T Kastrin
email: tamara.kastrin@ivz-rs.si

M Paragi

J Kolman

M Čižman

M Kraigher

Gubina

Manica Muller-Premru

Iztok Štrumbelj

Tjaša Žohar Čretnik

Jerneja Fišer

Ingrid Berce

Helena Ribič

Dušan Novak

Martina Kavčič

Tatjana Harlander

Irena Piltaver-Vajdec

Viktorija T Tomič

Kastrin

A Kraigher

Characterisation of invasive Haemophilus influenzae isolates in Slovenia, 1993-2008

The objectives of our study were to describe the epidemiology of invasive Haemophilus influenzae disease from 1993 to 2008 in Slovenia, a country with routine H. influenzae serotype b (Hib) conjugate vaccination since the year 2000. A total of 292 isolates of H. influenzae, recovered from a normally sterile site, were collected in the study period. The isolates were serotyped by slide agglutination and antibiotic susceptibility was determined. One hundred and eight isolates received after the year 2000 were serotyped by slide agglutination and by polymerase chain reaction (PCR) capsule typing, and both methods were compared. After the introduction of the routine Hib vaccination, the incidence of H. influenzae disease in children under the age of 5 years has decreased by 87.6% and type b was replaced by non-typeable H. influenzae as the predominant serotype. The proportion of serotype b decreased from 85.3% in the pre-vaccination period to 13.0% in the vaccination period and the proportion of noncapsulated isolates increased from 12.0 to 85.2%. The study of genetic relatedness by pulsed-field gel electrophoresis (PFGE) demonstrated that the isolates of serotypes b and f were genetically homogeneous within the serotype. The results of our national surveillance showed that the vaccine has been very efficient in preventing Hib invasive disease in Slovenia. Nevertheless, we see a need for further monitoring of invasive H. influenzae infections at a national level.

Introduction

Haemophilus influenzae is an important respiratory pathogen in both children and adults and, until the implementation of vaccination, in many countries, it was also one of the three leading causes of bacterial meningitis in young children. H. influenzae serotype b (Hib) was an important cause of paediatric morbidity and mortality. Hib conjugate vaccine has produced a dramatic decline in the incidence of invasive Hib disease over a very short period of time [START_REF] Heath | Non-type b Haemophilus influenzae disease: clinical and epidemiologic characteristics in the Haemophilus influenzae type b vaccine era[END_REF][START_REF] Peltola | Worldwide Haemophilus influenzae type b disease at the beginning of the 21st century: global analysis of the disease burden 25 years after the use of the polysaccharide vaccine and a decade after the advent of conjugates[END_REF][START_REF] Kriz | Large decrease in incidence of invasive Haemophilus influenzae b disease following introduction of routine vaccination in the Czech Republic[END_REF][4]. As a consequence, non-capsulated isolates are predominant in invasive H. influenzae disease in countries with Hib vaccination programmes [START_REF] Bajanca | Emergence of nonencapsulated and encapsulated non-b-type invasive Haemophilus influenzae isolates in Portugal (1989-2001)[END_REF][START_REF] Sarangi | Invasive Haemophilus influenzae disease in adults[END_REF]. In countries without Hib vaccination, H. influenzae remains a major cause of meningitis in very young children and increasing rates of antibiotic resistance have also been reported [START_REF] Hasegawa | High prevalence of type b betalactamase-non-producing ampicillin-resistant Haemophilus influenzae in meningitis: the situation in Japan where Hib vaccine has not been introduced[END_REF][START_REF] Saha | Direct detection of the multidrug resistance genome of Haemophilus influenzae in cerebrospinal fluid of children: implications for treatment of meningitis[END_REF][START_REF] Rahman | Haemophilus influenzae type-b and nonb-type invasive diseases in urban children (<5 years) of Bangladesh: implications for therapy and vaccination[END_REF].

In 1993, the national surveillance project, which followed the occurrence of invasive diseases caused by Neisseria meningitidis, H. influenzae and Streptococcus pneumoniae in Slovenia was initiated. After the introduction of regular Hib vaccination at the end of 1999, the main cause of vaccine-preventable bacterial invasive diseases in Slovenia became S. pneumoniae and N. meningitidis [START_REF] Paragi | Possibility of application of new pneumococcal conjugate vaccines in children in Slovenia[END_REF]. Nevertheless, the laboratory surveillance of invasive H. influenzae is needed in order to monitor the effectiveness of immunisation programmes and vaccines. The objective of this study was to characterise the epidemiology of invasive H. influenzae in Slovenia before and after Hib conjugate vaccine was introduced. In this study, we also evaluated two methods to identify the serotype, slide agglutination and molecular capsule typing, since accurate results are very important where H. influenzae has become a very rare cause of invasive disease.

Materials and methods

Bacterial isolates

All invasive isolates of H. influenzae, recovered from normally sterile sites, isolated in all Slovenian microbiological laboratories were collected at the National Institute of Public Health (NIPH) as a part of national surveillance system. Since 1993, all invasive isolates of H. influenzae isolated from children (0-14 years of age) have been collected and since 1996, the isolates from adult patients have also been collected.

From 1993 to 1999, in the so-called pre-vaccination period, 184 isolates were collected; of these, 160 were from children (0-14 years of age) and 24 were from adult patients (≥ 15 years of age). From 2000 to 2008, 108 isolates were collected; of these, 31 were from children and 77 were from adult patients. Altogether, 292 isolates were included in the study. The isolates were derived from 135 (46.2%) female and 157 (53.8%) male patients. Altogether, the isolates were derived from the following clinical specimens: blood only (155 isolates), cerebrospinal fluid only (51), both blood and cerebrospinal fluid (73), pleural aspirates [START_REF] Saha | Direct detection of the multidrug resistance genome of Haemophilus influenzae in cerebrospinal fluid of children: implications for treatment of meningitis[END_REF] and puncture joint exudates [START_REF] Bajanca | Emergence of nonencapsulated and encapsulated non-b-type invasive Haemophilus influenzae isolates in Portugal (1989-2001)[END_REF]. Isolates were regrown on chocolate agar (Merck KGaA, Darmstadt, Germany) and on Levinthal agar (Merck KGaA, Darmstadt, Germany) and incubated at 35°C for 24 h in 5% CO 2 . Isolates were routinely serotyped by slide agglutination and stored at -70°C.

Serotyping

Isolates were serotyped by slide agglutination using the Phadebact Haemophilus Test (Bactus AB, Huddinge, Sweden) and specific H. influenzae capsular antisera (BD, Maryland, USA). From the year 2000 onwards, all results were reviewed and molecular capsule typing by polymerase chain reaction (PCR) was done. Both methods were compared and Cohen's Kappa test was used for the statistical evaluation.

Bacterial DNA isolation and PCR Isolation of bacterial DNA for PCR was done using the MagNA Pure Instrument and the MagNA Pure LC DNA Isolation Kit III (Roche Diagnostics GmbH, Mannheim, Germany), according to the manufacturer's instructions. Each isolate was tested for the presence of the ompP2, bexA and capb genes by PCR. Capsulated isolates (isolates positive for bexA and negative for capb) were further tested for other cap-specific genes. Strains that lacked both the type b-specific and bexA gene regions were designated as non-typeable (NT). Strains that carried the type b-specific gene region and lacked bexA were designated as Hib -. Sequence-specific primers were previously described; for cap genes by Falla et al., ompP2 primers by Hobson et al. and bexA primers by van Ketel et al. [START_REF] Falla | PCR for capsular typing of Haemophilus influenzae[END_REF][START_REF] Hobson | Incidence and spread of Haemophilus influenzae on an Antarctic base determined using the polymerase chain reaction[END_REF][START_REF] Van Ketel | Detection of Haemophilus influenzae in cerebrospinal fluids by polymerase chain reaction DNA amplification[END_REF]. Amplification reactions were performed in a total reaction volume of 50 μl with 2 μl of template, 0.2 mM dNTP, 0.4 μM each primer and 0.01 U/μl Top Taq DNA polymerase (Qiagen, Hilden, Germany). PCR conditions were 3 min at 94°C, 30 s at 94°C, 30 s at 52°C, 1 min at 72°C, for 35 cycles, 10 min at 72°C and 4°C hold. PCR products were analysed on 1% agarose gel containing 0.1 μg/ml ethidium bromide. The following strains were used as positive controls; ATCC 9006 (capsule type a), ATCC 10211 (capsule type b), ATCC 9007 (capsule type c), ATCC 9008 (capsule type d), ATCC 8142 (capsule type e) and ATCC 9833 (capsule type f).

