936 resultados para Star complement
Resumo:
Atherosclerosis is an inflammatory disease characterized by accumulation of lipids in the inner layer of the arterial wall. During atherogenesis, various structures that are recognized as non-self by the immune system, such as modified lipoproteins, are deposited in the arterial wall. Accordingly, atherosclerotic lesions and blood of humans and animals with atherosclerotic lesions show signs of activation of both innate and adaptive immune responses. Although immune attack is initially a self-protective reaction, which is meant to destroy or remove harmful agents, a chronic inflammatory state in the arterial wall accelerates atherosclerosis. Indeed, various modulations of the immune system of atherosclerosis-prone animals have provided us with convincing evidence that immunological mechanisms play an important role in the pathogenesis of atherosclerosis. This thesis focuses on the role of complement system, a player of the innate immunity, in atherosclerosis. Complement activation via any of the three different pathways (classical, alternative, lectin) proceeds as a self-amplifying cascade, which leads to the generation of opsonins, anaphylatoxins C3a and C5a, and terminal membrane-attack complex (MAC, C5b-9), all of which regulate the inflammatory response and act in concert to destroy their target structures. To prevent uncontrolled complement activation or its attack against normal host cells, complement needs to be under strict control by regulatory proteins. The complement system has been shown to be activated in atherosclerotic lesions, modified lipoproteins and immune complexes containing oxLDL, for instance, being its activators. First, we investigated the presence and role of complement regulators in human atherosclerotic lesions. We found that inhibitors of the classical and alternative pathways, C4b-binding protein and factor H, respectively, were present in atherosclerotic lesions, where they localized in the superficial proteoglycan-rich layer. In addition, both inhibitors were found to bind to arterial proteoglycans in vitro. Immunohistochemical stainings revealed that, in the superficial layer of the intima, complement activation had been limited to the C3 level, whereas in the deeper intimal layers, complement activation had proceeded to the terminal C5b-9 level. We were also able to show that arterial proteoglycans inhibit complement activation in vitro. These findings suggested to us that the proteoglycan-rich layer of the arterial intima contains matrix-bound complement inhibitors and forms a protective zone, in which complement activation is restricted to the C3 level. Thus, complement activation is regulated in atherosclerotic lesions, and the extracellular matrix is involved in this process. Next, we studied whether the receptors for the two complement derived effectors, anaphylatoxins C3a and C5a, are expressed in human coronary atherosclerotic lesions. Our results of immunohistochemistry and RT-PCR analysis showed that, in contrast to normal intima, C3aR and C5aR were highly expressed in atherosclerotic lesions. In atherosclerotic plaques, the principal cells expressing both C3aR and C5aR were macrophages. Moreover, T cells expressed C5aR, and a small fraction of them also expressed C3aR, mast cells expressed C5aR, whereas endothelial cells and subendothelial smooth muscle cells expressed both C3aR and C5aR. These results suggested that intimal cells can respond to and become activated by complement-derived anaphylatoxins. Finally, we wanted to learn, whether oxLDL-IgG immune complexes, activators of the classical complement pathway, could have direct cellular effects in atherogenesis. Thus, we tested whether oxLDL-IgG immune complexes affect the survival of human monocytes, the precursors of macrophages, which are the most abundant inflammatory cell type in atherosclerotic lesions. We found that OxLDL-IgG immune complexes, in addition to transforming monocytes into foam cells, promoted their survival by decreasing their spontaneous apoptosis. This effect was mediated by cross-linking Fc receptors with ensuing activation of Akt-dependent survival signaling. Our finding revealed a novel mechanism by which oxLDL-IgG immune complexes can directly affect the accumulation of monocyte-macrophages in human atherosclerotic lesions and thus play a role in atherogenesis.
