---
abstract: |
    The propagation of an interfacial crack along a heterogeneous weak plane of a transparent Plexiglas block is followed using a high resolution fast camera. We show that the fracture front dynamics is governed by local and irregular avalanches with very large size and velocity fluctuations. We characterize the intermittent dynamics observed, i.e. the local pinnings and depinnings of the crack front which trigger a rich burst activity, by measuring the local waiting time fluctuations along the crack front during its propagation. The local front line velocity distribution deduced from the waiting time analysis exhibits a power law behavior, $P(v) \propto v^{-\eta}$ with $\eta = 2.55 \pm 0.15$, for velocities $v$ larger than the average front speed $\langle v \rangle$. The burst size distribution is also a power law, $P(S)\propto S^{-\gamma}$ with $\gamma=1.7 \pm 0.1$. Above a characteristic length scale of disorder $L_d \sim 15
    \mu m$, the avalanche clusters become anisotropic, and the scaling of the anisotropy ratio provides an estimate of the roughness exponent of the crack front line, $H=0.66$, in close agreement with previous independent estimates.
author:
- Knut Jørgen Måløy
- Stéphane Santucci
- Jean Schmittbuhl
- Renaud Toussaint
title: Local waiting time fluctuations along a randomly pinned crack front
---

The physics community has recently paid a lot of attention to the study of damaging processes [@celarie03; @hansen03; @afek05]. This interest is motivated not only by the practical benefits to many engineering domains, but also from a more fundamental point of view, by the diverse challenging questions brought forward, in particular in statistical physics [@herrmann90]. The role of heterogeneities during crack propagation is of central importance since they induce local pinnings of the crack front and subsequently trigger a very complex history of the fracture in the material. One of the consequences of this phenomenology is the roughness of fracture surfaces left by the crack. Indeed, cracks in heterogeneous media exhibit a self-affine morphology, with long range correlations. The associated roughness exponent was found to be very robust for different materials, over a broad range of length scales [@mandelbrot84; @brown85; @bouchaud90; @maloy92; @schmittbuhl93; @schmittbuhl95; @bouchaud97], and was further conjectured to be universal [@bouchaud90; @maloy92]. A recent work [@hansen03; @schmittbuhl03] suggests that the origin of these self-affine long range correlations comes from the elastic interactions within the damage zone and proposes a link between the roughness exponent and the critical exponent $\nu$ for the correlation length of the damage clusters. More generally, front propagation in random media has become a challenging problem related to the dynamics of interfaces in many different physical systems theoretically connected, such as crack fronts [@bouchaud97], magnetic domain walls [@Lemerle98], or wetting contact lines [@Prevost02; @Moulinet02; @Moulinet04], where elasticity and disorder compete to shape the interface.

In order to shed some light on the interactions between the crack front and material heterogeneities, a simplification to a two dimensional configuration -an interfacial crack- has been proposed both experimentally [@schmittbuhl97; @delaplace99] and theoretically [@schmittbuhl95b; @schmittbuhl03]. The interfacial configuration provides a higher resolution since all locations of the crack front belong to the same plane. Moreover, using a transparent material and a high resolution fast camera, the detailed complex crack dynamics can be captured, following the crack front with a high precision both in time and space [@maloy01]. So far experiments have been focused on the fracture front line morphology leading to the estimated roughness exponent $\zeta=0.55 \pm 0.03$ [@schmittbuhl97], followed up by a longer study showing $\zeta=0.63 \pm 0.03$ [@delaplace99]. First attempts have been recently performed to analyze the interfacial crack front dynamics [@maloy01; @santucci05]. These studies have shown that the fracture front propagation is intermittent and can be described in terms of a Family-Vicsek scaling [@family85] with a roughness $\zeta=0.6$ and a dynamic exponent $\kappa=1.2 \pm 0.2$.

In this Letter, we study a system first studied experimentally by Schmittbuhl and Måløy [@schmittbuhl97; @maloy01]. Whereas previous studies focused on the morphology of the interfacial crack [@schmittbuhl97], we focus on the local crack dynamics, and on the distribution in both time and space of the waiting time during pinning events. To address this problem, we introduce a new analysis procedure in order to study the local waiting time fluctations. The improved experimental techniques and resolution allow to show that the dynamics of the fracture front is driven by local irregular avalanches with very large size and velocity fluctuations, and anisotropic shapes whose scaling is directly linked to the self-affine scaling of the crack front itself. This new set of experiments also confirms earlier results on such systems [@schmittbuhl97; @maloy01].