Susceptibility testing

Susceptibility testing was performed for 108 isolates from 2000 to 2008. Susceptibilities to ampicillin, ampicillinsulbactam, azithromycin, tetracycline, trimethoprim/ sulfamethoxazole, cholamphenicol, ciprofloxacin, cefaclor and cefuroxime were tested by the disc diffusion method following the recommendations of the Clinical Laboratory Standards Institute (CLSI) [START_REF]Performance Standards for Antimicrobial Susceptibility Testing; Eighteenth Informational Supplement[END_REF]. The minimum inhibitory concentrations (MICs) for ampicillin, amoxicillin-clavulanic acid, cefotaxime and ceftriaxone were determined with the Etest (AB Biodisk, Solna, Sweden). Both methods were performed on Haemophilus Test Medium (HTM) agar (Oxoid, Hampshire, United Kingdom) under incubation at 35°C in 5% CO 2 for 16-18 h (disc diffusion) or 20-24 h (Etest). Standard quality control strains, H. influenzae ATCC 49247, ATCC 49766 and ATCC 10211, were included in each run. Beta-lactamase production was detected using a Cefinase™ disc (BBL, Becton Dickinson, MD, USA).

Pulsed-field gel electrophoresis

Pulsed-field gel electrophoresis (PFGE) of the selected isolates was performed using the commercial kit Genepath Group 1 (Bio-Rad, Hercules, USA), which included digestion with restriction enzyme SmaI. PFGE was run in 0.5× TBE buffer on 1% agarose (Bio-Rad, Hercules, USA) in the Gene Path@System, programme 12 (18.5 h, 14°C at 6 V/cm with a ramped pulse time of 1-17 s). After electrophoresis, the gels were stained for 30 min with 0.5 mg of ethidium bromide per litre. Staphylococcus aureus NCTC 8352 strain was used for a quality control. DNA bands were visualised on the Gel Doc XR system with the Quantity One Software (Bio-Rad, Hercules, USA). The software Fingerprinting II (Bio-Rad, Hercules, USA) was used to generate unweighted pair group method with arithmetic mean (UPMGA) dendrograms of fragment patterns with the dice coefficient (optimisation and position tolerance settings of 1.0%). PFGE-based clusters were defined as isolates with ≥80% genetic relatedness.

Results

Incidence and serotype distribution

In Slovenia, compulsory vaccination for Hib was introduced at the end of 1999. In the period 1993 to 1999, invasive H. influenzae was as frequent as invasive disease caused by S. pneumoniae in children under the age of 15 years [START_REF] Paragi | Possibility of application of new pneumococcal conjugate vaccines in children in Slovenia[END_REF]. After the year 2000, the incidence of invasive H. influenzae has rapidly fallen to, on average, 1 per 100,000 children (0-14 years of age) per year and no case of invasive H. influenzae type b disease has been reported in children under the age of 15 years since 2002 (Table 1).

After the introduction of the routine Hib vaccination, we observed a dramatic decline of invasive H. influenzae disease in children under the age of 5 years (Fig. 1). In the pre-vaccination period (1993-1999), the average incidence of H. influenzae invasive disease per year in the age group 0-1 was 28.3/100,000, and for children 2-4 years of age, it was 20.9/100,000 (together 24.6/100,000). In the period after the vaccine introduction, the average incidence of H. influenzae invasive disease per year for children 0-1 year of age was 4.2/100,000 and for children 2-4 years of age, it was 1.9/100,000 (together 3.05/100,000). The introduction of the routine vaccination made significant changes in the epidemiology of invasive H. influenzae, as we observed an 8-fold decrease in the incidence of H. influenzae invasive disease in the children population under the age of 5 years (from 24.6/100,000 to 3.05/100,000 or a 87.6% decrease).

Besides the decline of invasive H. influenzae disease in children, we also observed the change in serotype distribution. Before the vaccine introduction, the majority of all 184 cases were type b (157; 85.3%), followed by noncapsulated or NT isolates (22; 12.0%) and serotype f (4; 2.2%). After the vaccine introduction, most of the 108 cases were caused by NT (92; 85.2%), followed by serotype b (14; 13.0%) and serotype f (2; 1.9%). In the case of isolates 2). The compared methods showed good agreement (Cohen's Kappa test 0.745). The rate of discordance was 11.1% (12/108). Nevertheless, there was some important disagreement, especially the misclassification of two NT isolates as serotype b. Capsule type d isolates were found to have the highest discrepancy between the two tested methods, since all five isolates were misclassified. Moreover, the PCR capsule typing has the advantage of detecting the capsule-deficient Hib -, but in our case, there was no such an example. Therefore, we believe that PCR capsule typing should be used as a gold standard, since slide agglutination results can be misinterpreted in the case Out of these, 14 isolates (13%) were non-susceptible to ampicillin. Production of beta-lactamase was the principal mechanism of ampicillin resistance, occurring in 10.2% of isolates (11/108) (MIC ≥ 256 mg/l). Beta-lactamase production was tested also in the period 1993 to 1999, and it occurred in 13.6% of isolates. One isolate was defined as beta-lactamase-negative ampicillin-resistant (BLNAR); it was also resistant to amoxicillin-clavulanic acid, cefuroxime and cefaclor.

PFGE analysis

In this study, all of the encapsulated isolates within a particular serotype showed high genetic homogeneity. Among all 14 Hib isolates from the post-vaccine era, nine isolates belonged to one clonal cluster and three isolates to the second clonal cluster (Fig. 3). The six isolates with serotype f (four from the pre-vaccine period, two isolated since the year 2000) were clonally highly related. Among 11 isolates carrying the beta-lactamase, we observed no clustering, only three NT isolates were clonally related. Among the tested 23 NTHi isolates, genetic diversity was observed (results not shown).

Discussion

Surveillance of invasive H. influenzae disease in the Hib vaccine era is important for monitoring the effectiveness of Hib conjugate vaccines, as well as for monitoring the epidemiology of invasive H. influenzae. Prior to the introduction of Hib conjugate vaccine, this pathogen was an important cause of serious paediatric invasive disease.

Because of the introduction of Hib conjugate vaccine, disease due to invasive H. influenzae has become rare. This vaccine also prevents nasopharyngeal colonisation, which partly explains such effectiveness [START_REF] Peltola | Worldwide Haemophilus influenzae type b disease at the beginning of the 21st century: global analysis of the disease burden 25 years after the use of the polysaccharide vaccine and a decade after the advent of conjugates[END_REF].

In some countries, the re-emergence of H. influenzae type b in vaccinated children has been reported [START_REF] Peltola | Worldwide Haemophilus influenzae type b disease at the beginning of the 21st century: global analysis of the disease burden 25 years after the use of the polysaccharide vaccine and a decade after the advent of conjugates[END_REF][START_REF] Aracil | Molecular epidemiology of Haemophilus influenzae type b causing vaccine failures in the United Kingdom[END_REF][START_REF] Dargan | Reemergence of invasive Haemophilus influenzae type b disease in Alaska: Is it because of vaccination with polyribosylribitol phosphate outer membrane protein complex (PRP-OMPC) or failure to vaccinate with PRP-OMPC?[END_REF][START_REF] Galil | Reemergence of invasive Haemophilus influenzae type b disease in a well-vaccinated population in remote Alaska[END_REF][START_REF] Trotter | Rising incidence of Haemophilus influenzae type b disease in England and Wales indicates a need for a second catch-up vaccination campaign[END_REF]. Recent studies suggest that NT strains are now responsible for most of the H. influenzae disease [START_REF] Heath | Non-type b Haemophilus influenzae disease: clinical and epidemiologic characteristics in the Haemophilus influenzae type b vaccine era[END_REF][START_REF] Bajanca | Emergence of nonencapsulated and encapsulated non-b-type invasive Haemophilus influenzae isolates in Portugal (1989-2001)[END_REF][START_REF] Aracil | Molecular epidemiology of Haemophilus influenzae type b causing vaccine failures in the United Kingdom[END_REF][START_REF] Dworkin | The changing epidemiology of invasive Haemophilus influenzae disease, especially in persons>or=65 years old[END_REF]. Concern about a possible rise in the incidence of invasive infection with non-serotype b capsulate isolates after the widespread Hib vaccination exists. Indeed, reports regarding an expansion of H. influenzae type f clone were published [START_REF] Bruun | Clonal relationship of recent invasive Haemophilus influenzae serotype f isolates from Denmark and the United States[END_REF][START_REF] Campos | Antibiotic resistance and clinical significance of Haemophilus influenzae type f[END_REF]. The study by Cerquetti et al. documented the emergence of invasive H. influenzae type e disease [START_REF] Cerquetti | Invasive type e Haemophilus influenzae disease in Italy[END_REF]. Therefore, the need for surveillance to monitor developments concerning replacement as vaccination becomes prevalent worldwide and accurate serotyping to enable reliable results is of great importance [START_REF] Bajanca | Emergence of nonencapsulated and encapsulated non-b-type invasive Haemophilus influenzae isolates in Portugal (1989-2001)[END_REF][START_REF] Bruun | Clonal relationship of recent invasive Haemophilus influenzae serotype f isolates from Denmark and the United States[END_REF].