Resumo:
The study assessed whether plasma concentrations of complement factors C3, C4, or immunoglobulins, serum classical pathway hemolytyic activity, or polymorphisms in the class I and II HLA genes, isotypes and gene numbers of C4, or allotypes of IgG1 and IgG3 heavy chain genes were associated with severe frequently recurring or chronic mucosal infections. According to strict clinical criteria, 188 consecutive voluntary patients without a known immunodeficiency and 198 control subjects were recruited. Frequencies of low levels in IgG1, IgG2, IgG3 and IgG4 were for the first time tested from adult general population and patients with acute rhinosinusitis. Frequently recurring intraoral herpes simplex type 1 infections, a rare form of the disease, was associated with homozygosity in HLA -A*, -B*, -C*, and -DR* genes. Frequently recurrent genital HSV-2 infections were associated with low levels of IgG1 and IgG3, present in 54% of the recruited patients. This association was partly allotype-dependent. The G3mg,G1ma/ax haplotype, together with low IgG3, was more common in patients than in control subjects who lacked antibodies against herpes simplex viruses. This is the first found immunogenetic deficiency in otherwise healthy adults that predisposes to highly frequent mucosal herpes recurrences. According to previous studies, HSV effectively evades the allotype G1ma/ax of IgG1, whereas G3mg is associated with low IgG3. Certain HLA genes were more common in patients than in control subjects. Having more than one C4A or C4B gene was associated with neuralgias caused by the virus. Low levels of IgA, IgG1, IgG2, IgG3, and IgG4 were common in the general adult population, but even more frequent in patients with chronic sinusitis. Only low IgG1 was more common chronic than in acute rhinosinusitis. Clinically, nasal polyposis and bronchial asthma were associated with complicated disease forms. The best differentiating immunologic parameters were C4A deficiency and the combination of low plasma IgG4 together with low IgG1 or IgG2, performing almost equally. The lack of C4A, IgA, and IgG4, all known to possess anti-inflammatory activity, together with a concurrently impaired immunity caused by low subclass levels, may predispose to chronic disease forms. In severe chronic adult periodontitis, any C4A or C4B deficiency combined was associated with the disease. The new quantitative analysis of C4 genes and the conventional C4 allotyping method complemented each other. Lowered levels of plasma C3 or C4 or both, and serum CH50 were found in herpes and periodontitis patients. In rhinosinusitis, there was a linear trend with the highest levels found in the order: acute > chronic rhinosinusitis > general population > blood donors with no self-reported history of rhinosinusitis. Complement is involved in the defense against the tested mucosal infections. Seemingly immunocompetent patients with chronic or recurrent mucosal infections frequently have subtle weaknesses in different arms of immunity. Their susceptibility to chronic disease forms may be caused by these. Host s subtly impaired immunity often coincides with effective immune evasion from the same arms of immunity by the disease-causing pathogens. The interpretation of low subclass levels, if no additional predisposing immunologic factors are tested, is difficult and of limited value in early diagnosis and treatment.
Resumo:
New stars form in dense interstellar clouds of gas and dust called molecular clouds. The actual sites where the process of star formation takes place are the dense clumps and cores deeply embedded in molecular clouds. The details of the star formation process are complex and not completely understood. Thus, determining the physical and chemical properties of molecular cloud cores is necessary for a better understanding of how stars are formed. Some of the main features of the origin of low-mass stars, like the Sun, are already relatively well-known, though many details of the process are still under debate. The mechanism through which high-mass stars form, on the other hand, is poorly understood. Although it is likely that the formation of high-mass stars shares many properties similar to those of low-mass stars, the very first steps of the evolutionary sequence are unclear. Observational studies of star formation are carried out particularly at infrared, submillimetre, millimetre, and radio wavelengths. Much of our knowledge about the early stages of star formation in our Milky Way galaxy is obtained through molecular spectral line and dust continuum observations. The continuum emission of cold dust is one of the best tracers of the column density of molecular hydrogen, the main constituent of molecular clouds. Consequently, dust continuum observations provide a powerful tool to map large portions across molecular clouds, and to identify the dense star-forming sites within them. Molecular line observations, on the other hand, provide information on the gas kinematics and temperature. Together, these two observational tools provide an efficient way to study the dense interstellar gas and the associated dust that form new stars. The properties of highly obscured young stars can be further examined through radio continuum observations at centimetre wavelengths. For example, radio continuum emission carries useful information on conditions in the protostar+disk interaction region where protostellar jets are launched. In this PhD thesis, we study the physical and chemical properties of dense clumps and cores in both low- and high-mass star-forming regions. The sources are mainly studied in a statistical sense, but also in more detail. In this way, we are able to examine the general characteristics of the early stages of star formation, cloud properties on large scales (such as fragmentation), and some of the initial conditions of the collapse process that leads to the formation of a star. The studies presented in this thesis are mainly based on molecular line and dust continuum observations. These are combined with archival observations at infrared wavelengths in order to study the protostellar content of the cloud cores. In addition, centimetre radio continuum emission from young stellar objects (YSOs; i.e., protostars and pre-main sequence stars) is studied in this thesis to determine their evolutionary stages. The main results of this thesis are as follows: i) filamentary and sheet-like molecular cloud structures, such as infrared dark clouds (IRDCs), are likely to be caused by supersonic turbulence but their fragmentation at the scale of cores could be due to gravo-thermal instability; ii) the core evolution in the Orion B9 star-forming region appears to be dynamic and the role played by slow ambipolar diffusion in the formation and collapse of the cores may not be significant; iii) the study of the R CrA star-forming region suggests that the centimetre radio emission properties of a YSO are likely to change with its evolutionary stage; iv) the IRDC G304.74+01.32 contains candidate high-mass starless cores which may represent the very first steps of high-mass star and star cluster formation; v) SiO outflow signatures are seen in several high-mass star-forming regions which suggest that high-mass stars form in a similar way as their low-mass counterparts, i.e., via disk accretion. The results presented in this thesis provide constraints on the initial conditions and early stages of both low- and high-mass star formation. In particular, this thesis presents several observational results on the early stages of clustered star formation, which is the dominant mode of star formation in our Galaxy.
