Background
==========

Epithelial ovarian cancer (EOC), which compromises 90% of all ovarian malignancies, is the leading cause of death from gynaecological cancer in the western world \[[@B1]\]. The pathology underlying this disease is not fully understood, but an inflammatory process is one factor suggested to participate in tumourigenesis \[[@B2]\]. Chronic inflammatory conditions caused by talc or asbestos exposure, endometriosis or other pelvic inflammatory diseases are related to an increased incidence of EOC \[[@B3]\]. Several classical mediators of inflammation participate in the ovulatory process, proposing each ovulation to have resemblance with a localized inflammatory reaction \[[@B4]\]. The importance of inflammation/ovulation in ovarian tumourigenesis is further supported by the observed reduction in the relative risk to develop EOC in women with a decrease in the total number of ovulations during a lifetime, i.e. due to childbearing or the use of contraceptive pills \[[@B5]\]. This was already suggested three decades ago by Fathalla \[[@B6]\] as the \"incessant ovulation hypothesis\". Tubal ligation and hysterectomy without oophorectomy, which reduces local inflammation, also decreased the risk to develop EOC, while inflammatory conditions in the pelvis, e.g. endometriosis, were associated with increased risk of EOC \[[@B5]\].

A measure to evaluate the role of inflammation in tumourigenesis is to examine the correlation between the use of non-steroidal anti-inflammatory drugs (NSAIDs) and the risk to develop cancer. The use of NSAIDs or aspirin causes a reduction in the risk to develop colorectal- (CRC) and to a less extent, prostate- and breast cancer \[[@B7]\]. Inconsistent results have been published for EOC, but several studies suggest an inverse relationship between the use of NSAIDs and the incidence of this malignancy \[[@B8]\]. Several *in vivo*\[[@B9]\] and *in vitro*\[[@B10]-[@B13]\] experiments have demonstrated reduced tumour growth \[[@B9]\], decreased proliferation \[[@B11]\], cell cycle arrest \[[@B10]\], attenuated metalloprotease-dependent motility and invasive activity \[[@B13]\], and reduced expression of vascular endothelial growth factor expression \[[@B14]\] by NSAIDs in models for EOC.

COX-1 and COX-2 are key enzymes in the synthesis of prostanoids by converting arachidonic acid to PGG~2~and subsequently to PGH~2~\[[@B15]\]. PGE~2~is derived from PGH~2~by a synthase, prostaglandin E synthase (PGES). Three isoforms of PGES have been identified, microsomal prostaglandin E synthase (mPGES-1 and mPGES-2) and cytosolic PGES (p23) \[[@B15]\]. Prostaglandin E~2~(PGE~2~) was implicated in tumour progression \[[@B15]\] and increased contents of prostanoids (PGE~2~and TxB~2~) in ovarian tumours have been described \[[@B16],[@B17]\]. Later studies have reported PGE~2~as a regulator of proliferation and apoptosis in ovarian cancer cell lines \[[@B18]\]. Several reports have shown that either COX-1 or COX-2 is up-regulated in EOC \[[@B14],[@B19]-[@B21]\]. Ovarian tumours with increased content of COX-2 were associated with chemotherapy resistance and poor prognosis \[[@B22]\] while COX-1 was suggested to participate in neo-vascularization \[[@B14]\].

PGE~2~is ligand for at least four membrane-bound receptors, EP~1--4~. EP~2~was induced in colon polyps in mice with a targeted deletion of the adenomatosis polyposis coli (APC) gene \[[@B23]\] and this receptor has also a key role in the ovulatory process \[[@B24]\]. Studies in EP~1~receptor knockout mice and experiments with selective receptor antagonists, have demonstrated a role for this receptor in colon and breast carcinogenesis \[[@B25]\]. PGE~2~is produced by a variety of cells and has a broad range of effects in individual cells and organs.

We choosed to analyse the rate-limiting enzymes (COX-1, COX-2 and mPGES-1) for PGE~2~-synthesis and two of its receptors (EP~1--2~) in specimen from normal ovaries and from epithelial ovarian tumours of different grades and stages, as an approach to delineate the role for PGE~2~in ovarian tumorigenesis, since the prostanoid itself is quickly redistributed and degraded in whole tissue biopsies. Furthermore, the combined techniques of immunoblotting and immunohistochemistry allowed us to determine the contents as well as the cell-specific localizations of the individual proteins. The cell- and stage specific increases of COX-1, COX-2, mPGES-1 and EP~1--2~, support the hypothesis that PGE~2~-synthesis and signalling are of importance for malignant transformation and progression in EOC. The observed augmentations of PGE~2~-signalling capacity have implications for future therapies.

Materials and methods
=====================

Human tissues
-------------

Biopsies from normal human ovaries were obtained from 18 women undergoing laparotomy or laparoscopy for non- ovarian diseases/benign pelvic conditions. Ovarian epithelial tumours tissues were obtained from 36 women (approved by the Ethics Committee of the Medical Faculty, Göteborg University) (Table [1](#T1){ref-type="table"}). Tissues were immediately washed in ice-cold saline, snap-frozen in liquid nitrogen and stored at -70°C until analysis \[[@B26],[@B27]\]. All samples were examined by an experienced pathologist and classified according to FIGO for diagnosis.

######

Histological description

  *Sample no*.   *P-H*   *Sample no*.   *P-H*   *Grade*         *Stage*
  -------------- ------- -------------- ------- --------------- ---------
  1              NF      27             BLS                     I
  2              NF      28             BLS                     IB
  3              NF      29             BLS                     IA
  4              NF      30             BLM                     IA
  5              NF      31             BLM                     IIB
  6              NF      32             BLM                     II

  7              NF      33             AS      High            II
  8              NF      34             AM      High            IB

  9              NP      35             AS      High/Moderate   III
  10             NP      36             AS      High/Moderate   I
  11             NP      37             AS      Moderate        III
  12             NP      38             AS      Moderate        III
  13             NP      39             AS      Moderate        III
  14             NP      40             AS      Moderate        II
  15             NP      41             AS      Moderate        II
  16             NP      42             AS      Poor            III
  17             NP      43             AS      Poor            III
  18             NP      44             AS      Poor            III

  19             BS      45             AS      Poor            III
  20             BS      46             AS      Poor            III
  21             BS      47             AS      Poor            III
  22             BS      48             AS      Poor            III
  23             BM      49             AS      Poor            II
  24             BM      50             AS      Poor            II
  25             BM      51             AM      Poor            III
  26             BM      52             AM      Poor            III

                         53             AU      Undiff          III
                         54             AU      Undiff          I

Histological description of ovarian tissue including sample numbers which can be found in representative immunoblots and immunohistochemistry figures. Abbreviations: P-H; patho-histologic description, NF; normal fertile, NP; normal postmenopausal, BS; benign serous, BM; benign mucinous, BLS; borderline type serous, BLM; borderline type mucinous, AS; adenocarcinoma serous, AM; adenocarcinoma mucinous, AU; adenocarcinoma undifferentiated type.

Immunoblotting
--------------

Soluble tissue extracts were prepared from 45 tissue biopsies (Table [1](#T1){ref-type="table"}), and immunoblotting was performed as previously described \[[@B26],[@B27]\]. Thirty-five μg of total protein was loaded into each well for 1D SDS PAGE (4--12% Bis-Tris NuPage gels, Invitrogen, Paisley, UK). The blotting-membranes were incubated with blocking buffer containing the following primary antibodies from Cayman Chemical Co. (Ann Arbor, MI, USA): COX-1 (cat. no. 160110, monoclonal, dilution 1:1,000), COX-2 (cat. no. 160126, rabbit polyclonal, dilution 1:1,000), mPGES-1 (cat. no. 160140, rabbit polyclonal, dilution 1:500), EP~1~receptor (cat. no. 101740, rabbit polyclonal, dilution 1:500) and EP~2~receptor (cat. no. 101750, rabbit polyclonal, dilution 1:500). COX-1 and COX-2 electrophoresis standards from Cayman Chemical Co. (cat. no. 360100, 360120) were used as positive controls. The specificity of the COX-2 antibody was verified by the addition of a blocking peptide to the antibody solution prior to immunodetection (Cayman Chemical Co,. cat. no. 360106). Ovaries obtained from immature rats stimulated with pregnant mare serum gonadotrophin (PMSG) and human chorionic gonadotropin (hCG), (preovulatory ovaries) were used as positive control for mPGES-1 and EP~1--2~. Immunoreactive proteins were visualized by chemiluminescence using alkaline-phosphatase-conjugated secondary goat anti-mouse or goat anti-rabbit antibodies (dilution 1:40 000), and the CDP-Star^®^substrate (Tropix, Bedford, UK). The conditions were kept constant during the analysis of the immunoblots and each blot contained an internal control sample (see below and Figure legend 1 for details) in order to compare the levels of expression between blots \[[@B26],[@B27]\].