In Slovenia, a country with a population of approximately 2 million (∼280,000 children under 15 years of age), the epidemiologic situation of invasive H. influenzae diseases has been constantly monitored since 1993 [START_REF] Paragi | Possibility of application of new pneumococcal conjugate vaccines in children in Slovenia[END_REF]. According to the law on communicable diseases, some vaccine-preventable diseases are compulsory notified directly to the NIPH. All medical laboratories are sending isolates to the reference laboratory at the NIPH for serotyping and resistance determination. Via this project, all invasive strains of H. influenzae were intentionally collected and the evaluated results reflect the national level.

We demonstrated that the introduction of the Hib vaccine in Slovenia at the end of 1999 led to changes in invasive H. influenzae epidemiology. The incidence of invasive H. influenzae disease in children aged less than 5 years decreased 8-fold and reached an average of 3 per 100,000 per year in the vaccination era. We also showed the change in the serotype distribution of invasive H. influenzae: the proportion of serotype b decreased from 85.3% in the prevaccination era to 13.0% in the vaccination era and the increase of proportion of NT isolates from 12.0 to 85.2% was noted. The results coincide with data published for Portugal [START_REF] Bajanca | Emergence of nonencapsulated and encapsulated non-b-type invasive Haemophilus influenzae isolates in Portugal (1989-2001)[END_REF]. In both periods, we identified only a few isolates of serotype f. We detected only one case of vaccine failure receiving four doses and, moreover, no case of Hib has been observed in the children aged less than 5 years since the year 2001. We also observed no case of capsule- In surveillance, it is very important to carry out reliable serotyping, especially to discriminate between Hib and other serotypes or NTHi. Because Hib has become a rare cause of invasive disease, the need to identify the serotype correctly has increased. Therefore, we compared the standard slide agglutination serotyping with molecular capsule typing by PCR. Several studies have favoured PCR capsule typing [START_REF]Serotyping discrepancies in Haemophilus influenzae type b disease-United States, 1998-1999[END_REF][START_REF] Bokermann | Evaluation of methodology for serotyping invasive and nasopharyngeal isolates of Haemophilus influenzae in the ongoing surveillance in Brazil[END_REF][START_REF] Laclaire | Identification of Haemophilus influenzae serotypes by standard slide agglutination serotyping and PCR-based capsule typing[END_REF][START_REF] Satola | Capsule gene analysis of invasive Haemophilus influenzae: accuracy of serotyping and prevalence of IS1016 among nontypeable isolates[END_REF]. In our study, the rate of discordance was 11.1% (12/108). The most common error was the misidentification of NTHi as capsulated (in most cases as type d) by slide agglutination. Considering the facts that serotyping by slide agglutination is less accurate, it is unable to detect Hib -and invasive H. influenzae infections have become rare-we recommend the PCR capsule typing for confirming the serotype result. Because of the low numbers of invasive H. influenzae isolates, mistyping might have a big influence on the surveillance results.

Antibiotic resistance in H. influenzae was first detected in 1972 with an ampicillin-resistant isolate and, since then, A) serotype b B) serotype f C) isolates carrying the beta-lactamase Fig. 3a-c the resistance to several other antibiotics has developed. Therefore, it is also important to monitor the antibiotic susceptibility in invasive H. influenzae. Our results show that resistance to ampicillin was the most frequently detected resistance. The main mechanism of resistance was beta-lactamase production (11 out of 14 ampicillinresistant isolates), as was the case in other studies [START_REF] Cerquetti | Antimicrobial susceptibility of Haemophilus influenzae strains isolated from invasive disease in Italy[END_REF][START_REF] Tristram | Antimicrobial resistance in Haemophilus influenzae[END_REF]. In Slovenia, BLNAR isolates of invasive H. influenzae were very rare. Indeed, we detected only one isolate in the period 2000 to 2008. These data coincide with multi-centre European studies, where considerable variation from different countries, from 1.5 to 33.9%, was observed [START_REF] Hoban | The PROTEKT surveillance study: antimicrobial susceptibility of Haemophilus influenzae and Moraxella catarrhalis from community-acquired respiratory tract infections[END_REF]. There is also some evidence that the prevalence of ampicillin resistance of H. influenzae in Europe may be decreasing due to a reduction in the number of betalactamase-positive isolates, whereas the prevalence of BLNAR strains is relatively stable [START_REF] Hoban | The PROTEKT surveillance study: antimicrobial susceptibility of Haemophilus influenzae and Moraxella catarrhalis from community-acquired respiratory tract infections[END_REF][START_REF] Jansen | Longitudinal European surveillance study of antibiotic resistance of Haemophilus influenzae[END_REF]. In Spain, however, an increase of BLNAR strains has been reported [START_REF] García-Cobos | Ampicillin-resistant non-betalactamase-producing Haemophilus influenzae in Spain: recent emergence of clonal isolates with increased resistance to cefotaxime and cefixime[END_REF]. In Japan and South Korea, they are confronted with high rates of BLNAR strains [START_REF] Hasegawa | High prevalence of type b betalactamase-non-producing ampicillin-resistant Haemophilus influenzae in meningitis: the situation in Japan where Hib vaccine has not been introduced[END_REF][START_REF] Tristram | Antimicrobial resistance in Haemophilus influenzae[END_REF][START_REF] Kim | Diversity of ampicillin resistance genes and antimicrobial susceptibility patterns in Haemophilus influenzae strains isolated in Korea[END_REF]. In Slovenia, we did not observe any increase in ampicillin resistance and, according to the PFGE results, ampicillin-resistant isolates were not clonally related.

The analysis of genetic relatedness of invasive H. influenzae from Slovenia showed that isolates of serotype b were mostly clonally related. This observation coincides with other studies [START_REF] \meats | Characterization of encapsulated and noncapsulated Haemophilus influenzae and determination of phylogenetic relationships by multilocus sequence typing[END_REF][START_REF] Musser | Global genetic structure and molecular epidemiology of encapsulated Haemophilus influenzae[END_REF][START_REF] Saito | Subtyping of Haemophilus influenzae strains by pulsed-field gel electrophoresis[END_REF]. The H. influenzae type f isolates also showed very high degree of homogeneity, which is in concordance with previously published data [START_REF] Bruun | Clonal relationship of recent invasive Haemophilus influenzae serotype f isolates from Denmark and the United States[END_REF]. On the other hand, most of the NT isolates did not cluster and the high levels of diversity indicated different clonal origins. A clone of serotype f was genetically unrelated to Hib or NT isolates, as expected [START_REF] Bajanca | Emergence of nonencapsulated and encapsulated non-b-type invasive Haemophilus influenzae isolates in Portugal (1989-2001)[END_REF][START_REF] Omikunle | Limited genetic diversity of recent invasive isolates of non-serotype b encapsulated Haemophilus influenzae[END_REF].

In summary, data from our surveillance strongly indicate that, after the introduction of routine vaccination, the incidence of H. influenzae invasive disease and its epidemiological pattern have changed remarkably. Therefore, we see a need for further monitoring of invasive H. influenzae infections at the national level.

  Hib = H. influenzae serotype b from children 0 to 5 years of age in the period 1993 to 1999, the majority of 151 cases were type b (142; 94.0%), followed by NT (7; 4.6%) and serotype f (2; 2.2%). In the vaccine period in the population of children 0 to 5 years of age, there were only 23 cases of invasive H. influenzae disease; most of them were NT (16; 70%), followed by type b (6; 26%) and serotype f (1; 4%) (Fig.2). In the period 2000-2001, three children with Hib meningitis were previously vaccinated. Two of them were vaccinated with only one dose. The onset of diseases was 1 to 3 months after Hib vaccination. One child with cancer who received four doses of vaccine developed Hib meningitis five months later.Analysis of isolates by serotyping and PCR typingOne hundred and eight isolates received in the period from 2000 to 2008 were serotyped by slide agglutination and by PCR capsule typing. By slide agglutination, there were two isolates type a, 16 isolates type b, two isolates type c, five isolates type d, three isolates type f and 80 isolates were NTHi (non-typeable H. influenzae). All 80 isolates originally serotyped as NT were confirmed by PCR capsule typing. Twelve of twenty-eight isolates reported as encapsulated by slide agglutination (two Hia, two Hic, five Hid, one Hif and two Hib) were shown to be NT by PCR. None of the 108 tested isolates were Hib -(Table

Fig. 1 Fig. 2

 12 Fig. 1 Incidence of invasive Haemophilus influenzae disease per year according to age groups in the pre-vaccination period (1993-1999) and in the vaccination period (2000-2008) in Slovenia

Table 2

 2 Comparison of typing of 108 invasive H. influenzae isolates by slide agglutination and by PCR capsule typing in the period 2000 to 2008 in Slovenia Hib -. As a result of the decline in Hib invasive disease caused by the introduction of vaccination, NTHi has become the most important cause of H. influenzae invasive disease in Slovenia.

