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1.
Saudi Pharm J ; 26(8): 1089-1097, 2018 Dec.
Artículo en Inglés | MEDLINE | ID: mdl-30532629

RESUMEN

In recent years, the decreased efficacy of existing antibiotics toward management of emergent drug-resistant strains has necessitated the search for novel antibiotics from natural products. In this regard, Bacillus sp is well known for producing variety of secondary metabolites of potential use. Therefore, we performed an investigation to isolate and identify Bacillus sp from oral cavity for production of novel antimicrobial compounds. We extracted, purified, and identified a novel bioactive compound by B. megaterium (KC246043.1). The optimal production of compound was observed on de Man Rogosa and Sharpe broth by incubating at 37 °C, and pH 7.0 for 4 days. The bioactive compound was extracted by using n-butanol (2:1 v/v), purified on TLC plates with detection at Rf 7.8 cm; further characterized and identified as a cyclic ploypeptide sharing structural similarity with bacitracin. Minimum inhibitory concentration of bioactive compound was found to be 0.25, 0.5, 1.0, 3.125 and 6.25 µg/ml against Micrococcus luteus ATCC10240, Salmonella typhi ATCC19430, Escherichia coli ATCC35218. Pseudomonas aeruginosa ATCC27853 and Staphylococcus aureus ATCC25923 respectively, with no activity against Candida albicans ATCC10231. Our findings have revealed a novel cyclic peptide compound from B. megaterium with broad spectrum antimicrobial activity against both Gram positive and Gram negative bacteria.

2.
Bratisl Lek Listy ; 118(5): 269-272, 2017.
Artículo en Inglés | MEDLINE | ID: mdl-28516788

RESUMEN

INTRODUCTION: The direct protective effects of resveratrol against oxidative stress have been demonstrated in neuroglial cells, the mechanisms of these effects are not fully understood. The aim of this research was to study the effect of resveratrol on AL induced cerebral injury in rat. METHODS: We divided the groups as follows with 10 animals each: a) Group I - served as control receiving normal drinking water and diet ad libitum. b) Group II - animals were administered aluminum at a dose level of 100 mg/kg body weight for a period of 6 weeks daily through oral gavage. c) Group III - animals were administered aluminum at a dose level of 100 mg/kg body weight and resveratrol at a dose of 10 mg/kg body weight intraperitoneally for a period of 6 weeks daily. After 6 weeks rats were anesthetized and decapitated. Brains were removed immediately and frozen in liquid nitrogenRESULTS: The levels of SOD and GPx antioxidant enzymes were decreased in all of the groups receiving aluminium, but it was less severe in resveratrol treated group. SOD and GPx levels in aluminium + resveratrol group were higher than in the aluminum group (p < 0.05). MDA level, as an index of lipid peroxidation, increased significantly in all of the groups receiving aluminium. MDA level was lower in aluminium + resveratrol group compared to aluminum group and the difference was significant (p < 0.05). CONCLUSIONS: This study suggests that resveratrol is effective in preventing AL induced toxicity by reducing MDA production in cerebral tissue. Resveratrol also attenuated SOD and GPx suppression in cerebral tissue significantly. Our findings provide the rationale for further studies directed to understanding the mechanism of resveratrol in preventing neurodeterioration (Tab. 1, Ref. 35).


Asunto(s)
Compuestos de Aluminio/toxicidad , Antioxidantes/farmacología , Peroxidación de Lípido/efectos de los fármacos , Fármacos Neuroprotectores/farmacología , Estilbenos/farmacología , Animales , Encéfalo/metabolismo , Masculino , Degeneración Nerviosa/prevención & control , Neuroglía/efectos de los fármacos , Estrés Oxidativo/efectos de los fármacos , Ratas , Ratas Wistar , Resveratrol
3.
Bratisl Lek Listy ; 117(9): 543-546, 2016.
Artículo en Inglés | MEDLINE | ID: mdl-27677200