Immunohistochemistry
--------------------

Frozen biopsies from 18 normal ovaries and ovarian tumours (Table [1](#T1){ref-type="table"}) were cryosectioned (5--7 μm) and mounted on electrically charged glass slides, fixed in cold acetone at -20°C for 10 min and air dried in room temperature. The endogenous peroxidase activity was blocked by treatment for 4 min with peroxidase block from DAKO EnVision™+System, Peroxidase (AEC) kit (DAKO Corporation, USA). Primary antibodies against COX-1 (1:100), COX-2 (Cayman Chemical Co., cat. no. 160112, monoclonal, 1:100), mPGES-1 (1:50), EP~1~(1:50) EP~2~(1:50) and CK8 (1:400) diluted in TBS were applied overnight at 4°C, followed by biotinylated goat anti-mouse immunoglobulin (1:60) (VECTASTAIN^®^ABC kit, Vector Laboratories, Inc., Burlingame, CA) for 45 min at 37°C and finally avidin-biotin-peroxidase complex (VECTASTAIN^®^ABC kit, Vector Laboratories) at 37°C for 30 min. The enzymatic reaction was developed using AEC Chromogen Substrate Buffer (DAKO EnVision™+System, Peroxidase (AEC) kit, DAKO). Slides were counterstained with haematoxylin and mounted in 10% glycerol. The monoclonal COX-2 antibody used here was evaluated previously for immunohistochemistry by blocking experiments using a specific peptide \[[@B28]\]. Antibodies against cytokeratin 8 (CK8) (monoclonal, Low Molecular Weight, DAKO, Copenhagen, Denmark), was used as a marker for epithelial cells. Primary antibodies were replaced by equal amounts of TBS for negative controls. The sections were viewed in a Nikon microphot FX microscope and photographed with a Nikon Coolpix 990 digital camera.

Densitometric scanning
----------------------

Semi-quantitative measurements of proteins from the immunoblots were made by densitometry (Fluor-S™ Multimager, Quantity One ver. 4.1.0., BioRad, Hercules, CA, USA). The optical density (OD) of each band was measured. An ovarian sample was used as an internal standard on each blot, and the measured value of this sample was set to 100%. The signal from each band was then compared to the standard and the obtained relative value was used for statistical analysis \[[@B26],[@B27]\].

Statistics
----------

Values are given as mean ± SEM. ANOVA followed by Fischer\'s LSD post-hoc test was used for statistical analysis of the data obtained by densitometric scanning. A p-value less than 0.05 was considered to be significant. Data is presented in a histogram and with a typical immunoblot of selected samples for each analysed protein.

Results
=======

Increases of COX-1, COX-2, mPGES-1 and EP~1~in adenocarcinomas
--------------------------------------------------------------

Significant (p \< 0.05) increases of COX-1, COX-2, mPGES-1 and EP~1~were demonstrated in the adenocarcinomas (AC) in comparison with normal ovarian tissue, benign adenomas and borderline tumours (B/BL) (Figure [1](#F1){ref-type="fig"}, [2](#F2){ref-type="fig"}, [3](#F3){ref-type="fig"}, [4](#F4){ref-type="fig"}, [5](#F5){ref-type="fig"}). EP~2~was also increased in comparison to the B/BL tumours. An increase, although not significant, of COX-2, was noticed in the B/BL group, compared to specimens from normal ovaries.

![Relative protein expressions (mean ± SEM) of COX-1 in normal ovaries (N = pre- and postmenopausal ovaries (n = 10), BB = benign- and borderline type tumours, (n = 13), and AC = adenocarcinomas (n = 22).**(a)**P \< 0.05 vs normal samples (N), **(b)**P \< 0.05 vs benign/borderline (BB). The measurements are presented as percentage changes compared to a reference sample (tumour tissue). Below each histogram a representative immunoblott is presented. Each number correlates to the patho-histological description of the sample (see Table 1).](1476-4598-5-62-1){#F1}

![Relative protein expressions (mean ± SEM) of COX-2 in normal ovaries (N = pre- and postmenopausal ovaries (n = 10), BB = benign- and borderline type tumours, (n = 13), and AC = adenocarcinomas (n = 22).**(a)**P \< 0.05 vs normal samples (N), **(b)**P \< 0.05 vs benign/borderline (BB). The measurements are presented as percentage changes compared to a reference sample (normal ovarian tissue). Below each histogram a representative immunoblott is presented. Each number correlates to the patho-histological description of the sample (see Table 1).](1476-4598-5-62-2){#F2}

![Relative protein expressions (mean ± SEM) of mPGES-1in normal ovaries (N = pre- and postmenopausal ovaries (n = 10), BB = benign- and borderline type tumours, (n = 13), and AC = adenocarcinomas (n = 22).**(a)**P \< 0.05 vs normal samples (N), **(b)**P \< 0.05 vs benign/borderline (BB). The measurements are presented as percentage changes compared to a reference sample (normal ovarian tissue). Below each histogram a representative immunoblott is presented. Each number correlates to the patho-histological description of the sample (see Table 1).](1476-4598-5-62-3){#F3}

![Relative protein expressions (mean ± SEM) of EP~1~in normal ovaries (N = pre- and postmenopausal ovaries (n = 10), BB = benign- and borderline type tumours, (n = 13), and AC = adenocarcinomas (n = 22).**(a)**P \< 0.05 vs normal samples (N), **(b)**P \< 0.05 vs benign/borderline (BB). The measurements are presented as percentage changes compared to a reference sample (rat preovulatory ovary). Below each histogram a representative immunoblott is presented. Each number correlates to the patho-histological description of the sample (see Table 1).](1476-4598-5-62-4){#F4}

![Relative protein expressions (mean ± SEM) of EP~2~in normal ovaries (N = pre- and postmenopausal ovaries (n = 10), BB = benign- and borderline type tumours, (n = 13), and AC = adenocarcinomas (n = 22).**(b)**P \< 0.05 vs benign/borderline (BB). The measurements are presented as percentage changes compared to a reference sample (normal ovarian tissue). Below each histogram a representative immunoblott is presented. Each number correlates to the patho-histological description of the sample (see Table 1).](1476-4598-5-62-5){#F5}

To examine if the pattern of expression was influenced by the degree of differentiation (grade) in the malignant group of tumours (AC), these tumours were dived into three groups; i) borderline tumours and highly differentiated AC (BL+H); ii) high/moderately and moderately differentiated AC (H/M+M); and iii) poorly differentiated and undifferentiated AC (P+U). The rationale to include highly differentiated AC (H) with the borderline (BL) type tumours was that these tumours are clinically considered to have more benign prognosis. The expressions of COX-1, mPGES-1 and EP~1~were all significantly elevated in both the H/M+M and P+U group compared to the more differentiated tumours in the BL+M group. (Figure [6](#F6){ref-type="fig"}). There was also an increase of EP~2~in the same groups, although not significant. COX-2 expression differed between tumours in the same histological group, but the majority of the tumours exhibited a strong signal for COX-2 (18/22 of the AC, 21/36 of all tumours), while a few tumours demonstrated a weak band (4/22 of the AC, 15/36 of all tumours). Amongst the four AC with low levels of expression, one was highly differentiated (H), two were in the group of high/moderately differentiated (H/M) and one was moderately differentiated (M). The expression patterns were further analyzed in the AC according to FIGO-stage (Figure [7](#F7){ref-type="fig"}). COX-2 demonstrated significant increases in both stage II and III cancers, compared to stage I. An increase was also shown for EP~1~in stage III tumours compared to stage I. No differences were observed for COX-1, mPGES-1 or EP~2~.

![Relative expressions (mean ± SEM) of COX-1, COX-2, mPGES-1, EP~1~and EP~2~. Tissue contents in tumours related to grade of differentiation. (BL+H = borderline type tumours and highly differentiated tumours (n = 8), H/M+M = highly to moderately, and moderately differentiated tumours (n = 7), P+U = poorly and un-differentiated tumours (n = 13).**(a)**P \< 0.05 vs borderline type tumours and highly differentiated tumours (B/BL), **(b)**P \< 0.05 vs highly to moderately and moderately differentiated tumours (H/M+M).](1476-4598-5-62-6){#F6}

![Relative expressions (mean ± SEM) of COX-1, COX-2, mPGES-1, EP~1~and EP~2~. Tissue contents in malignant tumours (adenocarcinomas) related to stage. Stage I (n = 7), stage II (n = 6) and stage III (n = 14).**(a)**P \< 0.05 vs stage I, **(b)**P \< 0.05 vs stage II.](1476-4598-5-62-7){#F7}

A representative blot from each protein analyzed is presented in Figure [1](#F1){ref-type="fig"}, [2](#F2){ref-type="fig"}, [3](#F3){ref-type="fig"}, [4](#F4){ref-type="fig"}, [5](#F5){ref-type="fig"}. The major band for all the examined proteins migrated at their expected molecular weights (M~r~). For mPGES-1, EP~1~, and EP~2~, additional bands with higher and lower M~r~were observed in the group of malignant tumours (AC) (Figure [3](#F3){ref-type="fig"}, [4](#F4){ref-type="fig"}, [5](#F5){ref-type="fig"}). The additional M~r~species most likely represents phosphorylated forms of mPGES-1 and EP~1--2~. However, these bands for EP~1--2~might also represent splice variants of the receptors \[[@B29]\].