	Serotype by SA	PCR capsule type
		a	b	c	d	e	f	NT	b -	Total
	a							2		2
	b		1 4					2		1 6
	c							2		2
	d							5		5
	e							0		0
	f						21		3
	NT							80		80
	Total	0	14	0	0	0	2	92	0	108
	SA = slide agglutination; NT = non-typeable

deficient

Acknowledgements We thank Špela Hostnik, Marko Bezenšek, Mirjana Ćulafić and Breda Logonder for their technical assistance in the laboratory.


G J H M Ruijs

Ms Marjan J Bruins
email: m.j.bruins@isala.nl

MD Maurice J H M Wolfhagen

PhD Jurjen Schirm

PhD ; Gijs

MD J Ruijs

Isala Klinieken

Evaluation of a rapid immunochromatographic test for the detection of norovirus in stool samples

Keywords: norovirus, feces/virology, gastroenteritis, sensitivity/specificity, rapid test norovirus, feces/virology, gastroenteritis, sensitivity/specificity, rapid test

Evaluation of a rapid immunochromatographic test for the detection of norovirus in stool samples

Noroviruses (NoVs) have a leading role in causing gastroenteritis worldwide, causing high morbidity rates among patients of all ages [START_REF] Patel | Noroviruses: a comprehensive review[END_REF]. Formerly identified as 'small round structured viruses' and 'Norwalk like virus', NoVs are now known as single-stranded RNA viruses, belonging to the genus Norovirus and part of the family Caliciviridae [START_REF] Green | Caliciviridae: The Noroviruses[END_REF]. The genus comprises five genogroups I-V (GI-GV), of which GI, GII and GIV are human pathogens [3].

Strains of GI and GII are the most common agents of gastroenteritis [START_REF] Patel | Noroviruses: a comprehensive review[END_REF]. Gastroenteritis caused by NoV has an incubation period of 24-48 hours, although earlier onset does occur.

Symptoms usually last 2-3 days and include nausea, vomiting, abdominal cramps, non-bloody diarrhoea and sometimes fever [START_REF] Patel | Noroviruses: a comprehensive review[END_REF]. NoV may be acquired from contaminated food or water and is excreted in stool and vomit. Since very low doses of viral particles are infectious, rapid spreading through faecal-oral or air-borne transmission easily causes an epidemic, especially in institutions such as hospitals and nursing homes [START_REF] Patel | Noroviruses: a comprehensive review[END_REF]. Rapid detection of NoV in stool is essential in both sporadic cases of gastroenteritis and in outbreak prevention and management. Until recently the available test methods were reverse transcription PCR (RT-PCR) and enzyme immunoassays (EIAs) for the detection of viral RNA and antigen respectively. Both methods take several hours to perform however [START_REF] Hoehne | Detection of norovirus genogroup I and II by multiplex real-time RT-PCR using a 3'-minor groove binder-DNA probe[END_REF]5], whereas the newly developed rapid antigen test RIDA ® QUICK Norovirus (RQN assay; R-Biopharm, Darmstadt, Germany) gives a result in approximately 20 minutes.

We evaluated the RQN assay by testing all stool samples submitted to the Laboratorium voor The Netherlands) by incubation at 25°C for 10 min., at 48°C for 30 min. and at 95°C for 5 min. Of the obtained cDNA 10 µl was amplified using an Applied Biosystems 7500 Real-Time PCR System, using primer and probe sets as described by Hoehne et al. [START_REF] Hoehne | Detection of norovirus genogroup I and II by multiplex real-time RT-PCR using a 3'-minor groove binder-DNA probe[END_REF], in a 25 µl reaction containing 12.5 µl TaqMan® Universal PCR Master Mix (Applied Biosystems), 15 pmol of each primer and 10 pmol probe by incubation at 50°C for 2 min., at 95°C for 10 min., and subsequently 40 cycles at 95°C for 15 seconds and 60°C for 1 min. Appropriate control reactions were included in each RT-PCR run.

In total 538 stool samples from 420 patients (98 hospitalized patients, 39 nursing home inhabitants, 25 general practice patients and 258 outpatients) were tested. Of these, one sample showed inhibition of the PCR and was excluded. Of the remaining 537 samples, 98 (18.2%) were PCR-positive and 60 (11.2%) were positive by the RQN assay (Table 1). Using the RT-PCR as the gold standard the sensitivity, specificity, positive and negative predictive values of the RQN assay were 57.1% (56/98), 99.1% (435/439), 93.3% (56/60) and 91.2% (435/477) respectively.

The sensitivity of the RQN assay was low, but the specificity was excellent. The test allows single sample testing within 20 minutes and is easy to perform and interpret.

Apostel et al. tested 113 stored stool specimens with the RQN assay and RT-PCR [START_REF] Apostel | RIDA ® QUICK Norovirus: a new dimension for norovirus detection[END_REF].

Sensitivity and specificity of the RQN assay were 86.0% and 94.6% respectively. They found similar results when the same samples were tested with the RIDASCREEN ® Norovirus EIA (R-Biopharm), in which NoV GI and GII antigen in stool is detected in a microwell plate (76.8 and 98.2% respectively). Other studies comparing the RIDASCREEN ® Norovirus EIA to RT-PCR reported sensitivities of the EIA between 44 and 76% and specificities between 47 and 96%, which are more consistent with our findings for the RQN assay [START_REF] Dimitriadis | Evaluation of a commercial enzyme immunoassay for detection of norovirus in outbreak specimens[END_REF][START_REF] González | Evaluation of a commercial enzyme immunoassay for the detection of norovirus antigen in fecal samples from children with sporadic acute gastroenteritis[END_REF][START_REF] Gray | Below you find our responses to the Reviewers' comments to the first submission of our manuscript[END_REF][10]. The difference between Apostel's and our RQN assay sensitivity results may be explained by differences between the two patient populations, the prevalent viral genotypes in these populations and the stage of infection at which sampling took place.

The RQN assay and the RIDASCREEN ® Norovirus EIA seem to perform equally well, but the rapid RQN assay saves valuable test time compared to the EIA. The lower sensitivities of both the rapid test and the EIA compared to RT-PCR may be explained by the inability of both tests to detect low viral loads. It is important to test well homogenized stool as soon as possible after the onset of symptoms, when viral shedding is highest.

In addition to the most frequently detected GII strains, also strains belonging to GIV have been reported to cause diarrhoea. La Rosa et al. recently found GIV strains in sewage and in stools from patients with acute gastroenteritis [11]. This indicates that future techniques must be able to detect a wider range of NoV variants.

The rapid immunochromatographic RQN assay is a valuable tool for the rapid screening of NoV infection. Its high specificity enables early confirmation of an outbreak, and easy follow-up of positive patients. A negative test result, however, should be followed up by RT

Medische

  Microbiologie en Infectieziekten (LMMI), Zwolle, The Netherlands, from patients suspected of NoV infection in the period of January-April 2009 and compared the results to those of a real-time RT-PCR. The RQN assay is an immunochromatographic test which detects NoV GI and GII in stool. The membrane in the test cassette contains a test line with attached to it monoclonal antibodies to NoV and a control line with anti-mouse IgG. A stool suspension is prepared in dilution buffer. The first conjugate containing biotinylated anti-NoV is added to the supernatant of the suspension and the mix is pipetted into the sample well on the test cassette. The sample migrates along the membrane, crossing the test line and the control line. If NoV is present, antigen-antibody complexes bind to the test line. Unbound anti-NoV binds to the control line. The second conjugate containing streptavidin-peroxidase is added to the reaction window on the test cassette, allowing the streptavidin to bind to the biotin. Excess biotin is washed away and the substrate (H 2 O 2 ) with the chromophore tetramethylbenzidine (TMB) is added. Reaction between substrate and TMB turns both test and control lines blue when conjugate is bound to biotinylated antibody. If no NoV is present in the stool sample only the control line turns blue. The real-time RT-PCR for the detection of NoV GI and GII was performed at the Laboratory for Infectious Diseases, Groningen, The Netherlands. Stool suspensions were prepared in phosphate-buffered saline and NoV RNA was extracted from the supernatant using the MagNA Pure LC Total Nucleic Acid Isolation Kit (Roche Diagnostics, Almere, The Netherlands) according to the manufacturer's instructions. First reverse transcription was performed in a 20 µl reaction containing 5 µl RNA using the TaqMan® Reverse Transcription Reagents kit (Applied Biosystems, Nieuwerkerk a/d IJssel,

Table 1 .

