and Physiological Optics 41, no. 3: 486-495.
Katarzyna Przekoracka; Krzysztof Michalak; Andrzej Michalski; Jan Olszewski; Joanna Paluch; Anna Przekoracka-Krawczyk. The influence of soft multifocal contact lenses with high additions on the eye–hand coordination. OphthaTherapy 2019, 6, 252 -258.
AMA StyleKatarzyna Przekoracka, Krzysztof Michalak, Andrzej Michalski, Jan Olszewski, Joanna Paluch, Anna Przekoracka-Krawczyk. The influence of soft multifocal contact lenses with high additions on the eye–hand coordination. OphthaTherapy. 2019; 6 (4):252-258.
Chicago/Turabian StyleKatarzyna Przekoracka; Krzysztof Michalak; Andrzej Michalski; Jan Olszewski; Joanna Paluch; Anna Przekoracka-Krawczyk. 2019. "The influence of soft multifocal contact lenses with high additions on the eye–hand coordination." OphthaTherapy 6, no. 4: 252-258.
To assess the visual performance of multifocal contact lenses (MFCLs) with high addition powers designed for myopia control. Twenty-four non-presbyopic adults (mean age 24 years, range 18–36 years) were fitted with soft MFCLs with add powers of +2.0 D (Add2) and +4.0 D (Add4) (RELAX, SwissLens) and single vision lenses (SVCL; Add0) in a counterbalanced order. In this double-masked study, half of the participants were randomly fitted with 3 mm-distance central zone MFCLs while the other half received 4.5 mm-distance central zone MFCLs. Visual acuity was measured at distance (3.0 m) and at near (0.4 m). Central and peripheral contrast sensitivity was evaluated at distance using the Gabor patch test. The area under the logarithmic contrast sensitivity function curve (ALCSF) was calculated and compared between the groups (i.e. different additions powers used). Near and distance visual acuities were not affected by the lenses, neither Add2 nor Add4, when compared to Add0, however, CZ3 significantly reduced distance visual acuity with Add4 when compared to CZ4.5 (−0.08 logMAR vs. for CZ3 and -0.18 logMAR for CZ4.5, p = 0.013). MFCLs impaired central ALCSF only when Add2 was used (15.99 logCS for Add2 and 16.36 logCS for SVCLs, p = 0.021). Peripheral ALCSF was statistically lower for both addition powers of the MFCLs when compared to SVCLs (12.70 for Add2 and Add4, 13.73 for SVCLs, p = 0.009). The above effects were the same for both central zones used. MFCLs with CZ3 diameter and high add power (Add4) slightly reduced distance visual acuity when compared to CZ4.5 but no reduction in this parameter was found with medium add power (Add2). Central contrast sensitivity was impaired only by MFCLs with the lower add power (Add2). Both add powers in the MFCLs reduced peripheral contrast sensitivity to a similar extent.
Katarzyna Przekoracka; Krzysztof Michalak; Jan Olszewski; Fabrizio Zeri; Andrzej Michalski; Joanna Paluch; Anna Przekoracka-Krawczyk. Contrast sensitivity and visual acuity in subjects wearing multifocal contact lenses with high additions designed for myopia progression control. Contact Lens and Anterior Eye 2019, 43, 33 -39.
AMA StyleKatarzyna Przekoracka, Krzysztof Michalak, Jan Olszewski, Fabrizio Zeri, Andrzej Michalski, Joanna Paluch, Anna Przekoracka-Krawczyk. Contrast sensitivity and visual acuity in subjects wearing multifocal contact lenses with high additions designed for myopia progression control. Contact Lens and Anterior Eye. 2019; 43 (1):33-39.
Chicago/Turabian StyleKatarzyna Przekoracka; Krzysztof Michalak; Jan Olszewski; Fabrizio Zeri; Andrzej Michalski; Joanna Paluch; Anna Przekoracka-Krawczyk. 2019. "Contrast sensitivity and visual acuity in subjects wearing multifocal contact lenses with high additions designed for myopia progression control." Contact Lens and Anterior Eye 43, no. 1: 33-39.