Cell-specific localisation of COX-1, COX-2, mPGES-1, EP~1~and EP~2~in the normal ovary
--------------------------------------------------------------------------------------

Tissue biopsies from nine normal ovaries were used for immunohistochemistry. Four of the ovaries were from fertile women and five from post-menopausal women undergoing surgery for benign non-ovarian diseases. Each ovary was consecutively sectioned and stained for cytokeratin 8 (CK8), a marker for epithelial cells (Figure [8A](#F8){ref-type="fig"}, [9A](#F9){ref-type="fig"}) and the individual proteins in the PGE~2~synthesis- and signalling pathway. DAPI was used for nuclear staining.

![Immunohistochemical analysis of normal ovaries; (**a-f**) Postmenopausal ovary with surface epithelium; stained with antibodies against CK8 (**a**); COX-1 (**b**); COX-2 (**c**); mPGES-1 (**d**);EP~1~(**e**); EP~2~(**f**). *Arrow*= epithelial cells, *Star*= stroma cells. (Original magnification ×200, inserted pictures X400).](1476-4598-5-62-8){#F8}

![Immunohistochemical analysis of normal ovaries; (**a-d**)Premenopausal ovary with epithelial cells lining an inclusion cyst; stained with antibodies against CK8 (**a**); COX-1 (**c**); COX-2 (**d**); negative control (**b**). *Arrow*= epithelial cells, *Star*= stroma cells. (Original magnification X200, inserted pictures ×400).](1476-4598-5-62-9){#F9}

COX-1 was present in both surface epithelial cells (OSE) and epithelial cells lining the inclusion cysts (Figure [8B](#F8){ref-type="fig"}, [9C](#F9){ref-type="fig"}). Some staining was also observed in the stroma (Figure [8B](#F8){ref-type="fig"}). The signal for COX-2 in the OSE was negligible. However, weak staining was noticed in some areas of the underlying stroma (Figure [8C](#F8){ref-type="fig"}). An interesting observation was the clear staining for COX-2 in the epithelial cells of the inclusion cysts (Figure [9D](#F9){ref-type="fig"}). Staining for mPGES-1 was predominantly localized to cells in the stroma. Some of the epithelial cells on the ovarian surface demonstrated staining for mPGES-1 (Figure [8D](#F8){ref-type="fig"}). Both EP~1~and EP~2~were expressed in OSE, while only EP~2~was present in stroma cells, an expression pattern similar to that observed for mPGES-1 (Figure [8E,F](#F8){ref-type="fig"}).

Cell-specific localisation of COX-1, COX-2, mPGES-1, EP~1~and EP~2~in benign, borderline and malignant ovarian tumours
----------------------------------------------------------------------------------------------------------------------

Five benign cystadenomas (three serous and two mucinous), three BL (two serous and one mucinous), and three serous ovarian AC (one highly, one moderately and one poorly differentiated AC) were used for immunohistochemistry (IHC). Serial sections from each tumour were stained for the expression of COX-1, COX-2, mPGES-1, EP~1~and EP~2~. CK8 was used as a marker for epithelial derived cells (Figure [10A](#F10){ref-type="fig"}, [11A](#F11){ref-type="fig"}). The results are presented as representative pictures from a serous borderline type tumour (stage I, Figure [10A--F](#F10){ref-type="fig"}) and a poorly differentiated serous AC (stage II, Figure [11A--F](#F11){ref-type="fig"}).

![Immunohistochemical analysis of ovarian tumours; Serous borderline type tumour, stage I (**a-f**); Staining with antibodies against CK8 (**a**); COX-1 (**b**); COX-2 (**c**); mPGES-1 (**d**);EP~1~(**e**); EP~2~(**f**). *Arrow*= epithelial cells, *Star*= stroma cells. (Original magnification ×200, inserted pictures ×400).](1476-4598-5-62-10){#F10}

![Immunohistochemical analysis of ovarian tumours; Serous adenocarcinoma, poorly differentiated, stage II (**a-f**). Staining with antibodies against CK8 (**a**); COX-1 (**b**); COX-2 (**c**); mPGES-1 (**d**);EP~1~(**e**); EP~2~(**f**). *Arrow*= epithelial cells, *Star*= stroma cells. (Original magnification ×200, inserted pictures ×400).](1476-4598-5-62-11){#F11}

Distinct staining of COX-1 was demonstrated mainly in the epithelial cells of the BL tumour (Figure [10B](#F10){ref-type="fig"}). COX-2 exhibited an even more epithelial concentrated staining compared to COX-1 (Figure [10C](#F10){ref-type="fig"}). Both COX-1 and COX-2 was confined to the cytoplasm of the epithelial cells (inserts, Figure [10B--C](#F10){ref-type="fig"}). Microsomal PGES-1 was expressed predominantly in epithelial cells, but to some degree also in the stroma, although the staining was much less homogenous compared to COX-1 and COX-2 (Figure [10D](#F10){ref-type="fig"}). EP~1~and EP~2~demonstrated almost identical staining patterns with both receptors localised to the epithelial cells of the tumour (Figure [10E,F](#F10){ref-type="fig"}).

The staining pattern for the AC was different compared to that of the BL tumours. One exception was COX-1, which was still predominantly localised to the epithelial cells, some expression was also present in the stroma (Figure [11B](#F11){ref-type="fig"}). An increased stromal content was also noticed for COX-2 (Figure [11C](#F11){ref-type="fig"}). Intense staining was observed for mPGES-1, EP~1~and EP~2~in clusters of tumour cells (Figure 11[11D--F](#F11){ref-type="fig"}).

Discussion
----------

Numerous experimental models have convincingly demonstrated that the increased production of PGE~2~in various tumours, including EOC, is involved in tumorigenesis \[[@B19]\]. The reduced incidence of tumours by NSAIDs, as shown in epidemiological studies, supports the concept of the PGE~2~signalling pathway as an important factor in tumour formation and growth \[[@B7]\]. The present study demonstrates, for the first time, increased contents and cell-specific localisation of mPGES-1 and the PGE~2~receptors EP~1--2~in EOC of different grades and stages compared to normal ovaries. The study also confirms the earlier demonstrated expression patterns of COX-1 \[[@B14],[@B21]\] and COX-2 in EOC \[[@B19]\].

The ovulatory process exhibits several signs related to an inflammatory reaction, e.g. hyperaemia, extravasation of leukocytes, proteolytic- and collagenolytic activity \[[@B4],[@B30]\]. One of the key mediators in inflammation, the prostanoids, are also released during ovulation from the ovulating follicle and surrounding ovarian stroma, together with other autocrine/paracrine factors \[[@B31]\]. In the human ovary, COX-2 is present in the ovulating follicle during the preovulatory phase, followed by interstitial localisation of the enzyme after ovulation \[[@B32]\]. These prostanoids, in particular PGE~2~, are thought to contribute to proliferation and repair of OSE at the site of rupture, in addition to their crucial role(s) in the intrafollicular regulation of the ovulatory process \[[@B30]\]. Repetitive trauma to the epithelial cell surface, followed by exposure to mitogenic factors, is suggested to be an initiating event in ovarian tumourigenesis \[[@B6],[@B31]\]. When the EOC was established, elevated levels of the prostacyclins (PGI~2~) and tromboxane (TxA~2~) in plasma, as well as increased tumour contents of PGE~2~and TxB~2~were reported \[[@B16],[@B17]\]. Furthermore, ovarian tumours with high tissue contents of PGE~2~, PGF~2~α and 6-keto-PGF~1~α demonstrated a reduced response to chemotherapy \[[@B33]\].

COX-1 is constitutively expressed and plays a \"housekeeping role\" in many cells and has previously been demonstrated in normal OSE and in inclusion cysts \[[@B34]\] which are in line with the results of the present study. Furthermore, the contents of COX-1 was unaltered in the group of benign and borderline type tumours compared to normal ovaries, and the cellular localisation remained confined to the epithelial cells of these tumours. An increase of COX-1 was significant in the malignant tumours, but only in the less differentiated groups (H/M+M and P+U). COX-1 staining was no longer limited to the epithelial tumour cells since localisation to the underlying stroma also was observed. No correlation was found between FIGO stage and COX-1. Earlier studies have also reported an increase of COX-1 at both the mRNA and protein levels in EOC \[[@B14]\]. A stimulatory effect on neo-vascularisation was proposed since a correlation was demonstrated between COX-1 expression and the expressions of angiogenic factors (VEGF, HIF-1α, Flk1) \[[@B14]\]. Studies by Spinella and coworkers \[[@B12]\] demonstrated that endothelin (ET-1) increased COX-1 in ovarian carcinoma cells *in vitro*. Since ET-1 is known regulator of VEGF, this effect might be mediated by COX-1/PGE~2~in these cells. Interestingly, several studies on ovarian cancer cell lines have emphasised the contribution of COX-1 to ovarian tumourigenesis. In fact, COX-1 was the predominant isoform reported to be expressed \[[@B20],[@B34],[@B35]\]. A recent study \[[@B9]\] used mouse EOC cells (deletion of p53, or overexpression of c-myc/K-ras or c-myc/Akt) to demonstrate increased expression of COX-1 in these genetically engineered EOC cells. The conclusion, in accordance with the study by Kino and co-workers \[[@B35]\], was that COX-1 is the major regulator of PGE~2~synthesis *in vitro*.