 1 Pourshaban M, Iaconelli M, Muscillo M (2008) Detection of genogroup IV noroviruses in environmental and clinical samples and partial sequencing through rapid amplification of cDNA ends. Arch Virol 153:2077-2083 Results of the RQN assay compared with RT-PCR No. of samples with PCR result

	-

Table


Alberto Carrasco

Marc Mars
email: marc@usal.es

A counterexample to a recent version of the Penrose conjecture

Keywords: 04.20.q, 04.20.Cv, 04.70.Bw, 02.40.k, 02.40.Vh

By considering suitable axially symmetric slices on the Kruskal spacetime, we construct a counterexample to a recent version of the Penrose inequality in terms of so-called generalized apparent horizons.

Introduction

In a serious attempt [START_REF] Bray | s which imply the Penrose conjecture[END_REF] to prove the Penrose inequality in the general case, Bray and Khuri were led to conjecture a new version of the Penrose inequality in terms of so-called generalized apparent horizons. In fact, they proved that if a certain system of PDEs admit solutions with the right boundary behaviour, then such a Penrose inequality follows. In this paper we show that this inequality cannot be true in general by finding slices of the Kruskal spacetime (i.e. the maximally extended Schwarzschild spacetime) for which the outermost generalized apparent horizon has area strictly larger than 16πM 2 , where M is the ADM mass of the spacetime. We start with a brief discussion on the Penrose inequality, with the aim of putting the Bray and Khuri proposal into context (see [START_REF] Mars | Present status of the Penrose inequality[END_REF] for further details) and then show that there exist slices of Kruskal for which this inequality is violated. For the systems of PDEs proposed in [START_REF] Bray | s which imply the Penrose conjecture[END_REF], this means that a general existence theory cannot be expected with boundary conditions compatible with generalized apparent horizons. However, simpler boundary conditions (e.g. compatible with future and past apparent horizons) are not ruled out. This may in fact simplify the analysis of these equations.

Penrose [START_REF] Penrose | Naked singularities[END_REF] noticed that the total mass of a spacetime containing black holes that settle down to a stationary state must satisfy the inequality

M ADM ≥ |H| 16π , ( 1
)
where |H| is the area of the event horizon at one instant of time. Moreover, assuming the matter contents to satisfy the dominant energy condition and combining (1) with cosmic censorship, Penrose observed that new inequalities similar to [START_REF] Bray | s which imply the Penrose conjecture[END_REF] follow, where the righthand side is replaced by the area of certain surfaces which can be defined independently of the future evolution of the spacetime (in contrast to the event horizon). This type of inequalities are collectively termed Penrose inequalities. Their main interest is two-fold. Firstly, they provide strengthenings of the positive mass theorem. Secondly, since cosmic censorship is the basic physical ingredient supporting their validity, a direct proof of the inequality would give rather strong indirect support for the cosmic censorship conjecture.

There are several versions of the Penrose inequality. Typically, one considers closed (i.e. compact and without boundary) surfaces S embedded in a spacelike and asymptotically flat hypersurface Σ, which are bounding, i.e. such that S divides Σ into two open regions. The region containing the asymptotically flat end is called "exterior", while it complementary is the "interior" of S. Given two bounding surfaces S 1 and S 2 , we say that S 1 encloses S 2 provided the exterior of S 2 contains the exterior of S 1 . We denote by θ + and θ -the null expansions along the outer and inner future null directions respectively. A surface is called weakly outer trapped iff θ + ≤ 0 and marginally outer trapped surfaces (MOTS) if θ + = 0. In terms of the initial data set (Σ, g ij , K ij ), we have θ ± = p ± q, where p is the mean curvature of S ⊂ (Σ, g ij ) with respect to the outer unit normal m and q is the trace of the pull-back of the second fundamental form K ij onto S. The union of the interiors of all weakly outer trapped surfaces defines the so-called outer trapped set T + in Σ. The boundary of this set is a smooth MOTS [START_REF] Andersson | The area of horizons and the trapped region[END_REF].

The standard version of the Penrose inequality reads

M ≥ A min (∂T + ) 16π , ( 2
)
where A min (∂T + ) is the minimal area necessary to enclose ∂T + . The need of taking this minimal area enclosure comes from the fact that, under cosmic censorship, we know that the event horizon encloses ∂T + . However, the former could still have less area than ∂T + and, since its location is undetermined, the minimum of area of all enclosing surfaces should be taken. Inequality (2) also has a rigidity statement, namely that equality implies that (Σ, g ij , K ij ) is a slice of the Kruskal spacetime. By reversing the time orientation, the same argument yields (2) with ∂T + replaced by ∂T -, where T -is the union of the interiors of all bounding surfaces satisfying θ -≥ 0. In general, neither ∂T + encloses ∂T -nor vice versa. In the time-symmetric case K ij = 0, the inequality simplifies because T + = T -and its boundary is the outermost minimal surface (i.e. a minimal surface enclosing any other bounding minimal surface in Σ), and hence its own minimal area enclosure. The inequality in this case is called Riemannian Penrose inequality and it has been proven for one black hole in [START_REF] Huisken | The inverse mean curvature flow and the Riemannian Penrose inequality[END_REF] and in full generality in [START_REF] Bray | Proof of the Riemannian Penrose inequality using the positive mass theorem[END_REF] using a different method. In the non-time symmetric case, (2) is not invariant under time reversals. Moreover, the minimal area enclosure of a given surface S can be a rather complicated object typically consisting of portions of S together with portions of minimal surfaces (i.e. surfaces with p = 0) outside of S. This complicates the problem substantially. This has led several authors to propose simpler looking versions of the inequality, even if they are not directly supported by cosmic censorship. Two such extensions are

M ≥ A min (∂(T + ∪ T -)) 16π , M≥ |∂(T + ∪ T -)| 16π , ( 3
)
where |S| denotes the area of S (cf. [START_REF] Karkowski | The general Penrose inequality: lessons from numerical evidence[END_REF]). These inequalities are immediately stronger than [START_REF] Mars | Present status of the Penrose inequality[END_REF] and have the advantage of being invariant under time reversals. The second avoids even the use of minimal area enclosures. Neither version is supported by cosmic censorship and at present there is little evidence for their validity. However, both reduce to the standard version in the Riemannian case and both hold in spherical symmetry.

No counterexamples are known either. It would be interesting to have either stronger support for them, or else to find a counterexample. Recently, Bray and Khuri proposed a new method to approach the general (i.e. non time-symmetric) Penrose inequality. The basic idea was to modify the Jang equation [START_REF] Jang | On the positivity of energy in general relativity[END_REF], [START_REF] Schoen | Proof of the positive mass theorem II[END_REF] so that the product manifold Σ × R used to construct the graphs which define the Jang equation is endowed with a warped type metric of the form -ϕ 2 dt 2 + g instead of the product metric. The aim was to reduce the general Penrose inequality to the Riemannian Penrose inequality on the graph manifold. A discussion on the type of divergences that could possibly occur for the generalized Jang equation led the authors to consider a new type of bounding surfaces called generalized trapped surfaces and generalized apparent horizons, which are defined, respectively, by p ≤ |q| and p = |q|. This type of surfaces have very interesting properties. The most notable one is that, on any asymptotically flat initial data set containing at least one generalized trapped surface, there is always a unique C 2,α outermost generalized apparent horizon S out [START_REF] Eichmair | Existence, Regularity, and Properties of Generalized Apparent Horizons[END_REF]. Moreover, this surface has smaller area than any other surface enclosing it [START_REF] Eichmair | Existence, Regularity, and Properties of Generalized Apparent Horizons[END_REF]. Bray and Khuri's version of the Penrose inequality reads