Posturographic signals were recorded for 384 subjects of different ages and with old persons with gait disturbances. Four conditions were used: Eyes Open/Closed vs. Head Normal/Bent Back. ‘Center of Pressure’ (CoP) signals were decomposed into ‘Center of Mass’ (CoM) and the remaining difference between Center of Pressure and Center of Mass (CoPM). The Zero-Crossing points in which the Center of Mass and Center of Pressure paths cross each other have been extracted. Velocity of CoM, velocity of CoPM and acceleration of CoPM in Zero-Crossing points were analyzed to be potential markers of balance efficiency. Three factors causing the deterioration of balance quality were analyzed: closing eyes, bending the head back and patient age. The influence of the given factors was measured using the significance p of the t-Student test and Cohen's d effect size and applied to differences for the logarithms of three of the mentioned above variables measured without and with the given deteriorating factor. In the majority of comparisons, the proposed new parameters of balance quality possessed higher statistical power to detect deteriorated balance quality than the standard parameters: standard deviation of the signal and ellipse area covering 90% of the signal envelope. Most valuable are the velocity and acceleration of CoPM for the medio-lateral direction. Logarithms of the analyzed parameters are proposed to be used in analyses because they possess normal or close to normal distribution and they are less sensitive to single high values occurring often in measurements.
Krzysztof Piotr Michalak; Anna Przekoracka-Krawczyk; Ryszard Naskręcki. Parameters of the crossing points between center of pressure and center of mass signals are potential markers of postural control efficiency. PLOS ONE 2019, 14, e0219460 .
AMA StyleKrzysztof Piotr Michalak, Anna Przekoracka-Krawczyk, Ryszard Naskręcki. Parameters of the crossing points between center of pressure and center of mass signals are potential markers of postural control efficiency. PLOS ONE. 2019; 14 (7):e0219460.
Chicago/Turabian StyleKrzysztof Piotr Michalak; Anna Przekoracka-Krawczyk; Ryszard Naskręcki. 2019. "Parameters of the crossing points between center of pressure and center of mass signals are potential markers of postural control efficiency." PLOS ONE 14, no. 7: e0219460.
Vergence prism adaptability was evaluated in subjects with high symptomatic and asymptomatic heterophoria and compared to individuals with a heterophoria within normal range (the control group). A computer haploscope was used to measure phoria values and changes in the eye position after introducing 6 prism diopters base out in front of the right eye. Phoria values were measured with a nonius paradigm every minute for a period of 10 minutes during adaptation. The results showed that subjects with symptomatic heterophoria are characterized by a lower rate of prism adaptation and adapted to a smaller extent with respect to the control group. The group with high but asymptomatic heterophoria showed prolonged adaptation time but after several minutes of binocular viewing the subjects were able to adapt to the prism to a level similar to the control group. These findings suggest that an impairment in the slow vergence control system may be responsible for the inability to fully reduce vergence effort, which results in poor vergence ranges and asthenopic symptoms during prolonged viewing.
Anna Przekoracka-Krawczyk; Krzysztof Piotr Michalak; Paulina Pyżalska. Deficient vergence prism adaptation in subjects with decompensated heterophoria. PLOS ONE 2019, 14, e0211039 .
AMA StyleAnna Przekoracka-Krawczyk, Krzysztof Piotr Michalak, Paulina Pyżalska. Deficient vergence prism adaptation in subjects with decompensated heterophoria. PLOS ONE. 2019; 14 (1):e0211039.
Chicago/Turabian StyleAnna Przekoracka-Krawczyk; Krzysztof Piotr Michalak; Paulina Pyżalska. 2019. "Deficient vergence prism adaptation in subjects with decompensated heterophoria." PLOS ONE 14, no. 1: e0211039.
Krzysztof Piotr Michalak. Estimating correlation dimension of high-dimensional signals - quick algorithm. AIP Advances 2018, 8, 105201 .
AMA StyleKrzysztof Piotr Michalak. Estimating correlation dimension of high-dimensional signals - quick algorithm. AIP Advances. 2018; 8 (10):105201.
Chicago/Turabian StyleKrzysztof Piotr Michalak. 2018. "Estimating correlation dimension of high-dimensional signals - quick algorithm." AIP Advances 8, no. 10: 105201.
Long-term fluoroquinolone-associated disability (FQAD) after fluoroquinolone (FQ) antibiotic therapy appears in recent years as a significant medical and social problem, because patients suffer for many years after prescribed antimicrobial FQ treatment from tiredness, concentration problems, neuropathies, tendinopathies, and other symptoms. The knowledge about the molecular activity of FQs in the cells remains unclear in many details. The effective treatment of this chronic state remains difficult and not effective. The current paper reviews the pathobiochemical properties of FQs, hints the directions for further research, and reviews the research concerning the proposed treatment of patients. Based on the analysis of literature, the main directions of possible effective treatment of FQAD are proposed: (a) reduction of the oxidative stress, (b) restoring reduced mitochondrion potential ΔΨm, (c) supplementation of uni- and bivalent cations that are chelated by FQs and probably ineffectively transported to the cell (caution must be paid to Fe and Cu because they may generate Fenton reaction), (d) stimulating the mitochondrial proliferation, (e) removing FQs permanently accumulated in the cells (if this phenomenon takes place), and (f) regulating the disturbed gene expression and enzyme activity.