Resumo:
New stars in galaxies form in dense, molecular clouds of the interstellar medium. Measuring how the mass is distributed in these clouds is of crucial importance for the current theories of star formation. This is because several open issues in them, such as the strength of different mechanism regulating star formation and the origin of stellar masses, can be addressed using detailed information on the cloud structure. Unfortunately, quantifying the mass distribution in molecular clouds accurately over a wide spatial and dynamical range is a fundamental problem in the modern astrophysics. This thesis presents studies examining the structure of dense molecular clouds and the distribution of mass in them, with the emphasis on nearby clouds that are sites of low-mass star formation. In particular, this thesis concentrates on investigating the mass distributions using the near infrared dust extinction mapping technique. In this technique, the gas column densities towards molecular clouds are determined by examining radiation from the stars that shine through the clouds. In addition, the thesis examines the feasibility of using a similar technique to derive the masses of molecular clouds in nearby external galaxies. The papers presented in this thesis demonstrate how the near infrared dust extinction mapping technique can be used to extract detailed information on the mass distribution in nearby molecular clouds. Furthermore, such information is used to examine characteristics crucial for the star formation in the clouds. Regarding the use of extinction mapping technique in nearby galaxies, the papers of this thesis show that deriving the masses of molecular clouds using the technique suffers from strong biases. However, it is shown that some structural properties can still be examined with the technique.
Resumo:
The propagation of a shock wave, originating in a stellar interior, is considered when it approaches the surface of the star and assumes a self-similar character, "forgetting" its initial conditions. The flow behind the shock is assumed to be spatially isothermal rather than adiabatic to simulate the conditions of large radiative transfer near the stellar surface. The adiabatic and isothermal flows behind such a shock are compared. The exact shock-propagation laws, obtained by solving the equations in similarity variables, for different values of the parameter δ in the undisturbed density law, ρ0 ∝ xδ, and γ, the ratio of specific heats, are compared with the approximate values calculated by Whitham's characteristic rule and the two show a generally good agreement.
Resumo:
Koskenniemen Äärellistilaisen leikkauskieliopin (FSIG) lauseopilliset rajoitteet ovat loogisesti vähemmän kompleksisia kuin mihin niissä käytetty formalismi vittaisi. Osoittautuukin että vaikka Voutilaisen (1994) englannin kielelle laatima FSIG-kuvaus käyttää useita säännöllisten lausekkeiden laajennuksia, kieliopin kuvaus kokonaisuutenaan palautuu äärelliseen yhdistelmään unionia, komplementtia ja peräkkäinasettelua. Tämä on oleellinen parannus ENGFSIG:n descriptiiviseen kompleksisuuteen. Tulos avaa ovia FSIG-kuvauksen loogisten ominaisuuksien syvemmälle analyysille ja FSIG kuvausten mahdolliselle optimoinnillle. Todistus sisältää uuden kaavan, joka kääntää Koskenniemien rajoiteoperaation ilman markkerimerkkejä.