M ≥ |S out | 16π . ( 4
)
This inequality has several remarkable properties that makes it very appealing [START_REF] Bray | s which imply the Penrose conjecture[END_REF]. First of all, the definition of generalized apparent horizon, and hence the corresponding Penrose inequality, is insensitive to time reversals. Moreover, there is no need of taking the minimal area enclosure of S out , as this surface has less area than any of its enclosures. Since MOTS are automatically generalized trapped surfaces, S out encloses the outermost MOTS ∂T + . Thus, ( 4) is stronger than (2) and its proof would also establish the standard version of the Penrose inequality. Moreover, Khuri has proven [START_REF] Khuri | A note on the nonexistence of generalized apparent horizons in Minkowski space[END_REF] that no generalized trapped surfaces exist in Minkowski, which is a necessary condition for the validity of (4). Another interesting property of this version, and one of its motivations discussed in [START_REF] Bray | s which imply the Penrose conjecture[END_REF], is that the equality case in (4) covers a larger number of slices of Kruskal than in the equality case in [START_REF] Mars | Present status of the Penrose inequality[END_REF]. Recall that the rigidity part of any version of the Penrose inequality is that equality implies that (Σ, g ij , K ij ) is a hypersurface of Kruskal. However, which slices of Kruskal satisfy the equality case may depend on the version under consideration. The more slices have this property, the more accurate the version can be considered. For any slice Σ of Kruskal we can define its exterior region Σ + as the intersection of Σ with the domain of outer communications. Bray and Khuri noticed that whenever ∂Σ + intersects both the black hole and the white hole event horizons, then the standard version (2) gives, in fact, a strict inequality. Although [START_REF] Andersson | The area of horizons and the trapped region[END_REF] does not give equality for all slices of Kruskal, it does so in all cases where the boundary of Σ + is a C 2,α surface (provided this boundary -which is a generalized apparent horizon in this case -is, in fact, the outermost one). It follows that version (4) contains more cases of equality than (2) and is therefore more accurate. It should be stressed that the second inequality in [START_REF] Penrose | Naked singularities[END_REF] gives equality for all slices of Kruskal, so in this sense it would be optimal. Despite its appealing properties, ( 4) is not directly supported by cosmic censorship. The reason is that the outermost generalized apparent horizon need not always lie inside the event horizon. A simple example [START_REF] Mars | Present status of the Penrose inequality[END_REF] is given by a slice Σ of Kruskal such that ∂T + (which corresponds to the intersection of Σ with the black hole event horizon) and ∂T - (the intersection Σ with the white hole horizon) meet transversally. Since both surfaces are generalized trapped surfaces, Eichmair's theorem [START_REF] Eichmair | Existence, Regularity, and Properties of Generalized Apparent Horizons[END_REF] implies that there must exist a unique C 2,α outermost generalized apparent horizon enclosing both. This surface must therefore penetrate into the exterior region somewhere, as claimed. It becomes natural to study the outermost generalized apparent horizon in slices of this type in order to check whether (4) holds or not. The result is that there are examples for which (4) turns out to be violated. More precisely, in this paper we prove the following statement.

Theorem 1 In the Kruskal spacetime with mass M > 0, there exist asymptotically flat, spacelike hypersurfaces with an outermost generalized apparent horizon S out satisfying

|S out | > 16πM 2 .

Construction of the counterexample.

Let us consider the Kruskal spacetime of mass M > 0 with metric

ds 2 = 32M 3 r e -r/2M dûdv + r 2 dθ 2 + sin θ 2 dφ 2 ,
where r(ûv) solves the implicit equation ûv = e r/2M (r -2M)/(2M). In this metric ∂ v is future-directed and ∂ û is past-directed. The region {û > 0, v > 0} defines the domain of outer communications and {û = 0}, {v = 0} define, respectively, the black hole and white hole event horizons. Consider the one-parameter family of axially-symmetric

embedded hypersurfaces Σ = R × S 2 , with intrinsic coordinates ŷ ∈ R, x ∈ [-1, 1], φ ∈ [0, 2π], defined by the embedding Σ ≡ {û = ŷ -x, v = ŷ + x, cos θ = x, φ = φ} .
It is easy to check that these hypesurfaces are well-defined, smooth and asymptotically flat for all | | < 1. Morever, it is straightforward to show that Σ is spacelike everywhere for | | small enough. The discrete isometry of the Kruskal spacetime defined by {û, v} → {v, û} implies that under reflection with respect to the equatorial plane, i.e. (ŷ, x, φ) → (ŷ, -x, φ), the induced metric of Σ remains invariant, while the second fundamental form of Σ changes sign. The exterior region Σ + of Σ is given by {ŷ -| x| > 0}. For = 0, ∂Σ + is composed by a portion of the black hole event horizon and a portion of the white hole event horizon. Moreover, ∂T + is given by {ŷ -x = 0}, while ∂T -is {ŷ + x = 0} so that these surfaces intersect transversally on the circumference {ŷ = 0, x = 0} provided = 0. By Eichmair's theorem, there exists a C 2,α outermost generalized apparent horizon containing both ∂T + and ∂T -. Uniqueness implies that this surface must be axially symmetric and have equatorial symmetry. In order to locate it, we proceed in two steps. First we will show that an axial and equatorially symmetric generalized apparent horizon of spherical topology and lying in a sufficiently small neighbourhood of {ŷ = 0} exists, provided is small enough. We will also determine its embedding function to first order in . In the second step we prove that this surface is either the outermost generalized apparent horizon, or else, it has smaller area than any other generalized apparent horizon in Σ enclosing it. Thus, we consider surfaces of spherical topology defined by embedding functions {ŷ = y(x, ), x = x, φ = φ} and satisfying y(-x, ) = y(x, ). Since the outermost generalized apparent horizon is known to be C 2,α it is natural to consider the spaces of functions U m,α ≡ {y ∈ C m,α (S 2 ) : ∂ φ y = 0, y(-x) = y(x)}, i.e. the spaces of m-times differentiable functions on the unit sphere, with Hölder continuous m-th derivatives with exponent α ∈ (0, 1] and invariant under the axial Killing vector on S 2 and under reflection about the equatorial plane. Each space U m,α is a closed subset of the Banach space C m,α (S 2 ) and hence a Banach space itself. Let I ⊂ R be the closed interval where takes values. For each function y ∈ U 2,α the expression p -|q| defines a non-linear map f : U 2,α × I → U 0,α . Thus, we are looking for the outermost of the solutions y ∈ U 2,α of the equation f = 0. We know that when = 0, the hypersurface Σ is totally geodesic, which implies q = 0 for any surface on it. Consequently, all generalized apparent horizons on Σ =0 satisfy p = 0 and are, in fact, minimal surfaces. The only closed minimal surface in Σ =0 is the bifurcation surface {û = 0, v = 0}. Thus, the equation f (y, ) = 0 has y = 0 as the unique solution when = 0. It becomes natural to use the implicit function theorem for Banach spaces to show that there exists a unique solution y ∈ U 2,α of f = 0 in a neighbourhood of y = 0 for small enough. The implicit function theorem requires the operator f to have a continuous Fréchet derivative and the partial derivative D y f | (y=0, =0) to be an isomorphism. The appearance of an absolute value in |q| makes the Fréchet derivative of f potentially discontinuous [12]. However, the problem can be solved considering a suitable modification of f . Since the details are somewhat technical, we postpone the proof of this fact to an Appendix, where we establish the followig proposition.

Proposition 1 There exists a neighborhood Ĩ ⊂ I of = 0 such that f (y, ) = 0 admits a solution y(x, ) ∈ C 2,α (S 2 ) for all ∈ Ĩ. Moreover, y(x, ) is C 1 in and satisfies y(x, = 0) = 0.

Let us denote by S the surface defined by this solution. The proposition above implies that we can expand y(x, ) = Y 1 (x) + o( ). By linearizing the PDE f (y, ) = 0 in , it turns out that Y 1 satisfies the linear equation L(Y 1 (x)) = 3|x|, where L(z(x)) ≡ -(1 -x 2 ) 2 z + 2x ż + z. The right hand side of this equation corresponds (except for a positive multiplicative constant) to the linearization of |q|. By decomposing into Legendre polynomials P n (x), it is easy to show that the unique solution of this equation is

Y 1 (x) = 3 2 + ∞ n=1 a 2n P 2n (x), a 2n = 3(4n + 1)(-1) n+1 [2n(2n + 1) + 1] 2 2n (2n -2)! (n -1)!(n + 1)! ,
where convergence is in L 2 . This expression allows us to compute the area of S at once. After a straightforward calculation we find

|S | = 16πM 2 + 8πM 2 2 e 5 + 4 ∞ n=1 2n(2n + 1) + 1 4n + 1 a 2 2n + O( 3 ).
Since the second summand is strictly positive, it follows that |S | > 16πM 2 . If we could show that S is the outermost generalized apparent horizon, we would have a counterexample of (4). Before turning into this point, however, let us give an alternative argument to show that the area increases. This will shed some light into the underlying reason why the area of S is larger than 16πM 2 .