The observation in the present study of COX-2 as more or less absent from normal OSE confirms results reported earlier \[[@B21],[@B34],[@B36],[@B37]\]. A clear staining for COX-2 was first observed in the inclusion cysts, and some, although not significant, elevation was noticed in the B/BL group. Li et al. \[[@B34]\] reported a significantly higher expression level of COX-2 in BL compared to benign tumours (B). The majority of the analysed (by IHC) tumours in their material were BL (69 BL, 18 B and 27 AC), which potentially influenced their results. They found, however, that the content was lower in BL compared to AC, which is in line with the present study. The AC demonstrated a clear elevation of COX-2, in particular in tumours of lower grades (H/M+M, P+U) in the present study. In contrast to COX-1, a significant difference with elevated levels of COX-2 was also found for later stages of tumours (stages II-III). To our knowledge, this study is the first to quantify the COX-2 protein expression by immunoblotting in ovarian tumours. Several earlier studies have shown by IHC that COX-2 is up-regulated in ovarian neoplasm using different scoring systems of staining intensity \[[@B20]\]. Our results confirm the IHC data on COX-2 shown by others. The observed increase of COX-2 expression in EOC was correlated to poor differentiation, shorter time to tumour progression, resistance to chemotherapy, poor prognosis and significantly shorter survival time compared to patients with tumours staining negative for COX-2 \[[@B22],[@B36],[@B38]\], suggesting COX-2 to be an independent prognostic factor \[[@B36]\]. COX-2 expression was also significantly correlated with microvessel density and/or VEGF expression in advanced-stage ovarian serous carcinoma \[[@B37],[@B39],[@B40]\]. In our study, absence of or weak COX-2 expression was noticed in the majority of the B/BL tumours and in only four AC, all of them of high to moderately differentiated grades, and presumably better prognosis.A recent study describing positive COX-2 staining of preneoplastic OSE adjacent to COX-2 negative neoplastic cells, presumably of higher grades \[[@B41]\], supports our findings. A correlation to histological subtype was not found for COX-2 in the present study. The cell-specific localisation of COX-2 in the B/BL group was almost exclusive in the epithelial cell, similar to that of COX-1.

Interestingly, both COX-1 and COX-2 were expressed in OSE lining inclusion cysts in the present study. This observation might suggest that the appearance of COX-2 in these cells is an early sign of an altered phenotype (mesothelial to epithelial transition, \[[@B31]\]) with malignant potential. We have previously shown that the expressions of the adhesion molecules E-cadherin \[[@B42],[@B43]\] and claudin-3/4 \[[@B27]\] and the transcription factor C/EBPβ\[[@B44]\] correlated with malignancy in EOC. These proteins were also expressed in epithelial cells of inclusion cysts. Notably, the expression of C/EBPβ is a putative requirement for the regulation of COX-2 expression\[[@B45]\]. Li and co-workers \[[@B34]\] reported also the expression of COX-1 in OSE and inclusion cysts of the normal ovary, but both these two locations lacked COX-2 expression. Interestingly, in two independent studies COX-2 was not expressed in any of the ovarian cancer cell lines used(nine \[[@B34]\] and five \[[@B41]\]), although Denkert and co-workers \[[@B36]\] showed such expression in cell lines included in their study. The difference in COX-2 expression in cell-lines and tissue/tumour biopsies is further strengthened since positive COX-2 staining was more often found at the advancing margin of tumour invasion and new metastatic lesion \[[@B34]\]. An explanation to the findings of ovarian cancer cells in cell culture, not expressing COX-2, can be that cell lines are devoid of their basement membranes as well as the surrounding and supporting stroma cells. Recent studies have demonstrated important roles for stromal cells in tumourigenesis \[[@B46]\]. An autocrine- paracrine regulatory pathway was described for breast carcinoma and surrounding stromal cells, involving growth factors and cytokines \[[@B46]\]. Zhou and co-workers \[[@B47]\] demonstrated that stromal-epithelial interactions resulted in induction of C/EBPβ in malignant breast epithelial cells. One possibility is therefore that the expression of COX-2 in early stages of cellular transformation, e.g. in inclusion cyst formation, might be initiated by paracrine factors produced by the stromal cells, resulting in increased transcription, e.g. induced by C/EBPβ, of the *cox2*gene. The *cox2*promotor has previously been suggested to be of potential value for gene therapy in EOC, due to its tumour-specific activation in ovarian cancer cell lines *in vitro*\[[@B48]\]. Furthermore, studies on ovaries from women undergoing prophylactic oophorectomy (due to mutations in BRCA1, BRCA2, MSH1 or MLH1) demonstrated that the increase of COX-2 correlated to loss of epithelial basement membrane \[[@B49]\]. Additional studies are needed to establish the nature of interactions between epithelial cells in inclusions cyst and the surrounding basement membrane and stromal environment. Furthermore, the co-expression of COX-1 and COX-2 in epithelial cells of inclusion cysts and B/BL tumours, opens also the possibility fort an autocrine/paracrine regulation of the two COX isoforms by PGE~2~.

The expression and regulation of mPGES-1 share many similarities with that of COX-2, e.g. induced by pro-inflammatory stimuli and hormones \[[@B50]\]. This is in contrast to the two other known members of this family, mPGES-2 and cPGES, which are constitutively expressed in various cells and tissues \[[@B50]\]. Both these isoforms are functionally closer linked to COX-1, while mPGES-1 has a marked preference to COX-2 \[[@B50]\]. Staining of the normal ovary for mPGES-1 revealed expression in the stroma, while the OSE cells were mostly negative. This pattern was also observed in the BL with some staining of epithelial cells or cells associated to the epithelium. A significant increase was observed in the AC, but not in B/BL. This increase was correlated to grade, but not to stage. Intense staining was demonstrated in a cluster-like pattern, predominantly in the tumour stroma. This might to some extent reflect the presence of immune cells recruited to the tumour site as a part of an inflammatory reaction. A local, anti-inflammatory response to IL-1α was suggested \[[@B51]\] to involve production of cortisol in the normal OSE by an increase of 11β-HSD, while this enzyme was not expressed in cell lines derived from EOC \[[@B52]\]. Infiltration of macrophages into EOC was described by Klimp and co-workers \[[@B53]\] and their study demonstrated increased levels of COX-2 in tumour-associated macrophages. The role of mPGES-1 for PGE~2~production in these cells are essential since isolated peritoneal macrophages from mPGES-1 null mice produced minimal amounts of this prostanoids in response to pro-inflammatory stimuli (LPS) \[[@B50]\]. Similar results were obtained with macrophages from C/EBPβ-deficient mice as a result of ablated mPGES-1 expression. This emphasise the role of inflammation in EOC since C/EBPβ has been demonstrated to be major regulator of pro-inflammatory genes, in addition to COX-2 and mPGES-1 \[[@B50]\]. The cellular localization of mPGES-1 in the present study, suggested a close connection to the cells expressing EP~1--2~receptors, which also support an autocrine/paracrine regulatory pathway. An earlier study \[[@B35]\] showed the content of mPGES-1 in ovarian cancer cell lines, but the present study is the first, to our knowledge, to demonstrate the expression of mPGES-1 in EOC.

Previous studies have demonstrated that PGE~2~acted mainly via the EP~2~receptor in female reproduction and in tumourigenesis, while EP~1~was more involved in neuronal functions \[[@B29]\]. Significant increases were found for the expressions of both EP~1~and EP~2~in AC compared to benign tumours in the present study. Interestingly, one of the findings in the present study was a difference in the distribution of EP-receptors between stroma and tumour tissue. The majority of the EP~1--2~immunoreativity was found in OSE while only EP~2~could be demonstrated in the stroma. First, this suggests target cells for PGE~2~in both these cell compartments and secondly a separate function, mediated by the EP~2~receptor in the stroma. In addition, the immunblotting experiment demonstrated multiple bands for the two receptors. These bands could represent phosphorylated forms of the receptors as well as splice variants \[[@B29]\], and therefore have important implications for cell signalling. The two receptors regulates different intracellular signalling pathways, i.e. IP~3~/Ca^2=^(EP~1~) and cAMP (EP~2~). Phosphorylated residues and splice variants can potentially alter sensitivity, responsiveness and preferred signalling system within the cells \[[@B29]\], all of which can contribute to enhanced tumour growth. However, additional experiments are needed to explore these possibilities.