Resumo:
Alternative pathway (AP) of complement can be activated on any surface, self or non-self. In atypical hemolytic uremic syndrome (aHUS) the AP regulation on self surfaces is insufficient and leads to complement attack against self-cells resulting usually in end-stage renal disease. Factor H (FH) is one of the key regulators of AP activation on the self surfaces. The domains 19 and 20 (FH19-20) are critical for the ability of FH to discriminate between C3b-opsonized self and non-self surfaces and are a hot-spot for mutations that have been described from aHUS patients. FH19-20 contains binding sites for both the C3d part of C3b and self surface polyanions that are needed for efficient C3b inactivation. To study the dysfunction of FH19-20, crystallographic structures of FH19-20 and FH19-20 in complex with C3d (FH19-20:C3d) were solved and aHUS-associated and structurally interesting point mutations were induced to FH19-20. Functional defects caused by these mutations were studied by analyzing binding of the FH19-20 mutant proteins to C3d, C3b, heparin, and mouse glomerular endothelial cells (mGEnCs). The results revealed two independent binding interfaces between FH19-20 and C3d - the FH19 site and the FH20 site. Superimposition of the FH19-20:C3d complex on the previously published C3b and FH1-4:C3b structures showed that the FH20 site on C3d is partially occluded, but the FH19 site is fully available. Furthermore, binding of FH19-20 via the FH19 site to C3b did not block binding of the functionally important FH1-4 domains and kept the FH20 site free to bind heparin or an additional C3d. Binding assays were used to show that FH20 domain can bind to heparin while FH19-20 is bound to C3b via the FH19 site, and that both the FH19 site and FH20 are necessary for recognition of non-activator surfaces. Simultaneous binding of FH19 site to C3b and FH20 to anionic self structures are the key interactions in self-surface recognition by FH and thereby enhanced avidity of FH explains how AP discriminates between self and non-self. The aHUS-associated mutations on FH19-20 were found to disrupt binding of the FH19 or FH20 site to C3d/C3b, or to disrupt binding of FH20 to heparin or mGEnC. Any of these dysfunctions leads to loss of FH avidity to C3b bearing self surfaces explaining the molecular pathogenesis of the aHUS-cases where mutations are found within FH19-20.
Resumo:
The author presents adaptive control techniques for controlling the flow of real-time jobs from the peripheral processors (PPs) to the central processor (CP) of a distributed system with a star topology. He considers two classes of flow control mechanisms: (1) proportional control, where a certain proportion of the load offered to each PP is sent to the CP, and (2) threshold control, where there is a maximum rate at which each PP can send jobs to the CP. The problem is to obtain good algorithms for dynamically adjusting the control level at each PP in order to prevent overload of the CP, when the load offered by the PPs is unknown and varying. The author formulates the problem approximately as a standard system control problem in which the system has unknown parameters that are subject to change. Using well-known techniques (e.g., naive-feedback-controller and stochastic approximation techniques), he derives adaptive controls for the system control problem. He demonstrates the efficacy of these controls in the original problem by using the control algorithms in simulations of a queuing model of the CP and the load controls.
Resumo:
Streptococcus pneumoniae (pneumococcus) is a normal inhabitant of the human nasopharynx. Symptoms occur in only a small proportion of those who become carriers, but the ubiquity of the organism in the human population results in a large burden of disease. S. pneumoniae is the leading bacterial cause of pneumonia, sepsis, and meningitis worldwide, causing the death of a million children each year. Middle-ear infection is the most common clinical manifestation of mucosal pneumococcal infections. In invasive disease, S. pneumoniae gains access to the bloodstream and spreads to normally sterile parts of the body. The progression from asymptomatic colonization to disease depends on factors characteristic of specific pneumococcal strains as well as the status of host defenses. The polysaccharide capsule surrounding the bacterium is considered to be the most important factor affecting the virulence of pneumococci. It protects pneumococci from phagocytosis and also may determine its affinity to the respiratory epithelium. S. pneumoniae as a species comprises more than 90 different capsular serotypes, but not all of them are equally prevalent in human diseases. Invasive serotypes are rarely isolated from healthy carriers, but relatively often cause invasive disease. Serotypes that are carried asymptomatically for a long time behave like opportunistic pathogens, causing disease in patients who have impaired immune defenses. The complement system is a collection of blood and cell surface proteins that act as a major primary defense against invading microbes. Phagocytic cells with receptors for complement proteins can engulf and destroy pneumococcal cells opsonized with these proteins. S. pneumoniae has evolved a number of ways to subvert mechanisms of innate immunity, and this is likely to contribute to its pathogenicity. The capsular serotype, proteins essential for virulence, as well the genotype, may all influence the ability of pneumococcus to resist complement and its potential to cause disease. Immunization with conjugate vaccines produces opsonic antibodies, which enhance complement deposition and clearance of the bacteria. The pneumococcal vaccine included in the Finnish national immunization program in 2010 contains the most common serotypes causing invasive disease. Clinical data suggest that protection