Krzysztof Michalak; Aleksandra Sobolewska-Włodarczyk; Marcin Włodarczyk; Justyna Sobolewska; Piotr Wozniak; Bogusław Sobolewski. Treatment of the Fluoroquinolone-Associated Disability: The Pathobiochemical Implications. Oxidative Medicine and Cellular Longevity 2017, 2017, 1 -15.
AMA StyleKrzysztof Michalak, Aleksandra Sobolewska-Włodarczyk, Marcin Włodarczyk, Justyna Sobolewska, Piotr Wozniak, Bogusław Sobolewski. Treatment of the Fluoroquinolone-Associated Disability: The Pathobiochemical Implications. Oxidative Medicine and Cellular Longevity. 2017; 2017 ():1-15.
Chicago/Turabian StyleKrzysztof Michalak; Aleksandra Sobolewska-Włodarczyk; Marcin Włodarczyk; Justyna Sobolewska; Piotr Wozniak; Bogusław Sobolewski. 2017. "Treatment of the Fluoroquinolone-Associated Disability: The Pathobiochemical Implications." Oxidative Medicine and Cellular Longevity 2017, no. : 1-15.
Glutamine (GLN) is commonly known as an important metabolite used for the growth of cancer cells but the effects of its intake in cancer patients are still not clear. However, GLN is the main substrate for DNA and fatty acid synthesis. On the other hand, it reduces the oxidative stress by glutathione synthesis stimulation, stops the process of cancer cachexia, and nourishes the immunological system and the intestine epithelium, as well. The current paper deals with possible positive effects of GLN supplementation and conditions that should be fulfilled to obtain these effects. The analysis of GLN metabolism suggests that the separation of GLN and carbohydrates in the diet can minimize simultaneous supply of ATP (from glucose) and NADPH2(from glutamine) to cancer cells. It should support to a larger extent the organism to fight against the cancer rather than the cancer cells. GLN cannot be considered the effective source of ATP for cancers with the impaired oxidative phosphorylation and pyruvate dehydrogenase inhibition. GLN intake restores decreased levels of glutathione in the case of chemotherapy and radiotherapy; thus, it facilitates regeneration processes of the intestine epithelium and immunological system.
Krzysztof Piotr Michalak; Agnieszka Maćkowska-Kędziora; Bogusław Sobolewski; Piotr Woźniak. Key Roles of Glutamine Pathways in Reprogramming the Cancer Metabolism. Oxidative Medicine and Cellular Longevity 2015, 2015, 1 -14.
AMA StyleKrzysztof Piotr Michalak, Agnieszka Maćkowska-Kędziora, Bogusław Sobolewski, Piotr Woźniak. Key Roles of Glutamine Pathways in Reprogramming the Cancer Metabolism. Oxidative Medicine and Cellular Longevity. 2015; 2015 ():1-14.
Chicago/Turabian StyleKrzysztof Piotr Michalak; Agnieszka Maćkowska-Kędziora; Bogusław Sobolewski; Piotr Woźniak. 2015. "Key Roles of Glutamine Pathways in Reprogramming the Cancer Metabolism." Oxidative Medicine and Cellular Longevity 2015, no. : 1-14.
Objective. Lower frequencies of slow oscillations of the posturographic signals can be removed using high-pass filtering. This procedure releases postural reflexes possessing higher frequencies and lower amplitude range. Mutual dependence between the x and y components of posturographic signals was analyzed using principal component analysis (PCA). The posturographic signals of old patients with idiopathic gait disturbance were compared with the control group of similar age and with younger patients. There was also the analysis of the influence of the eyes state (open versus closed) and the head position (normal or bent back). The statistically significant differences in the mutual dependence between x and y components between the groups of patients were analyzed using MANOVA. The significant differences were observed mainly in the range of filter frequencies f = 0.1–1.5 Hz and f = 2.2–5.5 Hz with a maximum effect at approximately 4-5 Hz. A detailed post-hoc analysis is also presented. The differences in the higher frequency range suggest the main disturbance to be connected with the spinal reflexes. Visual and vestibular support appear insufficient for postural stability control in the idiopathic gait disturbance group. The results suggest that idiopathic gait disturbance is the final stage of the aging process of postural system.