Staining of cluster of cells in the AC, demonstrated for primarily for mPGES-1 and EP~1--2~, were earlier reported for both COX-1 and COX-2 \[[@B36]\]. Previous studies have actually localised COX enzymes to a large variety of cells, including both normal and tumour epithelial cells, normal and tumour vascular endothelium and smooth muscle cells, macrophages and fibroblast cells. The clearly defined staining of populations of malignant cells, found here and by others, may implicate specific functions, such as angiogenesis and invasion or a more active anti-tumour response for mPGES-1 and EP~1--2~in different populations of the malignant cells. Cluster like expression of COX-2 was recently reported to correlate to angiogenesis in prostate cancer \[[@B54]\].

Conclusion
==========

In the present study, statistically significant increases, as well as cell-specific localizations were demonstrated for COX-1, COX-2 and mPGES-1 in adenocarcinomas compared to the normal ovary and benign tumour tissue. These elevations in malignant cells can be a response to an inflammatory reaction, both chronic and acute, caused by a growing and potentially invasive tumour, and the interactions between tumor cells, stromal cells and the immune system.

The increase of COXs, mPGES-1 and EP receptors in epithelial ovarian tumours supports the hypothesis that PGE~2~is an important factor for progression (proliferation/angiogenesis) in ovarian tumours. The appearance of COX-2 in potential pre-malignant structures (inclusion cysts) may indicate a role in malignant transformation of epithelial cells, in addition to its earlier documented presence in malignant tumours. The results also suggest that the synthesis of PGE~2~is regulated by autocrine and paracrine factors (i.e. cytokines) as a result of epithelial-stromal interactions. Furthermore, mPGES-1 and the EP receptors may represent important targets for development of novel anti-inflammatory and anti-tumour therapies.

Acknowledgements
================

The authors would like to thank Anna Wickman Tordby for assistance with the statistical analysis. Support was provided by the Swedish Cancer Society (to K.S.), the Swedish Society of Medicine, the Swedish Medical Research Council (10375 to L.H.), the Norwegian Cancer Society (to L.H), the Novo Nordisk Research Foundation (to L.H.), Foundation of Assar Gabrielsson, Hjalmar Svensson and King Gustav V Jubilee Clinic Cancer Research.


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Spatial organization of multi-enzyme biocatalytic cascades.
Industrial biocatalysis is an economically attractive option for the production of valuable chemicals. Our repertoire of cheap building blocks and commodity target molecules is vastly enhanced by multi-enzyme biocatalytic cascades. In order to achieve suitable titers in complex novel biocatalytic schemes, spatial organization may become necessary to overcome barriers caused by slow or inhibited enzymes as well as instability of biocatalysts. A number of spatial organization strategies are currently available, which could be integrated in the design of complex cascades. These include fusion proteins, immobilization on solid supports, multi-dimensional scaffolding, and encapsulation within vessels. This review article highlights recent advances in cascade biocatalysis, discusses the role of spatial organization in reaction kinetics, and presents some of the currently employed strategies for spatial organization of multi-enzyme cascades.


Q:

How to handle branching when you're planning on doing a rewrite in the future?

My development team is moving to branching soon - we've been cursed with SourceSafe and we're moving to Team Foundation Server - and I'm curious about something.
Traditionally when we do major revisions to our product, to the point where not even the folder structure or the filenames stay the same, we do a new root folder in source control.
For example
$/V1.0
$/V1.1
$/V1.5
$/V2.0

and so forth.
I'm brand new to branching and one of the things I'm reading is that you can use different branches for the various versions of your product. Now, when you're talking about doing a hotfix or a small change or modification to the code - where at worst you might be adding new files - this makes sense.
However when doing a "V-Next" version of your product, where you are planning on doing a more or less complete rewrite of the product (not from scratch, but rather reworking it drastically), to the point where the folder structure and file names will likely be completely different, is that still something you would want to do through branching? Or would you want to create a new root ($/V2.0 above) to handle it?

A:

Our development team uses a pretty standard branching structure in Subversion. In the main repository we have 3 folders:

branches
tags
trunk

In your example, all of the V* folders would go under tags. All of the main development happens in trunk, and we use branches when we need to have a variation on what is in trunk for another project.
We also use branches to store drastic changes to trunk. This is good practice in case you need to fix a bug in trunk before your rewrites are complete. So, we'd create a "V-Next" branch under branches, and when it is complete, we would merge that branch back into trunk.


We have identified inadvertent errors in this manuscript, as described below:

1\. The legend to Figure 1D describes the quantification of 3 experiments but in fact is the quantification of one representative experiment of 3 total experiments that were conducted.

2\. In Figure 2E, the \"Tks5MO + Tks5 RNA\" sub-panel is a duplicate of the \"Tks5 MO\" panel.

3\. The legend to Figure 3A is incorrect, and should read \"Neural crest specific riboprobes against Sox10, crestin (ctn) and mitf\".

4\. In Figures 4A and 6B, the images shown are from Tg(FoxD3:GFP) labeled fish, not from Tg(Sox10:RFP) labeled fish as stated.

5\. In Figure 4D, the labels for the sub-panels \"T5\" and \"T5MO\" were reversed.

Corrected versions of Figures 2 and 4 are provided. We apologize for any confusion our inadvertent errors may have caused, but emphasize that these changes do not affect in any way the conclusions of our studies.

Figure LEGENDS

Figure 2.Decreased Tks5 expression results in neural crest-derived defects.

(A-B) Melanophores within the trunk region above the yolk sac extension in control MO-injected and Tks5 MO-injected embryos were qualitatively (A) and quantitatively (B) analyzed. n=15 embryos and SEM is shown by bar. p values obtained from Student\'s t-test. \*\* denotes p \<0.01.

\(C\) Melanophores present in the dorsal, ventral, and lateral pigment lines were quantified to determine degree of murine Tks5 rescue of the decreased pigmentation seen in morphants. Mean values (n=3) and SEM are shown in graph. p values obtained from Student\'s t-test. \*\* denotes p \<0.01.

\(D\) Alcian blue staining was performed on indicated embryos to identify craniofacial structures (Meckel\'s cartilage (mc), palatoquadrate (pq), ceratobranchials (ch), ethmoid plate (ep)). (\*) denotes missing structures.

\(E\) Alcian blue staining was performed on indicated embryos to determine if murine Tks5 could rescue craniofacial defects seen in morphants. Structures were identified as in (D). (\*) denotes missing structures.

A revised version of Figure 2 can be seen here:

![](pone.d66234d8-b722-4b6d-ab8a-73b5f396c37e.g001){#pone-d66234d8-b722-4b6d-ab8a-73b5f396c37e-g001}

\[\^\]

Figure 4.Neural crest derivatives require a Src-Tks5-dependent pathway in vivo.

\(A\) Tg(FoxD3:GFP) embryos (8 hpf) were treated with either vehicle (DMSO) or SU6656 for 24 hours and imaged by confocal microscopy to detect neural crest cells. (D= dorsal, V= ventral). Brackets indicate the position of the somites. Scale bar represents 50 mm.

(B-C) Embryos at 15 hpf were treated as indicated for 24 hours and analyzed for pigmentation defects. (B) Embryos where treatment was initiated at 15 hpf were examined for melanophore patterning in the trunk region above the yolk sac extension. (D=dorsal, V=ventral, A=anterior, P=posterior) (C) The total number of melanophores present in the dorsal and ventral pigment lines was counted for embryos within each group as described in Materials and Methods. Mean values (n=3) and SEM were shown in graph. \*\* denotes p \<0.01 for vehicle treated vs. SFK treated comparison.

(D-E) Embryos were injected as indicated and qualitatively analyzed for defects described previously. Morpholino and RNA concentrations detailed in Materials and Methods. (E) Morphants were identified as described in Figure 1D and embryos within each group were quantified (white = morphants, black = normal).

A revised version of Figure 4 can be seen here:

![](pone.d66234d8-b722-4b6d-ab8a-73b5f396c37e.g002){#pone-d66234d8-b722-4b6d-ab8a-73b5f396c37e-g002}

\[\^\]

**Competing Interests:**No competing interests declared.


Natural distribution.
Log-normal distributions describe data from diverse disciplines of science. However, the fundamental basis of log-normal distributions is unknown. We suggest that the skewed distributions are outcomes of natural processes i.e. they result from the principle of increasing entropy. Fluctuations during the course of evolution toward more probable states yield multiplicative variations about the mean. The non-linear dispersion of thermodynamic states, i.e. matter and energy defined by chemical potentials, underlies the skew. Cumulative curves of skewed distributions without integrable analytical forms are characteristic of natural processes.


Description

Unicode Conversion Gateway is a web-based proxy server to convert some of the Indian language web pages encoded in proprietary encodings into Unicode.Padma, a popular Firefox extension, is extended and reimplemented in PHP to create this proxy server

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abstract: In this paper, we analyze the process of assembling new matrix geometric means from existing ones, through function composition or limit processes. We show that for n a new matrix mean exists which is simpler to compute than the existing ones. Moreover, we show that for n the existing proving strategies cannot provide a mean computationally simpler than the existing ones.