We describe here experiments where two Plexiglas plates are annealed together to create a single block with a weak interface [@schmittbuhl97]. The plates are of dimensions: $32cm\times 14cm
\times 1cm$ and $34cm\times 12cm \times 0.4cm$, and annealed together at $205^{\circ}$C under several bars of normal pressure. Before annealing, both plates are sand-blasted on one side with $50 \mu m$ steel particles or $100 \mu m$ glass beads. Sand-blasting introduces a random topography which induces local toughness fluctuations during the annealing procedure. We have measured the profile of a sand-blasted Plexiglas surface, using a white light interferometry technique (performed at SINTEF Oslo laboratory) and found that the local irregularities have a characteristic size about $ 15 \mu
m$ [@santucci05b]. While the upper Plexiglas plate is clamped to a stiff aluminium frame, a press applies a normal displacement to the lower one (1cm thick) at a constant low speed which results in a stable crack propagation in mode I [@schmittbuhl97]. The fracture front is observed with a high resolution fast camera mounted on a microscope. Two different cameras have been used, a Kodak Motion Korder Analyzer CCD camera which records up to $500$ frames per second (fps) with a 512x240 pixel resolution, and lately a much more powerful one, a Photron Ultima CMOS camera. Using this camera at a spatial resolution of $1024 \times 512$ pixels, and an acquisition rate of $1000$ fps we can follow the stable crack front during more than $12s$ (recording up to $ 12288$ images). Different experiments have been performed varying the acquisition hardware, the microscope magnification corresponding to a pixel size between $1.7 $ to $ 10\mu m$, and the average front line speed ranging from $0.35 $ to $40 \mu m/s$. It is important to note that in all cases, the pixel size is smaller than the size of the local irregularities of about $20 \mu m$ due to the sand-blasting process.

\[Fig1\]

In order to analyze the local waiting time fluctuations and the burst dynamics, we propose the following procedure: the fracture front lines extracted from image analysis of the digital pictures (see Fig. \[Fig1\]a) are added to obtain a waiting time matrix ${\bf
W(x,y)}$. This matrix has the dimension of the original image and an initial value equal to zero. We add the value 1 to the matrix element $w$ corresponding to each pixel of the detected front line position $(x,y)$. This procedure is performed for all frames of a given experiment in order to obtain the final waiting time matrix ${\bf
W(x,y)}$. A gray scale map of this matrix is shown in Fig. \[Fig1\]b. The spatially random toughness along the weak interface generates a rough crack line in pinning the crack front (Fig. \[Fig1\]a), and triggers a rich burst activity on a wide range of length scales. The numerous and various regions of gray levels suggest this intermittent dynamics (Fig. \[Fig1\]b). It is important to mention that the image recording is so fast that there are basically no holes in the waiting time matrix ${\bf
W(x,y)}$, [*i.e.*]{} no regions of zero values (apart from below the first front, above the last one, and a few artifacts due to impurities in the sample). Then, we can deduce from ${\bf W(x,y)}$, a matrix ${\bf V(x,y)}$ of the local normal speed of the interface at the time when the front went through a particular position, by computing the inverse value of the corresponding matrix element $w$ of ${\bf W(x,y)}$ multiplied by the ratio of the pixel size $a$ and the typical time between two images $\delta t$. Therefore, we can associate to each pixel corresponding to the crack line in each image, a local front velocity $v =
\frac{1}{w}\frac{a}{\delta t}$. Finally, we can obtain the probability distribution functions of the local waiting time $w$ and the local front velocity $v$, by estimating the occurrence number of each measured waiting time or velocity on all the pixels in all the fracture front line images.

\[Fig2\]