RESUMEN

INTRODUCTION: Tendons are vulnerable to various types of acute or chronic injures. Different methods have been investigated to achieve better healing. Phenytoin is a drug which could stimulate fibroblasts to produce collagen. This experimental study was performed to assess the effect of phenytoin on tendon healing in a rat model of tendon rupture. METHODS: Thirty healthy rats were divided into 3 groups, 1) Sham group; 2) Tendon rupture; 3) Tendon rupture+phenytoin (100 mg/kg intraperitoneally) for 21 days. On 21st day after tendon injury, the rats were anesthetized and tendon tissue was sampled for studying by light and electron microscopy. RESULTS: Qualitative and quantitative microscopic comparisons of the repair tissues of both groups were made on the 21st day. The results obtained from light and electron microscopy studies showed that tendon tissue healing was significantly better in phenytoin group compared to the control group (p < 0.05). CONCLUSIONS: Systemic administration of phenytoin may have a positive effect on tendon healing by increasing fibroblast quantity, fibrillar collagen synthesis, vascularity, and suppressing inflammation (Tab. 2, Ref. 25).


Asunto(s)
Tendón Calcáneo/efectos de los fármacos , Tendón Calcáneo/lesiones , Modelos Animales de Enfermedad , Fenitoína/farmacología , Cicatrización de Heridas/efectos de los fármacos , Animales , Inyecciones Intraperitoneales , Masculino , Ratas , Ratas Wistar , Rotura
4.
Phys Rev Lett ; 110(15): 150503, 2013 Apr 12.
Artículo en Inglés | MEDLINE | ID: mdl-25167236

RESUMEN

We demonstrate quantum walks of a photon pair in a spatially extended Einstein-Podolsky-Rosen state coupled into an on-chip multiport photonic lattice. By varying the degree of entanglement we observe Anderson localization for pairs in a separable state and Anderson colocalization for pairs in an Einstein-Podolsky-Rosen entangled state. In the former case, each photon localizes independently, while in the latter neither photon localizes, but the pair colocalizes--revealing unexpected survival of the spatial correlations through strong disorder.

5.
Arch Razi Inst ; 78(2): 715-720, 2023 04.
Artículo en Inglés | MEDLINE | ID: mdl-37396721

RESUMEN

Type 2 severe acute respiratory syndrome caused by coronavirus infection has become the most well-known pandemic infectious viral disease in the present century. This study aims to find out the post-COVID-19 infection complications via a well-designed observational study. A total of 986 recovered cases (only the period ranged between 2 to 3 months after recovery) were obtained from public and private hospitals in Kirkuk and Erbil governorates\Iraq. The admitted patients were asked to answer a questionnaire through interviews; the laboratory findings were obtained from the patients. The results suggested that approximately half of post-COVID-19 patients (%45.606) were suffering from chest pain, while (%32.357) of the cases suffered headache and chest pain. Liver enzymes (ALT, AST, and ALP) showed abnormal percent values of 38.6,24.07, and 26.09, respectively. Renal function enzymes, mainly urea, were found to be abnormal in 45.37% of recovered individuals. Furthermore, abnormal LDH levels were found in (77.9%) of post-COVID-19 patients. This finding revealed that chest pain was an inflammatory condition and liver and renal enzyme disturbances, while elevation in LDH was the predominant long-term complication in post-COVID-19 patients.


Asunto(s)
COVID-19 , Humanos , Estudios de Cohortes , SARS-CoV-2 , Hígado , Dolor en el Pecho
6.
Pak J Biol Sci ; 25(6): 531-536, 2022 Jan.
Artículo en Inglés | MEDLINE | ID: mdl-36098188

RESUMEN

<b>Background and Objectives:</b> Bacterial cellulose (BC) is a microbial extracellular biopolymer formed by microbial strains like <i>Gluconacetobacter xylinus</i>. The objective of this study was to determine the antioxidant and anticoagulant of a microbial nano cellulose-ZnO-Ag (CNCs) composite and its components separately. <b>Materials and Methods:</b> Three components were used for nano cellulose-ZnO-Ag composite synthesis, Ag-nanoparticles, ZnO-nanoparticles and BC. The DPPH method was used to calculate the scavenging of free radical behaviour of four different composite samples. <b>Results:</b> Results of silver nanoparticles were found to have the highest antioxidant activity with IC<sub>50</sub> 65 µg mL<sup></sup><sup>1</sup>, followed by CNCs-ZnO-Ag composite (IC<sub>50</sub> 88.98 µg mL<sup></sup><sup>1</sup>) but ZnONPs IC<sub>50</sub> was 263 µg mL<sup></sup><sup>1</sup> and BC (IC<sub>50</sub> 955 µg mL<sup></sup><sup>1</sup>). The CNCs-ZnO-Ag composite, BC and AgNPs at 25 µg mL<sup></sup><sup>1</sup> had clotting times that were nearly identical to the control. The APTT increased to 56 Sec at 75 µg mL<sup></sup><sup>1</sup> of CNCs-ZnO-Ag composite related to control that recorded 33 Sec. <b>Conclusion:</b> Bacterial cellulose acquired new activity in nano form and also when conjugated with nanoparticles. The CNCs-ZnO-Ag composite is ready for pharmaceutical application as an antioxidant and anticoagulant after <i>in vivo</i> study.