Different techniques for broadcasting digital multimedia have been developed and optimized for reception by mobile wireless devices. Such techniques include Forward Link Only (FLO), Digital Multimedia Broadcasting (DMB), and Digital Video Broadcasting—Handheld (DVB-H). Digital multimedia broadcasting typically relies on one or more digital multimedia encoding standards, such as Moving Picture Experts Group (MPEG)-1, MPEG-2, MPEG-4, International Telecommunication Union (ITU) H.263, or ITU H.264. The ITU H.264 standard corresponds to MPEG-4, Part 10, entitled “Advanced Video Coding.” These coding standards generally support transmission efficiency of multimedia sequences by encoding data in a compressed manner.
Several broadcasting techniques deliver content as a series of physical or logical channels, providing a content selection experience similar to a conventional television. Each physical or logical channel carries digital data that encodes audio/video streams, audio/video clips, or other informational content. To switch channels, the mobile device acquires digital data, e.g., in the form of one or more packets or frames, from a selected channel and decodes the data to present the content to the user. Prolonged delays in selecting and presenting a channel are undesirable, and undermine the “channel surfing” experience to which users are accustomed. Accordingly, reduction of channel switching time is a significant concern in broadcasting.


Annika Sorenstam and Se Ri Pak, the LPGA Tour's top two players, were four strokes back along with Patricia Meunier-Lebouc. Pak and Sorenstam, paired together, shot 70s, and Meunier-Lebouc had a 71.

"Everybody expected even before this tournament began that this course would bring out the best players at the top," Park said.

The South Korean player recovered from a double-bogey on the par-3 5th hole, when her ball bounced into a stream, with four birdies over the next 13 holes.

"Starting off I could not hit greens to save my life," Park said. "The greens were not that easy today."

The weather at the Kingsmill course, site of a PGA Tour event last year _ changed from hot and sunny Friday to cold and wet Saturday, making the rough thicker and tee shots more critical.

"This is a U.S. Open-style course, in my opinion," said Kerr, attempting to become the tour's first U.S. winner since Meg Mallon last summer in the Canadian Women's Open. "The rough is thick; there aren't many par 5s."

Foreign players have won 16 straight events, and held 13 of the top 15 spots Saturday. Juli Inkster (U.S. Women's Open) and Mallon are the only U.S. winners in the last 28 tournaments.

The course's three par-5 holes, though, are providing players their best scoring opportunities. The lengths _ 491, 467 and 458 yards _ allow many players to reach the green in two. Park has played the par 5s at 5 under over three days. Kerr has played them 8 under and Sorenstam, the tour leader in driving distance, is 7 under.

Sorenstam and Pak formed a Dream Team pairing Saturday, but neither was able to make a move up the leaderboard. Sorenstam narrowly missed birdie putts on 15 and 16, then hit her tee shot on the par-3 17th to 4 feet for a birdie that moved her to 6 under. But she bogeyed the 18th to finish five under.

"I played pretty well, but I felt like I didn't get the most out of my round," Sorenstam said. "For three days I've been grinding and grinding. I've just been very close."

It was the first time this year that Pak and Sorenstam had been paired together.

"We're both very competitive. I enjoy playing with her because we inspire each other to do our best," Sorenstam said.

Ochoa, who had shared with the lead with Park at the beginning of play on Saturday, made her first bogey of the tournament on the fourth hole, when she drove her tee shot into a valley of deep rough left of the green.

She then bogeyed four of her next nine holes, and looked to be falling away entirely before hitting consecutive birdies on 15 and 16.

"I was close to being out of contention, but I just pulled it together on the last five holes," Ochoa said. "I told myself, 'Just settle down.'"

For the second straight day, Pettersen played herself out of the lead with bogeys on two of the final three holes. On Saturday she bogeyed 17 and 18 to finish six under par.


Q:

Enable/Disable debug code dynamically

I'm writing a decent sized JavaScript animation library, that I would like to include debugging code in. I could easily do a check :
if(myLib.debugger){
   console.warn('warning message');
}

However if this runs a couple thousand times a second, it would eventually cause performance issues. Add in a few more checks throughout the code and the effect will be even more noticeable.
What I'm wondering is if it would be possible to check onload if the debugger should be enabled, and if so... turn something like this:
//debugger if(!this.name) console.warn('No name provided');

into:
if(!this.name) console.warn('No name provided');

Leaving the code commented if its not enabled, and uncommenting it if it is, thus removing any possible performance issues. Could this be done somehow with a regular expression on the entire script if loaded in through ajax? I'm trying to avoid the need for 2 versions of the same code, lib.dbug.js and a lib.js.
Cross browser compatibility is not of great importance for this (I'm really only worried about new browsers), I see it as nice to have item. If its possible however, it would be a great thing to have.
Any insight would be greatly appreciated.

A:

The simplest way to do this would be to check if the debugger should be disabled and if so, replace it with a mock object that does nothing at the very start of your script:
if (!myLib.debugger) {
    window.console = (function () {
        var newConsole = {};
        var key;

        for (key in window.console) {
            if (typeof window.console[key] === 'function') {
                newConsole[key] = function () {};
            }
        }

        return newConsole;
    }());
}

The overhead of this approach should be negligible.


<?xml version="1.0" encoding="UTF-8" ?>

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          <Border info="org.netbeans.modules.form.compat2.border.EtchedBorderInfo">
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      </Constraints>

      <Layout class="org.netbeans.modules.form.compat2.layouts.DesignBoxLayout"/>
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        <Component class="javax.swing.JButton" name="clearButton">
          <Properties>
            <Property name="text" type="java.lang.String" editor="org.netbeans.modules.i18n.form.FormI18nStringEditor">
              <ResourceString bundle="org/neuroph/netbeans/classificationsample/Bundle.properties" key="MultiLayerPerceptronVisualizationTopComponent.clearButton.text" replaceFormat="org.openide.util.NbBundle.getMessage({sourceFileName}.class, "{key}")"/>
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          <Events>
            <EventHandler event="actionPerformed" listener="java.awt.event.ActionListener" parameters="java.awt.event.ActionEvent" handler="clearButtonActionPerformed"/>
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Q:

Zeroes of $\sin(z)-z^2$

I am studying for my prelims exam. I stumbled upon the following question.
Show that there are infinitely many zeroes of $\sin(z)-z^2$ in the complex plane.
Had it just been $f(z)=\sin(z)-z$, one can observe that $f(z+2\pi)=f(z)-2\pi$. One can, therefore, see that if $f$ takes zeros only finitely often, then $f$ must also take the value $-2\pi$ only finitely often. Picard’s theorem, therefore, tells us that $f$ is a polynomial, which is absurd.
This direct approach does not seem to work for my question. So, I tried using Rouche’s theorem. For that I take $g(z)=\sin(z).$ I know the zeroes of $\sin(z)$, my idea was to find a region containing $n$ zeroes of $sin(z)$ and show that on the boundary we have $$|f-g|<|f|+|g|.$$
I could not choose the suitable region such that the above relation holds on the boundary. I am not sure if it will work or not. Of course, if it works it will prove something stronger, namely, we will in a way have a handle on the location of zeroes.
Any hint would be appreciated. Moreover, my guess is that if $p(z)$ is any polynomial then $f(z)=\sin(z)-p(z)$ will have infinitely many zeroes in the complex plane. I would like to see an argument for this case. I am trying to use Rouche’s theorem but I am not able to make any progress. Also, if there is an alternate approach (which avoids Rouche’s theorem), it will also be much appreciated.

A:

Questions like this can typically be answered using the Hadamard factorization theorem.  The function $f(z)=\sin z-z^2$ has finite order, so if it has finitely many zeroes then its Hadamard factorization has the form $P(z)e^{Q(z)}$ for some polynomials $P$ and $Q$.  So, we would have the equation $$P(z)e^{Q(z)}=\sin z-z^2$$ for all $z\in\mathbb{C}$.  Differentiating three times we get $$R(z)e^{Q(z)}=-\cos z$$ for some other polynomial $R$.  But this is impossible, since the left side has finitely many zeroes and the right side has infinitely many zeroes.
(The same argument applies with $z^2$ replaced by any polynomial; you just have to differentiate enough times to make it away.)


I teach 6th and 8th Grade English Language Arts, with a wonderful, eager, and engaged group of children. Every child in my classroom wants to learn and succeed, and I encourage them to work hard, share their thinking, and push themselves to grow at every opportunity. While some students are still working their way through their first chapter book, others are zooming through my library.

My students are a diverse group of creative, enthusiastic, and inquisitive inner-city children who range from struggling readers, getting started with chapter books, to high-level readers who are grade-levels ahead.

Our curriculum focuses on using high-interest reading, and as much of it as possible, to help our students grow as readers, critical thinkers, and individuals. We believe that the best way to improve literacy is for children to read, read, and read some more, with teachers who can support their thinking as is it develops and blossoms.

Unfortunately, our schools budget is unable to provide the number and variety of books that we need to help our students thrive. At our middle school, we prioritize creating an environment where we can build literacy for all, support struggling learners, and help gifted students grow.