The velocity distribution $P(v/\langle v \rangle)$ is shown in Fig. \[Fig2\] in a log-log scale. A data collapse is obtained for all different experimental conditions by scaling the local velocity $v$ with the average crack front speed $\langle v \rangle $ which varies from one experiment to another. A clear power law behavior of the velocity distribution $P(v/\langle v \rangle) \sim (v/\langle v \rangle)^{-\eta}$ is observed for velocities larger than $\langle v \rangle$ with a crossover to a slowly increasing function for velocities smaller than $\langle v \rangle$. A linear fit to the experimental data for $v/\langle v \rangle > 1$ gives a slope $-\eta=-2.55 \pm 0.15$. The inserted figure shows a double logarithmic plot of the corresponding waiting time distribution $P(w/\langle w \rangle)$, where $w$ is the waiting time, and $\langle w \rangle$ the average waiting time for each experiment. A linear fit to the experimental data for $w<
\langle w \rangle$ has a slope $0.55 \pm 0.15$ consistent with the exponent $\eta-2$ deduced from the velocity distribution. The power law distribution of the local velocities confirms once again previous observations, revealing a non trivial underlying dynamics as observed on a fast video recording. It is important to note that even though the first moment of the velocity fluctuations $ \langle v \rangle $ exists, the second and higher moments are ill defined and dominated by the largest velocity fluctuations. In an earlier work, the velocity distribution was investigated with a different method, based on the distance between subsequent fronts at a given time interval [@maloy01]. However, such method proved out to produce results depending on the time interval chosen. Indeed, a short time between the front only gave contribution from the high velocity part of the distribution while a long time between the fronts gave a peak around the average velocity only. By using the concept of waiting time introduced in the present Letter, we are able to measure both high and low velocities. In the present case there exists a well defined length scale $a$ at which the velocity can be measured. Using different magnification of the microscope, we have checked the robustness of our procedure and shown the reproducibility of our results for different pixel sizes.

In order to analyze the local burst activity, we consider a thresholded matrix generated from the velocity matrix ${\bf V(x,y)}$, by setting the matrix elements $v$ equal to one for $v>C\cdot \langle v \rangle $ and zero elsewhere, where $C$ is a constant of the order of a few unities.

Fig. \[Fig1\]c shows the spatial distribution of clusters of different sizes obtained from a thresholded matrix with a threshold level $C=10$. The white clusters correspond to velocities $10$ times larger than the average crack front speed $\langle v \rangle$. Then, we can extract from this thresholded velocity matrix the size distribution of the high velocity bursts. The clusters connected to the first and last front, and thus belonging to the upper and lower white parts are excluded from the analysis.

On Fig. \[Fig3\], the cluster size distribution $P(S/ \langle S
\rangle)$ is shown for different experiments at a given threshold value $C=3$. First, we show a data collapse for all the different experiments performed by rescaling the clusters size $S$ with the average burst size $\langle S
\rangle $. Moreover, we clearly observe that the burst size distribution $P(S/ \langle S \rangle)$ follows a power law with an exponent $\gamma =1.7 $ proving that the burst dynamics occurs on all length scales. We have checked that this critical behavior and in particular the exponent $\gamma =1.7 \pm 0.1$ is really robust: normalizing by the average burst size $\langle S \rangle$, we can rescale all the different distributions corresponding to diverse experimental conditions and a wide range of threshold level values $2<C<20$ (see inset of Fig. \[Fig3\]).

We expect a connection between the spatial scaling of the bursts, and the self-affine scaling of the front line itself on large scales. To investigate this, we have for each cluster $S$ chosen the smallest rectangular bounding box enclosing it. The size of the bounding box gives the length scale $L_y$ of the clusters along the growth direction and the length scale $L_x$ of the clusters along the average front line orientation.

Fig. \[Fig4\] shows the dependence of the average size $\langle L_y \rangle$ on the length scale $\langle L_x \rangle$ in a double logarithmic plot, for a wide range of threshold values $2<C<20$, averaged over all the different experimental conditions (different pixels sizes and average crack front speeds). We clearly see that the avalanche clusters become anisotropic above a characteristic length scale $L_d
\sim 15 \mu m$. This typical size corresponds to the correlation length for the disorder introduced by the sand-blasting technique [@santucci05b]. Below $L_d$ the local toughness is marked by the same individual asperity and as a result the thresholded velocity bursts appear isotropic. A fit to the data points for $L_x > 15 \mu m$ gives a slope $H=0.66$ consistent with previous independent estimates of the roughness exponent $\zeta=0.63 \pm 0.03$ for the fracture front line. This result shows that the system exhibits self-affine scaling with the same roughness exponent $\zeta$ for the local burst as the fracture front line and brings a new confirmation of the roughness exponent found in our experiment, which is different and higher than most present theoretical or numerical predictions [@schmittbuhl95b; @bouchaud93; @roux94; @ramanathan98].

As mentioned in introduction, the scaling behavior of elastic interfaces in random media is involved in various physical systems. Actually, the discrepancy between theoretical and measured roughness exponent has also been reported recently, for contact lines of helium-4 [@Prevost02] and water meniscus [@Moulinet02; @Moulinet04] propagating on rough substrates. It confirmed that the Joanny-De Gennes model [@joanny84] usually proposed to describe the contact lines dynamics, which leads to the same kind of equation of motion for crack fronts [@Gao89], is not sufficient [@Moulinet04]. Interestingly the roughness exponent found respectively equal to $0.56 \pm 0.03$ and $0.52 \pm 0.04$ are close to the fracture front line roughness. Besides, for the helium-4 meniscus, power law avalanche size distributions have been measured with exponents $\gamma$ from $0.99$ to $1.3$, depending on the contact angle, which is different from the exponent $\gamma=1.7$ found in our experiments. However, avalanches are defined by Prevost et al [@Prevost02] based on subtraction between fronts, which is different from the present technique, and this $\gamma$ exponent could be sensitive to such definition.