Asunto(s)
Nanopartículas del Metal , Óxido de Zinc , Anticoagulantes/farmacología , Antioxidantes/farmacología , Bacterias , Celulosa , Plata
7.
Materials (Basel) ; 14(16)2021 Aug 10.
Artículo en Inglés | MEDLINE | ID: mdl-34442992

RESUMEN

With the advent of the industrial revolution 4.0, the goal of the manufacturing industry is to produce a large number of products in relatively less time. This study applies the Taguchi L27 orthogonal array methodological paradigm along with response surface design. This work optimizes the process parameters in the turning of Aluminum Alloy 7075 using a Computer Numerical Control (CNC) machine. The optimal parameters influenced the rate of metal removal, the roughness of the machined surface, and the force of cutting. This experimental investigation deals with the optimization of speed (800 rpm, 1200 rpm, and 1600 rpm) and feed (0.15, 0.20, and 0.25 mm/rev) in addition to cutting depth (1.0, 1.5, and 2.0 mm) on the turning of Aluminum 7075 alloy in a CNC machine. The outcome in terms of results such as the removal rate of material (maximum), roughness on the machined surface (minimum), along with cutting force (least amount) were improved by the L27 array Taguchi method. There were 27 specimens of Al7075 alloy produced as per the array, and the corresponding responses were measured with the help of various direct contact and indirect contact sensors. Results were concluded all the way through diagrams of main effects in favor of signal-to-noise ratios and diagrams of surfaces with contour diagrams for various combinations of responses.

8.
J Adv Res ; 7(5): 651-60, 2016 Sep.
Artículo en Inglés | MEDLINE | ID: mdl-27489732

RESUMEN

The potential use of many common hydrofluorocarbons and hydrocarbons as well as new hydrofluoroolefins, i.e. R1234yf and R1234ze(E) working fluids for a combined organic Rankine cycle and vapor compression refrigeration (ORC-VCR) system activated by low-grade thermal energy is evaluated. The basic ORC operates between 80 and 40 °C typical for low-grade thermal energy power plants while the basic VCR cycle operates between 5 and 40 °C. The system performance is characterized by the overall system coefficient of performance (COPS) and the total mass flow rate of the working fluid for each kW cooling capacity ([Formula: see text]). The effects of different working parameters such as the evaporator, condenser, and boiler temperatures on the system performance are examined. The results illustrate that the maximum COPS values are attained using the highest boiling candidates with overhanging T-s diagram, i.e. R245fa and R600, while R600 has the lowest [Formula: see text] under the considered operating conditions. Among the proposed candidates, R600 is the best candidate for the ORC-VCR system from the perspectives of environmental issues and system performance. Nevertheless, its flammability should attract enough attention. The maximum COPS using R600 is found to reach up to 0.718 at a condenser temperature of 30 °C and the basic values for the remaining parameters.

9.
East Mediterr Health J ; 11(4): 573-85, 2005 Jul.
Artículo en Francés | MEDLINE | ID: mdl-16700371

RESUMEN

We studied knowledge, attitudes and practices (KAP) regarding contraception of 1003 married women (aged 15-49 years) randomly recruited from private clinics (490 women) and community clinics (512 women) in Beirut in the year 2000. A standardized KAP questionnaire was administered to the 2 groups and differences between the groups were analysed. Contraceptive methods were used by two-thirds of the women. The private clinics group reported a significantly higher socioeconomic status and educational level than the community clinics group. Despite the free availability of contraceptive methods in the community clinics, the women's level of knowledge of, attitude towards and practice of contraception was significantly lower than those of women in the private clinics. Knowledge, attitudes and practices toward contraception did not depend on the free availability of contraceptive methods but rather on the socioeconomic and educational level of the women.