from middle-ear infection and possibly also from invasive disease depends largely on the capsular serotype, for reasons hitherto unknown. The general aim of this thesis is to assess the relative roles of the pneumococcal capsule and virulence proteins in complement evasion and subsequent opsonophagocytic killing. The main question is whether differences between serotypes to resist complement explain the different abilities of serotypes to cause disease. The importance of particular virulence factors to the complement resistance of a strain may vary depending on its genotype. Prior studies have evaluated the effect of the capsule and virulence proteins on complement resistance of S. pneumoniae by comparing only a few strains. In this thesis, the role of pneumococcal virulence factors in the complement resistance of the bacterium was studied in several genotypically different strains. The ability of pneumococci to inhibit deposition of the complement protein C3 on the bacterial surface was found to depend on the capsular serotype as well as on other features of the bacteria. The results suggest that pneumococcal histidine triad (Pht) proteins may play a role in complement inhibition, but their contribution depends on the bacterial genotype. The capsular serotype was found to influence complement resistance more than the bacterial genotype. A higher concentration of anticapsular antibodies was required for the opsonophagocytic killing of serotypes resistant to C3 deposition. The invasive serotypes were more resistant to C3 deposition than the opportunistic serotypes, suggesting that the former are better adapted to resist immune mechanisms controlling the development of invasive disease. The different susceptibilities of serotypes to complement deposition, opsonophagocytosis, and resultant antibody-mediated protection should be taken into account when guidelines for serological correlates for vaccine efficacy evaluations are made. The results of this thesis suggest that antibodies in higher quantity or quality are needed for efficient protection against the invasive serotypes.
Resumo:
A broad numerical survey of relativistic rotating neutron star structures was compiled using an exhaustive list of presently available equation of state models for neutron star matter. The structure parameters (spherical deformations in mass and radii, the moment of inertia and quadrupole moment, oblateness, and free precession) are calculated using the formalism proposed by Hartle and Thorne (1968). The results are discussed in relation to the relevant observational information. Binary pulsar data and X-ray burst sources provide information on the bulk properties of neutron stars, enabling the derivation of constraints that can be put on the structure of neutron stars and equation of state models.
Resumo:
Starting from the exact general relativistic expression for the total energy of selfgravitating spherically distributed matter and using the minimum energy priciple, we calculate the upper mass limit for a neutron star to be 3.1 solar masses.
Resumo:
We propose a physical mechanism to explain the origin of the intense burst of massive-star formation seen in colliding/merging, gas-rich, field spiral galaxies. We explicitly take account of the different parameters for the two main mass components, H-2 and H I, of the interstellar medium within a galaxy and follow their consequent different evolution during a collision between two galaxies. We also note that, in a typical spiral galaxy-like our galaxy, the Giant Molecular Clouds (GMCs) are in a near-virial equilibrium and form the current sites of massive-star formation, but have a low star formation rate. We show that this star formation rate is increased following a collision between galaxies. During a typical collision between two field spiral galaxies, the H I clouds from the two galaxies undergo collisions at a relative velocity of approximately 300 km s-1. However, the GMCs, with their smaller volume filling factor, do not collide. The collisions among the H I clouds from the two galaxies lead to the formation of a hot, ionized, high-pressure remnant gas. The over-pressure due to this hot gas causes a radiative shock compression of the outer layers of a preexisting GMC in the overlapping wedge region. This makes these layers gravitationally unstable, thus triggering a burst of massive-star formation in the initially barely stable GMCs.The resulting value of the typical IR luminosity from the young, massive stars from a pair of colliding galaxies is estimated to be approximately 2 x 10(11) L., in agreement with the observed values. In our model, the massive-star formation occurs in situ in the overlapping regions of a pair of colliding galaxies. We can thus explain the origin of enhanced star formation over an extended, central area approximately several kiloparsecs in size, as seen in typical colliding galaxies, and also the origin of starbursts in extranuclear regions of disk overlap as seen in Arp 299 (NGC 3690/IC 694) and in Arp 244 (NGC 4038/39). Whether the IR emission from the central region or that from the surrounding extranuclear galactic disk dominates depends on the geometry and the epoch of the collision and on the initial radial gas distribution in the two galaxies. In general, the central starburst would be stronger than that in the disks, due to the higher preexisting gas densities in the central region. The burst of star formation is expected to last over a galactic gas disk crossing time approximately 4 x 10(7) yr. We can also explain the simultaneous existence of nearly normal CO galaxy luminosities and shocked H-2 gas, as seen in colliding field galaxies.This is a minimal model, in that the only necessary condition for it to work is that there should be a sufficient overlap between the spatial gas distributions of the colliding galaxy pair.