616 F.Supp. 1186 (1985)
L.P. ACQUISITION COMPANY and L.P. Media, Inc., Plaintiffs,
v.
Carl L. TYSON, Acting Director of the Corporation and Securities Bureau of the Department of Commerce of the State of Michigan, et al., Defendants.
No. 85CV73341DT.
United States District Court, E.D. Michigan, S.D.
August 7, 1985.
*1187 Theodore Souris, Detroit, Mich., for plaintiffs.
William M. Saxton, Detroit, Mich., Joe D. Sutton, Office of Mich. Atty. Gen., Lansing, Mich., for defendants.

MEMORANDUM OPINION

(FINDINGS OF FACTCONCLUSIONS OF LAW)
DeMASCIO, District Judge.
Plaintiffs, L.P. Acquisition Company and L.P. Media, Inc. (LP or plaintiffs) filed a three-count complaint against Carl Tyson, Acting Director of the Securities & Exchange Bureau; Doug Ross, Director of the Michigan Department of Commerce; Frank Kelley, Michigan Attorney General; and The Evening News Association (ENA), seeking declaratory relief pursuant to 28 U.S.C. § 2201. Jurisdiction is based primarily upon 28 U.S.C. § 1331(a).
L.P. Acquisition is a wholly-owned subsidiary of L.P. Media. Both corporations were formed on July 26, 1985 for the purpose of acquiring ENA. The principals behind LP are A. Jerrold Perenchio and Norman Lear, self-described "entertainment industry executives." The ENA is a closely held corporation; i.e., its shares are not registered with the Securities and Exchange Commission (SEC) nor listed on any other exchange, a critical fact made clear to the court after study of briefs submitted by the parties. The ENA has approximately 333 shareholders and 45,000 shares outstanding. One-half of the shares and shareholders are located in Michigan; the remainder is found in 24 other states.
On July 28, 1985, LP commenced a cash tender offer of $1,000 per share directed to all shareholders of ENA wherever located. The offer is due to expire on August 23, 1985 and LP anticipates that it will begin to purchase shares on August 17, 1985. LP alleges voluntary compliance with § 14(d) of the Williams Act, 15 U.S.C. § 78n(d) and § 12(g) of the 1934 Securities Exchange Act (1934 Act), 15 U.S.C. § 78l(g). LP also alleges compliance with § 14(e) of the Williams Act, 15 U.S.C. § 78n(e), which plaintiffs *1188 contend applies to this (and every other) tender offer.
When making this tender offer, LP deliberately failed to comply with the requirements of the Michigan Take Over Offers Act (Take Over Act), Mich.Comp.Laws Ann. § 451.901 et seq., which LP contends is unconstitutional as applied to their tender offer. LP further contends that any attempt to apply the Michigan Blue Sky Law, Mich.Comp.Laws Ann. § 451.501 et seq. to plaintiffs' tender offer would be likewise unconstitutional. In this action, LP seeks preliminary and permanent injunctive relief enjoining defendants from attempting to apply the procedural and enforcement provisions of these Michigan acts to LP's tender offer. The state defendants have indicated that although they are prepared to enforce the Michigan acts as to LP's offer, they will await the decision of this court. LP represents that ENA will surely seek to enforce the Michigan acts. This matter is presently before the court on plaintiffs' motion for a preliminary injunction.
The crucial issue here is whether plaintiffs can demonstrate a likelihood of success on the merits. LP must show the likely existence of a constitutional violation causally related to the threatened action sought to be enjoined. Wilson v. Thompson, 593 F.2d 1375, 1384-85 (5th Cir.1979).
In alleging that the Michigan statutes are unconstitutional as applied to its tender offer, LP cites the Sixth Circuit opinion in Martin-Marietta Corp. v. Bendix Corp., 690 F.2d 558 (6th Cir.1982) as controlling in this case.[1] In that decision, the Sixth Circuit held that the Take Over Act and the Blue Sky Law violated the commerce clause as applied to a tender offer by Martin Marietta for outstanding shares of Bendix Corporation. Those shares were registered with the SEC and fully governed by the Williams Act.
In assessing the precedential value of the Martin-Marietta decision, our initial inquiry is whether LP's tender offer, for unregistered securities, is subject to any provision of the Williams Act, §§ 14(d), (e). There is no dispute that § 14(d) is not applicable to LP's tender offer. The only remaining provision, § 14(e), reads as follows:
It shall be unlawful for any person to make any untrue statement of a material fact or omit to state any material fact necessary in order to make the statements made, in the light of the circumstances under which they are made, not misleading, or to engage in any fraudulent, deceptive, or manipulative acts or practices, in connection with any tender offer or request or invitation for tenders, or any solicitation of security holders in opposition to or in favor of any such offer, request or invitation. (Emphasis added.)
LP contends that the language "in connection with any tender offer" renders § 14(e) applicable to its tender offer for ENA shares.
The relevant legislative history of the Williams Act indicates otherwise. Enacted in 1968 to correct a perceived gap in federal securities regulation which left cash tender offers for control blocks of equity securities completely unregulated, the act was the subject of the following discussion directed to Congress:
The bill before you deals with stock acquisitions in three specific contexts  first, the acquisition by means of a cash tender offer of more than 10% of any class of stock, of a publicly held company; second, other acquisitions by any person or group of more than 10% of any class of stock of a publicly held company; and third, the repurchase by a corporation of its own outstanding shares.
Testimony of SEC Chairman Cohen, Hearings on S.150 Before the Subcomm. on Securities of the Senate Comm. on Banking *1189 and Currency, 90th Cong., 1st Sess. 32-33 (1967) (emphasis added).
Throughout various Congressional proceedings relating to the Williams Act, there appears a reoccurring analogy to the proxy rules (applicable only to registered securities). A prime example is found in this statement contained in the committee reports of both houses:
The cash tender offer is similar to a proxy contest, and the committee could find no reason to continue the present gap in the Federal securities laws which leaves the cash tender offer exempt from disclosure provisions.
S.Rep. No. 550, 90th Cong., 1st Sess. 3 (1967); H.R.Rep. No. 1711, 90th Con., 2d Sess. 3 (1968), U.S.Code Cong. & Admin. News 1968, 2811, 2813.
It is clear from these passages that Congress intended that the Williams Act provisions be applicable to tender offers for registered equity securities. Moreover, a recent extensive review of the act's legislative history by Professor Alfred P. Conrad yields the conclusion that no senator or congressman was conscious of a difference in coverage between § 14(e) and any other subsections of the Williams Act. See Conard, Tender Offer Fraud: The Secret Meaning of Subsection 14(e), 40 Bus.Law 87, 89-93 (Nov. 1984).
Further evidence of legislative intent can be gleaned by comparison of the phrasing of § 14(e) with that of § 10(b) of the 1934 Act, where Congress expressly stated that the section applies to the
purchase or sale of any security registered on a national securities exchange or any security not so registered.