Asunto(s)
Anticoncepción , Conocimientos, Actitudes y Práctica en Salud , Población Urbana/estadística & datos numéricos , Mujeres , Adolescente , Adulto , Conducta de Elección , Anticoncepción/métodos , Anticoncepción/psicología , Anticoncepción/estadística & datos numéricos , Conducta Anticonceptiva/psicología , Conducta Anticonceptiva/estadística & datos numéricos , Estudios Transversales , Escolaridad , Empleo/estadística & datos numéricos , Femenino , Encuestas de Atención de la Salud , Humanos , Líbano , Persona de Mediana Edad , Paridad , Aceptación de la Atención de Salud/psicología , Aceptación de la Atención de Salud/estadística & datos numéricos , Embarazo , Sector Privado/estadística & datos numéricos , Sector Público/estadística & datos numéricos , Factores Socioeconómicos , Encuestas y Cuestionarios , Mujeres/educación , Mujeres/psicología
10.
Opt Express ; 9(10): 498-505, 2001 Nov 05.
Artículo en Inglés | MEDLINE | ID: mdl-19424368

RESUMEN

We propose to make use of quantum entanglement for extracting holographic information about a remote 3-D object in a confined space which light enters, but from which it cannot escape. Light scattered from the object is detected in this confined space entirely without the benefit of spatial resolution. Quantum holography offers this possibility by virtue of the fourth-order quantum coherence inherent in entangled beams.

11.
Opt Express ; 3(2): 81-8, 1998 Jul 20.
Artículo en Inglés | MEDLINE | ID: mdl-19381242

RESUMEN

A single-photon-sensitive intensified charge-coupled-device (ICCD) camera has been used to simultaneously detect, over a broad area, degenerate and nondegenerate photon pairs generated by the quantum-optical process of spontaneous parametric down-conversion. We have developed a new method for determining the quantum fourth- order correlations in spatially extended detection systems such as this one. Our technique reveals the expected phase-matching-induced spa- tial correlations in a 2-f Fourier-transform system.

12.
J Clin Pathol ; 48(7): 648-51, 1995 Jul.
Artículo en Inglés | MEDLINE | ID: mdl-7560173

RESUMEN

AIM: To assess levels of some biochemical variables in sickle cell disease patients from eastern Saudi Arabia during steady state and in crises states, with a view to comparing biochemical and clinical manifestations of the disease with those in other geographical locations. METHODS: Serum calcium, uric acid, total bilirubin, lactate dehydrogenase, hydroxybutyrate dehydrogenase, and haemoglobin were measured in 110 sickle cell patients when in steady state. The same variables were measured on 30 of the patients when they went into crisis. RESULTS: Serum calcium tended to be lower in sickle cell patients than in healthy controls, while uric acid tended to be in the high normal range. Crises did not make any difference to serum calcium but they increased the uric acid level significantly. All the other variables measured were significantly abnormal and more so during crises. CONCLUSIONS: Although the abnormal levels obtained for these biochemical variables in patients with sickle cell disease from eastern Saudi Arabia were similar to those from other geographical locations, there were noticeable differences in the severity of the abnormalities, which probably explains the differences in the clinical manifestations of the disease between geographical locations. Values of some of these variables could be adapted for use to monitor crises.


Asunto(s)
Anemia de Células Falciformes/sangre , Calcio/sangre , Ácido Úrico/sangre , Adolescente , Adulto , Anemia de Células Falciformes/enzimología , Bilirrubina/sangre , Niño , Preescolar , Femenino , Hemoglobinas/análisis , Humanos , Hidroxibutirato Deshidrogenasa/sangre , L-Lactato Deshidrogenasa/sangre , Masculino , Persona de Mediana Edad , Arabia Saudita
13.
Curr Med Res Opin ; 19(4): 298-305, 2003.
Artículo en Inglés | MEDLINE | ID: mdl-12841922