To that aim, let us now use coordinates {û, x, φ} in Σ . Then, the embedding of Σ becomes Σ ≡ {û, v = û + 2 x, x, φ}, and the corresponding embedding in Σ for the surfaces S is S = {û = u(x, ), x, φ}. Again, u admits an expansion u = U 1 (x) + o( ). The relationship between U 1 and Y 1 is simply

Y 1 = U 1 + x. It follows that U 1 satisfies L(U 1 (x)) = 3(|x| -x).
Similarly, if we take {v, x, φ} as coordinates for Σ , then the embedding of

S reads v = V 1 (x) + o( ), with V 1 satisfying the equation L(V 1 (x)) = 3(|x| + x). Thus, L(U 1 (x)) ≥ 0 and L(V 1 (x))
≥ 0 and neither of them is identically zero. Since L is an elliptic operator with positive zero order term, we can use the maximum principle to conclude that U 1 (x) > 0 and V 1 (x) > 0 everywhere. Geometrically, this means that S lies fully in Σ + for small enough. In fact, the maximum principle applied to L(Y 1 ) = 3|x| also implies Y 1 > 0. This will be used below.

We can now view S as a first order spacetime variation of the bifurcation surface. The variation vector ∂ is defined as the tangent vector to the curve generated when a point with fixed coordinates {x, φ} in S moves as varies. By the argument above, this vector is spacelike everywhere on the unperturbed surface S =0 . If we do a Taylor expansion of |S | around = 0, we see that the zero order term is |S =0 | = 16πM 2 , as this is the area of the bifurcation surface. The bifurcation surface is totally geodesic so that, in particular, its mean curvature vector vanishes. Consequently, the linear term in the expansion is identically zero as a consequence of the first variation of area

d|S | d = S ( H S , ∂ )η S , ( 5
)
where H S is the spacetime mean curvature vector of S and ( , ) denotes scalar product with the spacetime metric. For the second order term in the expansion, we take the derivative of ( 5) with respect to and evaluate at = 0. A simple computation gives

d 2 |S | d 2 =0 = 16πM 2 e 1 -1 U 1 (x)L(V 1 (x)) + V 1 (x)L(U 1 (x)) dx.
Since U 1 and V 1 are strictly positive and L(U 1 (x)), L(V 1 (x)) are non-negative and not identically zero, it follows

d 2 |S | d 2 =0
> 0 and hence that the area of S is larger than 16πM 2 for small . The fact that the area increases is therefore a consequence of the fact that the second order variation of area turns out to be strictly positive along the direction joining the bifurcation surface with S , and, in turn, this is tied to the fact that L(U 1 ) and L(V 1 ) have a sign. The right hand sides of these operators are (except for a constant) the linearization of |q| ± q and these objects are obviously non-negative in all cases. We conclude, therefore, that the fact that the area of S is larger than 16πM 2 is closely related to the defining equation p = |q|. It follows that the increase of area is a robust property which does not depend strongly on the choice of hypersurfaces Σ that we have made. In fact, had we chosen hypersurfaces

Σ ≡ {u = y -β(x), v = y + β(x), cos θ = x, φ = φ}, the corresponding equations would have been L(U 1 (x)) = |L(β(x))| -L(β(x)) and L(V 1 (x)) = |L(β(x))| + L(β(x)).
The same conclusions would follow provided the right hand sides are not identically zero.

Having shown that |S | > 16πM 2 for = 0 small enough, the next step is to analyze whether S is the outermost generalized apparent horizon or not. In fact, in order to have a counterexample of (4) we only need to make sure that no generalized apparent horizon with less area than S and enclosing S exists in Σ . We will argue by contradiction. Let Ŝ be a generalized apparent horizon enclosing S and with | Ŝ | < |S |. Then, since S is not area outer minimizing, its minimal area enclosure S does not coincide with S . Now, two possibilities arise: (i) either S lies completely outside S , or (ii) it coincides with S on a closed subset K , while the complement S \ K (which is non-empty) has vanishing mean curvature p everywhere. To exclude case (i), consider the foliation of Σ defined by the surfaces {ŷ = y 0 , x, φ}, where y 0 is a constant. A direct computation shows that the mean curvature p y 0 of these surfaces with respect to the outer normal is positive for all y 0 > 0. We noted above that Y 1 (x) > 0 everywhere. Thus, for small enough , the function y(x, ) is also strictly positive. Since S lies fully outside S , the coordinate function ŷ restricted to S achieves a positive maximum y somewhere. At this point, the two surfaces S and {ŷ = y } meet tangentially, with S lying fully inside {ŷ = y }. This is a contradiction to the maximum principle for minimal surfaces. It only remains to deal with case (ii). The same argument above shows that the function ŷ restricted to S \K cannot reach a local maximum. It follows that the range of variation of ŷ restricted to S is contained in the range of variation of ŷ restricted to S . Since max S ŷmin S ŷ = O( ), it follows that we can regard S as an outward variation of S of order when is taken small enough. The corresponding variation vector field ξ can be taken orthogonal to S without loss of generality, i.e. ξ = ξ m, where m is the outward unit normal to S . The function ξ vanishes on K and is positive in its complement U ≡ S \ K . Expanding to second order and using the first and second variation of area (see e.g. [START_REF] Chavel | Riemannian geometry, a modern introduction[END_REF]) gives

|S | = |S | + U p S ξη S + + 2 2 U |∇ S ξ| 2 + ξ 2 2 R S -R Σ -|A S | 2 + p 2 S + p S dξ d η S + O( 3 ),
where ∇ S , R S and A S are, respectively, the gradient, scalar curvature and second fundamental form of S , and R Σ is the scalar curvature of Σ . Now, the mean curvature p S of S reads p S = 3

M √ e |x|+o( ) and both R Σ and A S are of order (because Σ =0 has vanishing scalar curvature and S =0 is totally geodesic). Moreover R S = 1/(2M 2 )+O( ). Thus,

|S | = |S | + 2 U 3|x|ξ M √ e + |∇ S ξ| 2 2 + ξ 2 8M 2 η S + O( 3 ).
It follows that, for small enough , the area of S is larger than S contrarily to our assumption. This proves Theorem 1 and, therefore, the existence of counterexamples to the version (4) of the Penrose inequality. A final remark is in order. As already mentioned at the beginning, the existence of this counterexample does not invalidate the approach suggested by Bray and Khuri based on the generalized Jang equation to study the general Penrose inequality. It means, however, that the emphasis should not be put on generalized apparent horizons. It may be that the approach can serve to prove the standard version (2) as recently discussed in [START_REF] Bray | A Jang equation approach to the Penrose inequality[END_REF]. Alternatively, let us note that, since the slice Σ lies in the Kruskal spacetime, it is immediate that the generalized Jang equation admits solutions on Σ which blow up a non-empty subset of ∂Σ + and blown down on another non-empty subset of this boundary, provided the warping function ϕ 2 is chosen to be ϕ 2 = 1 -2M/r| Σ . The induced metric on the graph is then isometric to the Schwarzschild metric h = dr 2 1-2M/r + r 2 dΩ 2 restricted to r > 2M. The boundary is therefore a minimal surface (in fact, totally geodesic) despite the fact that ∂Σ is not smooth in Σ . This property turns out to be general for any slice Σ in an asymptotically flat spacetime with a hypersurface orthogonal Killing vector η which is timelike at infinity [START_REF] Chruściel | The classification of static vacuum spacetimes containing an asymptotically flat spacelike hypersurface with compact interior[END_REF]. Defining Σ + to be the largest connected subset of Σ containing the asymptotic end such that η is timelike, the so-called quotient metric h can be defined on Σ + . In general, ∂Σ + is not smooth. However, there exists a differentiable structure on Σ + such that ∂Σ + is smooth and either lies at infinity with respect to h, or else, this metric extends smoothly to the boundary, which becomes a totally geodesic submanifold [START_REF] Chruściel | The classification of static vacuum spacetimes containing an asymptotically flat spacelike hypersurface with compact interior[END_REF]. This fact seems to suggest that the PDE method of Bray and Khuri might be suitable even for approaching the second inequality in [START_REF] Penrose | Naked singularities[END_REF]. At present, however, this remains rather speculative.