Krzysztof Piotr Michalak; Anna Przekoracka-Krawczyk; Paweł Nawrot; Piotr Wozniak; Peter Vieregge. The Filtering of the Posturographic Signals Shows the Age Related Features. The Scientific World Journal 2014, 2014, 1 -9.
AMA StyleKrzysztof Piotr Michalak, Anna Przekoracka-Krawczyk, Paweł Nawrot, Piotr Wozniak, Peter Vieregge. The Filtering of the Posturographic Signals Shows the Age Related Features. The Scientific World Journal. 2014; 2014 (2):1-9.
Chicago/Turabian StyleKrzysztof Piotr Michalak; Anna Przekoracka-Krawczyk; Paweł Nawrot; Piotr Wozniak; Peter Vieregge. 2014. "The Filtering of the Posturographic Signals Shows the Age Related Features." The Scientific World Journal 2014, no. 2: 1-9.
The paper presents improvements to the Takens-Ellner (TE) algorithm estimating the correlation dimension (d) of high-dimensional signals. The signal being the sum of 4 Lorenz signals and possessing the correlation dimension d approximately equal to 8 was analyzed. The conversion of TE to the classic Grassberger-Proccacia (GP) algorithm is presented that shows the advantage of TE over the GP algorithm. The maximal d estimated for the given number of points in phase space is significantly higher for the TE algorithm than for the GP algorithm. The formula for the precision of individual d estimation is presented. The paper shows, how to estimate the distance corresponding to the end of the Linear Scaling Region in the correlation integral function, even before starting the procedure of d estimation. It makes it possible to reject the majority of longer distances from the analysis reducing the computation time considerably.
Krzysztof Piotr Michalak. How to estimate the correlation dimension of high-dimensional signals? Chaos: An Interdisciplinary Journal of Nonlinear Science 2014, 24, 033118 .
AMA StyleKrzysztof Piotr Michalak. How to estimate the correlation dimension of high-dimensional signals? Chaos: An Interdisciplinary Journal of Nonlinear Science. 2014; 24 (3):033118.
Chicago/Turabian StyleKrzysztof Piotr Michalak. 2014. "How to estimate the correlation dimension of high-dimensional signals?" Chaos: An Interdisciplinary Journal of Nonlinear Science 24, no. 3: 033118.
Previous studies revealed that people with binocular vision disorders have poor postural stability. However, most of the research was performed only on children and under binocular viewing condition, that could negatively affect the results. The aim of the current study was to investigate the influence of extra-ocular proprioceptive signals on postural stability in young adults with binocular vision disorders. Moreover, additional mental task was introduced to detect any postural compensation which could possibly hide the real influence of afferent extra-ocular signals.21 Subjects, aged 18–45 yrs, with horizontal strabismus, were qualified to binocular vision disorders (BVD) group. 41 subjects, aged 19–45 yrs, with no strabismus formed the normal binocular vision (NBV) group. Posturography data were collected in 2 separate parts: (1) quiet standing (Single-Task), and (2) performance of a mental task while standing (Dual-Task). Each part consisted of three 60-s viewing conditions, with: (1) dominant/fellow eye (DE), (2) non-dominant/strabismic eye (NDE), and with (3) both eyes closed (EC). Subjects were looking at X located at the distance of 150cm.Generally, BVD group showed elevated body balance during quiet stance compared to NBV group. Interestingly, better stabilization in BVD group occurred under NDE viewing. Surprisingly, additional mental task improved the postural stability in BVD group almost to the level of NBV group. These findings emphasize the role of the eye-muscle signals in postural control and suggest that suitable vision therapy can be the appropriate way to improve body balance/motor functions in people with binocular vision disorders
Anna Przekoracka-Krawczyk; Paweł Nawrot; Monika Czaińska; Krzysztof Piotr Michalak. Impaired body balance control in adults with strabismus. Vision Research 2014, 98, 35 -45.
AMA StyleAnna Przekoracka-Krawczyk, Paweł Nawrot, Monika Czaińska, Krzysztof Piotr Michalak. Impaired body balance control in adults with strabismus. Vision Research. 2014; 98 ():35-45.
Chicago/Turabian StyleAnna Przekoracka-Krawczyk; Paweł Nawrot; Monika Czaińska; Krzysztof Piotr Michalak. 2014. "Impaired body balance control in adults with strabismus." Vision Research 98, no. : 35-45.
Krzysztof Michalak; H Nawrocka-Bogusz. The changes of the frequency specific impedance of the human body due to the resonance in the kHz range in cancer diagnostics. Journal of Physics: Conference Series 2011, 329, 1 .