RESUMEN

BACKGROUND: To detail specific effects of long-acting risperidone on individuals with schizophrenia and their way of life in a series of four cases. METHOD: Four patients with schizophrenia were selected from four different psychiatric centres. Patients were established on an oral dose of risperidone (1-4 mg/day) for 2 weeks. Based on their oral dose, they then received intramuscular injections of 25 mg or 50 mg of long-acting risperidone every 2 weeks, which could be adjusted according to clinical response. Assessments of efficacy (Positive And Negative Syndrome Scale, Clinical Global Impression-Severity) and safety (Extrapyramidal Symptom Rating Scale) were made at intervals throughout a 1-year period. RESULTS: Patients demonstrated a variety of reasons for receiving a long-acting injectable antipsychotic drug, including insufficient control of symptoms, adverse events and convenience. After 1 year of treatment with long-acting risperidone, all patients showed improvements in their symptoms of schizophrenia over their original stable condition, and benefited from a considerable reduction or total disappearance of pre-existing extrapyramidal symptoms. Patients were more socially interactive, with no signs of sedation, fatigue, confusion, depression or anxiety, and none were considered to have relapsed or to require hospitalisation. Three of the four patients were considered to have had no signs of illness after 1 year, one of whom had returned to college and another to work. They demonstrate that patients can be switched from oral and depot medications without problems. There was little pain or discomfort and no inflammatory response experienced at the injection site. CONCLUSION: The cases demonstrate the suitability of long-acting risperidone in patients benefiting from long-term treatment and suggest its potential in all patients who are at risk of relapse.


Asunto(s)
Antipsicóticos/uso terapéutico , Risperidona/uso terapéutico , Esquizofrenia/tratamiento farmacológico , Adulto , Anciano , Química Farmacéutica , Preparaciones de Acción Retardada , Humanos , Inyecciones Intramusculares , Masculino , Persona de Mediana Edad , Risperidona/administración & dosificación , Psicología del Esquizofrénico , Resultado del Tratamiento
14.
Vision Res ; 34(21): 2907-15, 1994 Nov.
Artículo en Inglés | MEDLINE | ID: mdl-7975325

RESUMEN

The addition of a uniform increment of luminance (L) to a faded retinally-stabilized target results in the subjective reappearance of the image with contrast opposite to that of the target. This phenomenon, called apparent phase reversal (APR), reveals a nonlinear gain mechanism in the adaptation process. The magnitude of the threshold increment to elicit APR (Lapr) is a measure of the state of stabilized adaptation. In the experiments reported here, Lapr was studied as a function of background luminance (Lo) and contrast (m) of the adapting stimulus. It was found that Lapr increases with increasing Lo, but does not depend on m. The data are analyzed within the context of a previously proposed model of stabilized image fading consisting of a multiplicative inverse gain followed by a subtractive process. It was found that the addition of a contrast processing stage was required to account for the relationship between Lapr and m.


Asunto(s)
Adaptación Ocular/fisiología , Luz , Sensibilidad de Contraste/fisiología , Humanos , Matemática , Modelos Biológicos , Reconocimiento Visual de Modelos/fisiología , Umbral Sensorial/fisiología
15.
Vision Res ; 33(15): 2127-38, 1993 Oct.
Artículo en Inglés | MEDLINE | ID: mdl-8266654

RESUMEN

Fading time of a retinally-stabilized difference-of-Gaussian (DOG) stimulus depends on the background luminance, contrast and spatial frequency content of the stimulus. A model of the visual system including a nonlinear multiplicative, non-local and fast process followed by a linear subtractive, local and slower process accounts for these effects. Analysis of the fading time data allows us to estimate the spatiotemporal characteristics of the proposed adaptation processes. The model is consistent with recent models of normal light adaptation from the probe-flash paradigm.


Asunto(s)
Sensibilidad de Contraste/fisiología , Retina/fisiología , Adaptación Ocular/fisiología , Humanos , Luz , Estimulación Luminosa , Umbral Sensorial , Factores de Tiempo
16.
Hear Res ; 175(1-2): 140-51, 2003 Jan.
Artículo en Inglés | MEDLINE | ID: mdl-12527132