From its definition, it follows that Q(Y, )(x) is C 1,α and that the functional

Q Y, has Fréchet derivative D Y, Q(H, δ)(x) = A Y, (x)H(x) + B Y, (x) Ḣ(x) + C Y, (x)δ, where A Y, (x) ≡ ∂ 1 Q| (Y (x), Ẏ (x),x, ) , B Y, (x) ≡ ∂ 2 Q| (Y (x), Ẏ (x),x, ) and C Y, (x) ≡ ∂ 4 Q| (Y (x), Ẏ (x),x, ) .
We note that these three functions are C 1,α and that A Y, , C Y, are odd, while B Y, is even (as a consequence of the symmetries of Q). Defining the linear map D

Y, |Q|(H, δ) ≡ -σ(A Y, H + B Y, Ḣ + C Y, δ), it follows from (A.1) that |Q(Y + H, + δ)| -|Q(Y, )| = D Y, |Q|(H, δ) + R Y, (H, δ) with R(H, δ) U 0,α = o( (H, δ) U 2,α ×I ).
In order to conclude that D Y, |Q| is the derivative of |Q(Y, )|, we only need to check that, it is (i) welldefined (i.e. that its image belongs to U 0,α ) and (ii) that it is continuous, i.e. that D Y, |Q|(H, δ) U 0,α < C (H, δ) U 2,α ×I for some constant C. To show (i), the most difficult term is -σB Y, Ḣ, because B Y, (x) is even and need not vanish at x = 0. However Ḣ is an odd function, and hence -σB Y, Ḣ is continuous. To show it is also Hölder continuous, we only need to consider points x 1 = -a and x 2 = b with 0 < a < b (if x 1 • x 2 ≥ 0, the sign function remains constant, so -σB Y, Ḣ is in fact C 1,α ). Calling w(x) ≡ -σ(x)B Y, (x) Ḣ(x) and using that w(x) is even, we find

|w(x 2 ) -w(x 1 )| = |w(b) -w(-a)| = |(w(b) -w(a)| = d(B Y, Ḣ) dx x=ζ |b -a| ≤ ≤ d(B Y, Ḣ) dx x=ζ |b -a| 1-α |x 2 -x 1 | α ≤ d(B Y, Ḣ) dx x=ζ |x 2 -x 1 | α . (A.2)
where ζ ∈ (a, b) and we have used that |b -a| α ≤ |b + a| α = |x 2 -x 1 | α and |b -a| < 1. This proves that -σB Y, Ḣ is Hölder continuous with exponent α.

To check (ii), we first notice that w(x) obsviously satisfies sup

x |w| < C (H, δ) U 2,α ×I because B Y, (x) is C 1,α . It remains to bound the Hölder constant [w] α ≡ sup x 1 =x 2 |w(x 2 )-w(x 1 )| |x 2 -x 1 | α . Combining (A.2) with the fact that B Y, (x) is C 1,α , the bound [w] α ≤ C (H, δ) U 2,
α ×I follows at once. This proves (ii) for the term -σB Y, Ḣ. A similar argument applies to -σA Y, H and -σC Y, δ and we conclude that D Y, |Q| is indeed a continuous operator.

In order to apply the implicit function theorem, it is furthermore necessary that |Q| ∈ C 1 (U 2,α × I) (i.e. that D Y, |Q| depends continuously on (Y, )). This means that given any convergent sequence (Y n , n ) ∈ V r 0 , the corresponding operators D Yn, n |Q| also converge. Denoting by (Y, ) ∈ V r 0 the limit of the sequence, we need to prove that D Yn, n |Q| -D Y, |Q| £(U 2,α ×I,U 0,α ) → 0. It suffices to find a constant K (which may depend on (Y, )), such that where ∇B is the gradient of B and K ⊂ R 4 is a compact domain depending only on r 0 and Y 1 defined so that, for all (Y, ) ∈ V r 0 , the quadruple (Y (x), Ẏ (x), x, ) ∈ K, for all x ∈ [-1, 1]. Inequality (A.4) is already of the form (A.3) (recall that B is smooth). It only remains to bound the Hölder constant of z ≡ σ(B Y, -B Yn, n ) Ḣ in a similar way. As before, this is done by distinguishing two cases, namely when x 1 • x 2 ≥ 0 and when x 1 • x 2 < 0. Obtaining an inequality of the form sup cL(H), where L is the elliptic operator defined above, which is an isomorphism between U 2,α and U 0,α . Thus, the implicit function theorem can be used to conclude that there exists an open neighbourhood Ĩ ⊂ I of = 0 and a C 1 map Ỹ : Ĩ → U 2,α such that Ỹ ( = 0) = Y 1 and y = Ỹ ( ) defines a C 2,α generalized apparent horizon embedded in Σ . This proves Proposition 1.

(D

  Yn, n |Q| -D Y, |Q|)(H, δ) U 0,α < K (H, δ) U 2,α ×I (Y n -Y, n -) U 2,α ×I (A.3)for all (H, δ) ∈ U 2,α × I. Again, the most difficult case involves σ(B Y, -B Yn, n ) Ḣ, so we concentrate on this term. Using the mean value theorem on the functionB ≡ ∂ 2 Q (recall that B Y, (x) = B| (Y (x), Ẏ (x),x, ) ) gives sup x |σ(B Y, -B Yn, n ) Ḣ| ≤ 2 sup K |∇B| sup x | Ḣ| (Y n -Y, n -) U 2,α ×I , (A.4)

x 1 =x 2 ,x 1 •x 2

 212 ≥0 |z(x 2 )-z(x 1 )| |x 2 -x 1 | α ≤ K 1 (H, δ) U 2,α ×I (Y n -Y, n -) U 2,α ×I is standard, because σ(x) is a constant function. When x 1 • x 2 < 0,we exploit the parity of the functions as in (A.2) to get|z(x 2 ) -z(x 1 )| ≤ d((B Yn , n -B Y, ) Ḣ) dx x=ζ |x 2 -x 1 | α , where ζ ∈ (a, b) and we are asummingx 1 = -a, x 2 = b, 0 < a < b without loss of generality. Bounding the right hand side in terms of K 2 (H, δ) U 2,α ×I (Y n -Y, n -) U 2,α ×I |x 2 -x 1 | α isagain standard, since the sign function σ(x) has already disappeared. This, combined with (A.4) gives (A.3) and hence continuity of the derivative of D Y, |Q| with respect to (Y, ) ∈ V r 0 . The final requirement to apply the implicit function theorem to F = P -|Q| is to check that D Y F | (Y 1 , =0) is invertible. A simple computation gives D Y F | (Y 1 , =0) (H) =

Acknowledgments

We are very grateful to M. Sánchez for his interest and inestimable help and to H.L. Bray and M. Khuri for useful comments. Financial support under the projects FIS2006-05319 (Spanish MEC), GR-234 (Junta de Castilla y León) and P06-FQM-01951 (Junta de Andalucía) are acknowledged. AC acknowledges the Ph.D. grant AP2005-1195 (MEC).

Appendix A. Proof of Proposition 1

Firstly, let us consider surfaces in Σ defined by {ŷ = y(x, ), x, φ} such that the embedding function has the form y = Y , where Y ∈ U 2,α . An explicit computation of the mean curvature p on such surfaces gives p = P(Y (x), Ẏ (x), Ÿ (x), x, ), where dot denotes derivative with respect to x and where P :

), which reflects the fact that the extrinsic curvature of Σ changes sign under a transformation x → -x. Let us write P (Y, )(x) ≡ P(Y (x), Ẏ (x), Ÿ (x), x, ) and similarly

This functional has the property that, for > 0, the solutions of F (Y, ) = 0 correspond exactly to the solutions of f (y, ) = 0 via the relation y = Y . Moreover, the functional F is well-defined for all ∈ I, in particular at = 0. Therefore, by proving that F = 0 admits solutions in a neighbourhood of = 0, we will conclude that f = 0 admits solutions for > 0 and the solutions will in fact belong to a neighbourhood of y = 0 since y = Y .

In order to show that F admits solutions we will use the implicit function theorem. A direct calculation yields

This operator is an isomorphism between U 2,α and U 0,α . Let Y 1 ∈ U 2,α be the unique solution of the equation L(Y ) = 3|x|. For later use, we note that Q(Y 1 , = 0) = -3cx. This vanishes only at x = 0. This is the key property that allows us to prove that F is C 1 (U 2,α × I).

The C 1 (U 2,α × I) property of the functional P (Y, ) is standard. More subtle is to show that |Q| is C 1 (U 2,α × I) in a suitable neighbourhood of (Y 1 , = 0). Let r 0 > 0 and define

First of all we need to show that |Q| is (Fréchet-)differentiable on V r 0 , i.e. that for all (Y, ) ∈ V r 0 there exists a continuous linear mapping

The key observation is that, by choosing r 0 small enough, we have

where σ(x) is the sign function, (i.e. σ(x) = +1 for x ≥ 0 and σ(x) = -1 for x < 0). For x away from a neightbourhood of 0, this is a consequence of the fact that Q(Y 1 , = 0) = -3cx, which is negative for x > 0 and positive for x < 0. Taking r 0 small enough, and using that Q is a smooth function of their arguments, the same inequalities hold for any (Y, ) ∈ V r 0 . Moreover, the function Q(Y, )(x) is odd in x, so it passes through zero at x = 0. Hence, in a small enough neighbourhood of x = 0, the relation (A.1) holds provided we can prove that Q(Y, ) is strictly decreasing at x = 0. But this follows inmediately from the fact that dQ(Y 1 , =0) dx | x=0 = -3c and Q is a smooth function of its arguments.