AMA StyleKrzysztof Michalak, H Nawrocka-Bogusz. The changes of the frequency specific impedance of the human body due to the resonance in the kHz range in cancer diagnostics. Journal of Physics: Conference Series. 2011; 329 ():1.
Chicago/Turabian StyleKrzysztof Michalak; H Nawrocka-Bogusz. 2011. "The changes of the frequency specific impedance of the human body due to the resonance in the kHz range in cancer diagnostics." Journal of Physics: Conference Series 329, no. : 1.
The paper presents the modifications of the classic Takens-Ellner (TE) algorithm that are necessary to estimate the dimensional complexity (d) of the medium- and high-dimensional signals. The main idea is the fitting of the fourth-degree polynomial to the relation d=fn(W) (where W is window width) in order to find the point of minimum slope in this relation. This point corresponds to the plateau area being the feature of the low-dimensional signals and representing the range of the optimal W used in the calculations. The point of minimum slope is represented by the local minimum in the first derivative function (third-degree polynomial). The exclusion of the attractor pairs of points lying approximately closer than the autocorrelation time removes the tendency to down-estimate d observed in the classic TE algorithm. The procedure of the choice of the embedding parameters was modified: The lag (L) was calculated for the given embedding dimension (m) and W was calculated by using the formula L=W/(m-1) in order to obtain the desired values of W for generating the precise relation d=fn(W) being the basis for the polynomial fitting. The cubic interpolation of the signal is proposed for the noninteger L's. Three signals possessing the dimensional complexities dA$\approx${}4, dB$\approx${}6, and dC$\approx${}8 and being the sums of two, three, and four Lorenz signals, respectively, were analyzed. Their lengths were 65~536 points. The applied algorithm gives a precise estimation of d for every signal A, B, and C. Also presented are the results of (a) the method for the estimation of the cubic interpolation error, (b) the analysis for signals contaminated with the white noise, and (c) the comparison between the original signals and the surrogates.
Krzysztof Piotr Michalak. Modifications of the Takens-Ellner algorithm for medium- and high-dimensional signals. Physical Review E 2011, 83, 026206 .
AMA StyleKrzysztof Piotr Michalak. Modifications of the Takens-Ellner algorithm for medium- and high-dimensional signals. Physical Review E. 2011; 83 (2):026206.
Chicago/Turabian StyleKrzysztof Piotr Michalak. 2011. "Modifications of the Takens-Ellner algorithm for medium- and high-dimensional signals." Physical Review E 83, no. 2: 026206.
The non-linear analysis of medium- and high-dimensional signals (HDS) encounters often difficulties due to the problem of the choice of the proper window width. This problem occurs due to the fact that the autocorrelation time (tau) of HDS reflecting the natural scale of the signal is similar or higher than the predictability of HDS and the predictability points to some degree to the maximal acceptable window width (W). The new approach to the embedding process is proposed in this paper that uses the constant W instead of the constant L. The lag is calculated by using the formula L = W/(m - 1). If L is non-integer, the cubic interpolation is performed to find the values of the signal between the given points. A forecasting analysis of two signals of the known structure and dimensional complexity is performed by employing the new approach. The analyzed signals consist of 3 and 4 Lorenz signals of different time scales, respectively. The used measure of the predictability is the predictive time t(p05) that is defined as the prediction time for which the correlation coefficient rho between the real and the predicted points equals 0.5. The relations t(p05)(W) possess the maxima that correspond to the autocorrelation times of the individual components. These maxima are observed approximately at W(i) = (0.6-1)tau(i), where i is the index of the given component of the signal. The saturation of predictability is observed for consecutive maxima in most cases at the embedding dimension equal to about m(i*) = 2 . d(k) + 1, where d(k) is the sum of the dimensional complexities of the components, whose autocorrelation time is equal or less than the W(i). Thus, it is clearly visible that only the components of the time scale equal or less than W(i) are demonstrated in the results of the analysis.
Krzysztof Piotr Michalak. Distinguishing Separate Components in High-dimensional Signals by Using the Modified Embedding Method and Forecasting. Annals of Biomedical Engineering 2009, 38, 200 -207.
AMA StyleKrzysztof Piotr Michalak. Distinguishing Separate Components in High-dimensional Signals by Using the Modified Embedding Method and Forecasting. Annals of Biomedical Engineering. 2009; 38 (1):200-207.
Chicago/Turabian StyleKrzysztof Piotr Michalak. 2009. "Distinguishing Separate Components in High-dimensional Signals by Using the Modified Embedding Method and Forecasting." Annals of Biomedical Engineering 38, no. 1: 200-207.