Resumo:
In order to describe the atmospheric turbulence which limits the resolution of long-exposure images obtained using ground-based large telescopes, a simplified model of a speckle pattern, reducing the complexity of calculating field-correlations of very high order, is presented. Focal plane correlations are used instead of correlations in the spatial frequency domain. General tripple correlations for a point source and for a binary are calculated and it is shown that they are not a strong function of the binary separation. For binary separations close to the diffraction limit of the telescope, the genuine triple correlation technique ensures a better SNR than the near-axis Knox-Thompson technique. The simplifications allow a complete analysis of the noise properties at all levels of light.
Resumo:
Star formation properties in Giant Extragalactic H II Regions (GEHRs) are investigated using optical photometry and evolutionary population synthesis models. Photometric data in $BVR$ bands and in the emission line of H-alpha are obtained by CCD imaging at Vainu Bappu Observatory, Kavalur. Aperture photometry is performed for 180 GEHRs in galaxies NGC 1365, 1566, 2366, 2903, 2997, 3351, 4303, 4449, 4656 and 5253. Thirty six of these GEHRs having published spectroscopic data are studied for star formation properties. The population synthesis model is constructed based on Maeder's stellar evolutionary and Kurucz stellar atmosphere models, to synthesize observational quantities of embedded clusters in GEHRs. The observed H-alpha luminosity is a measure of the number of massive stars while the contribution to BVR bands is from intermediate mass (5-15 solar mass) stars when the cluster is young and from evolving supergiants when the cluster is old (age >/= 6~Myr). Differential reddening between gas and embedded stars is essential to constrain the dereddened cluster colors within the range of youngest clusters. Obscuring dust closely associated with gas, which is distributed in filaments and clumps, as in the case of 30 Doradus, is the most likely configuration giving rise to net reduction of extinction towards stars. The fraction of the stellar photons escaping the nebula unattenuated is estimated to be 50%. GEHRs are rarely found to be simple systems containing stars from single generation. In the present sample such regions in addition to being older than 3~Myr, have their Lyman continuum luminosity reduced by as much as 60%, compared to the observed $B$ band luminosity for a normal IMF. The missing ionizing photons may be escaping the nebula, leading to the ionization of extra-H II region ionized medium. Co-existence of young (age = 5 Myr; stars producing ionizing photons) and old populations (~10~Myr; Red Supergiants) is found to be common in GEHRs. The emission and continuum knots are seen spatially separated (40-100 pc) on CCD images in NGC 2997, 4303 and 4449 and may be direct evidences for the co-existence of young and old populations in giant star forming complexes. Triggering of star formation from earlier bursts is the most likely cause of new generation of stars, and may be a common phenomenon in GEHRs. Spatial separation between the young and old stars (~30 pc) had been earlier reported in 30 Doradus. Thus GEHRs in nearby galaxies share many of the properties shown by 30 Dor, the nearest GEHR. (SECTION: Dissertation Summaries)
Resumo:
We examine three hierarchies of circuit classes and show they are closed under complementation. (1) The class of languages recognized by a family of polynomial size skew circuits with width O(w), are closed under complement. (2) The class of languages recognized by family of polynomial size circuits with width O(w) and polynomial tree-size, are closed under complement. (3) The class of languages recognized by a family of polynomial size, O(log(n)) depth, bounded AND fan-in with OR fan-in f (f⩾log(n)) circuits are closed under complement. These improve upon the results of (i) Immerman (1988) and Szelepcsenyi (1988), who show that 𝒩L𝒪𝒢 is closed under complementation, and (ii) Borodin et al. (1989), who show that L𝒪𝒢𝒞ℱL is closed under complement