RESUMEN

This study compares the effects of mutations in the gap junction protein connexin 26 (Cx26), on outer hair cells (OHCs), inner hair cells (IHCs) and auditory nerve/brainstem among carriers of these mutations. One hundred and twenty eight individuals, from a village with widespread consanguinity and congenital deafness, due to three Cx26 mutations, were selected among relatives of deaf persons, and divided into non-carriers, carriers of one mutation, homozygous to one mutation, or compound heterozygous carriers of two different mutations. Distortion product otoacoustic emissions (DPOAEs), auditory brainstem responses (ABRs) and audiometric evaluation were compared in these genetic groups. Hearing loss among homozygotes and compound heterozygotes was comparable and ranged from mild to profound. Most ABRs from these groups showed no responses or partial responses (peaks III, V) with prolonged latencies, but some individuals had all peaks at normal latencies. DPOAEs were absent, except sporadic responses. Carriers of one mutation had significantly smaller DPOAEs compared to non-carriers, although normal pure tone audiograms and ABRs were found in these groups. In conclusion, based on DPOAEs, Cx26 mutations may impact OHC function among carriers of one or two Cx26 mutations. IHC/nerve impairment among homozygotes and compound heterozygotes is variable. OHCs may be more susceptible to Cx26 mutations compared to IHCs and the auditory nerve and brainstem pathway activated by them.


Asunto(s)
Conexinas/genética , Sordera/genética , Sordera/fisiopatología , Potenciales Evocados Auditivos del Tronco Encefálico , Heterocigoto , Mutación , Emisiones Otoacústicas Espontáneas , Adolescente , Adulto , Anciano , Anciano de 80 o más Años , Audiometría de Tonos Puros , Niño , Preescolar , Conexina 26 , Consanguinidad , Sordera/congénito , Homocigoto , Humanos , Persona de Mediana Edad , Distorsión de la Percepción
17.
IEEE Trans Pattern Anal Mach Intell ; 5(4): 441-5, 1983 Apr.
Artículo en Inglés | MEDLINE | ID: mdl-21869129

RESUMEN

Image design involves determining the object distribution which produces a prescribed image at the output of a given imaging system. We solve the problem of generating two parallel lines at the output of an imaging system that is modeled by a linear band-limited system foliowed by a point nonlinearity of the hardlimiting type. It is shown that a solution always exists whatever the system's bandwidth. In principle, infinite two-line resolution is achievable. In practice, resolution much higher than the conventional resolution of the imaging system is possible.

18.
IEEE Trans Image Process ; 4(9): 1252-7, 1995.
Artículo en Inglés | MEDLINE | ID: mdl-18292021

RESUMEN

Images that are to be transmitted through a distorting imaging system may be deliberately altered to compensate for that distortion. The authors consider an incoherent diffraction-limited imaging system followed by an ideal high-contrast detector that prints binary images, and seek a binary input image (a mask) that generates a desired prescribed binary output image. They have developed a method for determining the optimal binary mask by formulating the problem as a mixed linear integer program (MLIP) and using the branch and bound method to solve it.

19.
IEEE Trans Image Process ; 2(1): 18-26, 1993.
Artículo en Inglés | MEDLINE | ID: mdl-18296191

RESUMEN

Image detection under low-light-level conditions is treated as a hypothesis-testing problem in which the observations are modeled as a shot-noise process. Since computing the likelihood ratio for shot-noise processes is not feasible, the use of a one-dimensional test statistic obtained by filtering and sampling the observations is proposed. The filter is chosen to maximize a generalized signal-to-noise ratio. The likelihood ratio for the one-dimensional test statistic is evaluated numerically by inverting the corresponding characteristic function under each hypothesis.

20.
IEEE Trans Neural Netw ; 7(3): 700-8, 1996.
Artículo en Inglés | MEDLINE | ID: mdl-18263466

RESUMEN

The performance of neural networks for which weights and signals are modeled by shot-noise processes is considered. Examples of such networks are optical neural networks and biological systems. We develop a theory that facilitates the computation of the average probability of error in binary-input/binary-output multistage and recurrent networks. We express the probability of error in terms of two key parameters: the computing-noise parameter and the weight-recording-noise parameter. The former is the average number of particles per clock cycle per signal and it represents noise due to the particle nature of the signal. The latter represents noise in the weight-recording process and is the average number of particles per weight. For a fixed computing-noise parameter, the probability of error decreases with the increase in the recording-noise parameter and saturates at a level limited by the computing-noise parameter. A similar behavior is observed when the role of the two parameters is interchanged. As both parameters increase, the probability of error decreases to zero exponentially fast at a rate that is determined using large deviations. We show that the performance can be optimized by a selective choice of the nonlinearity threshold levels. For recurrent networks, as the number of iterations increases, the probability of error increases initially and then saturates at a level determined by the stationary distribution of a Markov chain.

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