15 U.S.C. § 78j(b) (emphasis added).
If Congress had intended to apply § 14(e) tender offers to unregistered securities, it would have used this type of language in that section. Moreover, to interpret § 14(e) broadly would render an absurd result by extending coverage of its provisions to foreign and totally intrastate tender offers, as well as those made for the securities of closely held corporations.[2] That Congress would intend for only one subsection of an extensive regulatory scheme to have this cosmic scope defies logic. The court would suggest that Congress' choice of the phrase "any tender offer" was intended to refer to the form tender offers take  whether for cash or securities, for all or a portion of the outstanding shares, and the type of transmittal through which the tender offer is made.
We conclude that the scope of § 14(e) is limited to tender offers for registered equity securities, made by means of interstate commerce, the mails, or national securities exchanges. In so concluding, the court is mindful of the SEC's broad interpretation of § 14(e), which suggests that the provision governs tender offers for non-registered securities. Having failed to glean any legislative intent for such an interpretation, however, we find that the commission was acting beyond its statutory authority. Accordingly, we give no weight to the SEC's interpretation.
As LP's tender offer for ENA's unregistered securities is not governed by the Williams Act, LP's reliance on the Martin-Marietta decision is misplaced. Implicit throughout Judge Kennedy's opinion is that Bendix shares were registered with the SEC, that the Martin-Marietta tender offer was fully subject to the requirements of the Williams Act, and, accordingly, that Bendix shareholders were afforded the protection of the federal securities laws, rules and regulations:
We find that to the extent that the state statutes confer power on state authorities to interfere with the timing of an interstate tender offer made under the Williams Act, or to compel the revision of the solicitation or tender offer as a condition of proceeding, they impose an unconstitutional burden on interstate commerce. 690 F.2d at 565 (emphasis added).
*1190 Because Martin-Marietta deals with a tender offer made for registered securities, fully governed by the Williams Act, that decision has no application here.
Finally, we must address whether, despite the absence of any applicable federal law, the Take Over Act has an undue burden on interstate commerce; i.e., beyond that necessary to protect a legitimate state interest. A state statute must be upheld if it "regulates even-handedly to effectuate a legitimate local public interest, and its effects on interstate commerce are only incidental ... unless the burden imposed on such commerce is clearly excessive in relation to the putative local benefits." Pike v. Bruce Church, Inc. 397 U.S. 137, 142, 90 S.Ct. 844, 847, 25 L.Ed.2d 174 (1970).
An examination of the major features of the Take Over Act is in order. On its face, the act applies to offers to acquire equity securities of corporations with more than 100 shareholders, either incorporated in or having their principal place of business in Michigan. Excepted from the provisions are "friendly" tender offers, i.e., either approved by incumbent management or self tenders by the corporation itself. Section 451.904(2)(d), (f). The act requires the offeror to file a registration statement with the Department of Commerce (department) ten days prior to commencement of any offer. Section 451.905(3). The department is empowered to stay the effectiveness of the offer if it orders a hearing to consider a violation of the act. Section 451.905(4). The department may issue cease and desist orders, § 451.914(1), and refer violations to the attorney general and/or local prosecutors. The act also affords target companies standing to seek enforcement.
The act also requires that a tender offer be open for not less than 60 days. Additionally, if the price or consideration is increased, it is considered as a new offer, subject to being kept open for an additional 60 days, limited by a 90-day cap. During this time period, the offeror may not purchase shares from Michigan shareholders. The offeror may still purchase shares during this period from non-Michigan shareholders. Section 451.904(2). The act contains anti-fraud requirements that are quite similar to the provisions of § 14(e) of the Williams Act. Section 451.905.
The protection of resident shareholders of a Michigan corporation is a legitimate state interest.[3] This is particularly true in the absence of any applicable federal regulation and under the facts of this case. The ENA is a closely held corporation with 50 percent of its shares and shareholders located in Michigan. The corporation owns a major newspaper that impacts upon the entire state and two radio stations in Michigan's largest city. Each of these factors underscore the need for regulation of a hostile tender offer. These state interests outweigh the incidental burden the application of the Take Over Act will have on interstate commerce. We are loathe to deny enforcement of a state regulatory statute under the circumstances apparent here.
Thus, we conclude that Congress never intended § 14(e) to apply to tender offers for unregistered securities; that when Congress enacted the Williams Act, it declined an opportunity to amend § 28(a), the scope section that preserves the jurisdiction of state agencies performing like functions over unregistered securities, so long as the actions of state regulatory agencies do not conflict with provisions of the federal act; that Congress has made clear its willingness to leave the states free to regulate tender offers for unregistered securities and to tolerate the burden on interstate commerce, if any, such state regulations may cause; that the SEC's contrary interpretation is more expansive than the act will permit; that the Michigan acts are not unconstitutional on their face or as applied to the LP tender offer for the shares in ENA.
Having so concluded, LP cannot succeed on the merits of their claim of entitlement to injunctive relief, the only relief LP *1191 seeks. Accordingly, plaintiffs' complaint must be dismissed.[*]
IT IS SO ORDERED.
NOTES
[1]  Plaintiffs also rely on the United States Supreme Court decision of Edgar v. MITE Corp., 457 U.S. 624, 102 S.Ct. 2629, 73 L.Ed.2d 269 (1982), wherein the Court held that an Illinois take-over statute imposed an undue burden on interstate commerce. The tender offer in MITE was concerned solely with registered equity securities fully subject to the Williams Act.
[2]  The number of closely held corporations in the United States is presently over three million, as compared with approximately seven thousand equity securities registered under the 1934 Act. U.S. Statistical Abstract 1984, at 532; I.R.S. SOI Bulletin, Winter 1983-84, at 23.
[3]  In Martin-Marietta, Judge Kennedy acknowledged that the protection of Michigan shareholders is a legitimate state interest. 690 F.2d at 566.
[*]   The court has examined plaintiffs' amended complaint filed moments before the completion of this opinion. We hold that our findings and conclusion apply to the amended complaint as well.


As I noted in my previous post, Erick Erickson recently started a movement in response to the Occupy Wall Street movement. The occupiers have as a slogan that they are the 99%. To counter this, Erickson hit on the idea of the 53%. This is the percentage of Americans who pay the federal income tax. His message is that complaints should cease, people should not blaming Wall Street, and people should pay their taxes.

During an interview on CNN Erickson responded to the criticisms of the Occupiers by asserting that life is not fair. He also made this point in his post:

Well, these people apparently forgot that life is not fair and are demanding the government intervene to legislate that life suddenly become fair. They are claiming to be the â€œ99%â€ against the evil 1% of rich people who work on Wall Street. They are posting pictures to a website holding up their sob stories. Some are terribly tragic, but most? Boo-freakinâ€™-hoo. Life is not, never has been, and never will be fair.

While Erickson does not actually present a developed argument, he seems to be contending that the Occupiers are in error regarding their protest and their desire to change the economic and political system. They are in error, as he seems to see it, because they supposedly want to make things fair and this will never occur. I am not sure if he means that unfairness is a matter of necessity in the sense that fairness is a logical or practical impossibility. However, it seems to suffice to take his claim at face value, namely that life will never be fair.

Interestingly, his response to this is rather like that of the Stoics and reminds me of what James Stockdale wrote about the story of Job: life is not fair and this is something we simply must deal with.

As a runner and martial artist, I have long found Stoicism appealing. However, there is the question about whether or not Erickson is right.

To steal a bit from Thomas Hobbes, life can be divided up into two main domains: the natural world and the artificial world. The natural world consists of all the natural thinks, such as streams, rocks, planets, animals, humans and so on. The artificial world is the domain of what we humans create and includes our social and political structures, including the economy.

The natural world is clearly not fair in the sense that natural processes do not consistently bring about what people (and animals) actually deserve. The just and unjust are killed in earthquakes, the wise and the fools perish of cancer, the good drown as readily as the bad, the kind are consumed in fire as swiftly as the cruel. As I say to my students, stuff just happens and deserving has nothing to do with it (to steal a bit from Unforgiven). As far as the evidence indicates, justice and fairness are lacking in the purely natural world.

This fact does, of course, cause some thinkers to raise the problem of evil in regards to God. After all, if there is supposed to be an omniscient, omnipotent and good God, then we would expect there be to justice in the natural world. It need not be a perfect world (as Leibniz argued), but such a being should surely be up to providing a fair world. There are, of course, various replies to this problem of evil-but none of them really seem to adequately solve the problem. One stock reply is that God balances the books in the afterlife, which hardly explains why He does not get the book keeping done properly here. The most reasonable inferences from the evidence are that either God does not exist or God is lacking perfection in power, knowledge or goodness.

In regards to the natural world, I agree with Erickson-life in the natural world is clearly not fair and this will almost certainly never change. It would be the height of foolishness to protest against this. Rather, wisdom lies in trying to mitigate the situation through preparations, technology, and good decision making.

However, as noted above, we are not merely creatures of the natural world who must live in a world not of our making. We are also the creators of the artificial world-that of society, politics, economics and so on. While this domain is obviously shaped by the natural world, it is a human construct and it is within our collective power. As such, whether our institutions are fair or not seems to be a matter of choice. Since we create and sustain them, it would seem to follow that we can change unfair aspects to be more fair. To think that our creations are beyond our control and that we simply have to live under their unchanging ways is to fall victim to the fallacy of reification.

To use an obvious analogy, imagine that I ran my classes in a way comparable to our economic system. For example, while students could work hard to get good grades, the grades also could be bought or acquired in other ways (like family influence or via connections). Also, the students would have access to the class material and my time on a non-equal basis (well off and well connected students would have the most, while the poor students would have far, far less). Imagine that some students complained that it was unfair. If I replied “life is not fair”, that would be absurd. After all, the class is under my control-I could just as easily make the class fair in the sense that the grade each student receives isÂ primarily dependent on their effort and ability. The same could be done with our economic system. After all, it was not forged by the hand of God and dropped from the sky. Nor is it ruled by unbreakable laws of nature. True, people do like to talk as if the economic system is an entity in its own right that follows immutable laws-but this is no more true of our economic system than it is true of my classes. The rules are ours to change, be they fair or unfair. As such, to say that life is not fair is merely an expression of a problem rather than a refutation of criticism of unfairness. Naturally, it could be argued that it is right to be unfair, but that seems to be absurd.

To forestall an obvious mistakenÂ reply, unfairness and inequality are different things: it can be completely fair to have an unequal distribution of goods. To go back to the class analogy, it can obviously be just and fair for students to have various grades-provided that the grades are based on merit. In fact, it would be unfair for students to get the same grades regardless of effort and accomplishments. To use another obvious analogy, a race can also be fair and yet end with an unequal distribution of awards. After all, not everyone can be first-just the best runner.Â People often “confuse” calls for fairness with calls for equal distribution (often as an intentional part of a straw man attack) but they are not the same thing at all.

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Configuration - This product is made to order and can be customized to suit your requirement. Product Specification : The mobile pedestal units are a must have accessory for storage. Structure: 18mm thick pre laminated board with 2 mm thick PVC edge banding Configuration: Three drawers, including one large drawer for file storage Size: 640mm tall x 400mm...

Configuration - This product is made to order and can be customized to suit your requirement. Product Specification : The mobile pedestal units are a must have accessory for storage. Structure: 18mm thick pre laminated board with 2 mm thick PVC edge banding Configuration: Three drawers, including one large drawer for file storage Size: 640mm tall x 400mm...