Recent simulations based on a quasi-static model and interpreted as a stress weighted percolation problem [@schmittbuhl03] give for the first time consistent results with the experimental roughness and dynamic exponent [@maloy01; @santucci05]. The insensitivity of the velocity distribution in our experiments on the average velocity of the front gives support to the quasi-static assumptions used in these simulations. However, the simulated process zone was not observed in our experiments above the micrometer scale. It should be mentionned that dynamical effects have also been introduced in a model [@ramanathan98] with a full elastodynamic description where elastic waves may trigger instabilities and modify the roughness of the crack front, leading to the value $\zeta=0.5$ [@Bouchaud02].

No theory or simulations so far have investigated the local velocity or the burst fluctuations. It will be of great interest to perform these analysis on the numerical models for a direct comparison with our experimental work. This will hopefully clarify the importance of dynamical effects in modeling the fracture front propagation.

We thank A. Hansen, E.G. Flekk[ø]{}y, and J.P. Vilotte for fruitful discussions, and E.L. Hinrichsen at SINTEF-Oslo for his hospitality. This work was supported by the CNRS/NFR PICS program, the NFR Petromax and SUP program, and the french programs ACI “RNCC” and ACI “ALEAS”.

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1963–64 Greek Cup

The Greek Cup 1963–64 was the 22nd edition of The Greek Football Cup, or Greek Cup for short.

The Final was scratched and AEK Athens were awarded the cup after the semi-final between Panathinaikos and Olympiacos was abandoned in the 115th minute with the score at 1-1 and both teams were ejected from the competition due to riots from the supporters of both clubs against their teams for the same reasons that the final of 1961-62 season was unfinished.

1 The match was abandoned in the 116th minute with the score at 1-1 due to riots from the supporters of both clubs against their teams for the same reasons that the 1961-62 final was unfinished; both teams were ejected from the competition.

1.
AEK Athens F.C.
–
AEK F. C. abbreviated as AEK, known in European competitions as AEK Athens F. C. is a Greek association football club based in Nea Filadelfeia suburb of Athens. Established in Athens, in 1924, by Greek refugees from Constantinople, in the wake of the Greco-Turkish War, its name is a direct reference to the origins of the founders. The clubs emblem is the eagle, used by the Palaiologos dynasty and traditionally by the Byzantine Empire, as a remembrance of the Byzantine legacy. AEK is one of the three most successful teams in Greek football, winning 30 national titles and the only to have won all the competitions organised by the Hellenic Football Federation. They are one of the most popular Greek clubs with millions of fans in Greece and Cyprus, and in Greek communities worldwide, mainly in Australia, United Kingdom, and North America. The club has appeared several times in European competitions, in which they are the second most successful Greek football club in terms of achievements and they have also reached once the quarter-finals of the European Cup and twice the quarter-finals of the UEFA Cup Winners Cup. AEK is a member of the European Club Association, traditional rivalries of AEK are considered the matches against Olympiakos and Panathinaikos, the other two major clubs of the capital. PAOK is another of the clubs rivalries, the large Greek population of Constantinople, not unlike those of the other Ottoman urban centres, continued its athletic traditions in the form of numerous athletic clubs. Clubs such as Enosis Tataoulon and Iraklis from the Tatavla district, Megas Alexandros and Hermes of Galata and Olympias of Therapia existed to promote the Hellenic athletic and these were amongst a dozen Greek-backed clubs that dominated the sporting landscape of the city in the years preceding World War I. After the war, with the influx of mainly French and English soldiers to Constantinople, taxim, Pera, and Tatavla became the scene of weekly competitions in not only football, but of athletics, cycling, boxing, and tennis. Of the clubs in the city, though, football was dominated by Enosis Tataoulon, Hermes, one of the most popular clubs, was formed in 1875 by the Greek community of Pera. In 1920, a group of Constantinopolitan refugees met at the athletic shop Lux of Emilios Ionas and Konstantinos Dimopoulos on Veranzerou Street, in the center of Athens, and created AEK. GK, Kitsos, DF, Ieremiades, DF, Asderis, MF, Kechagias, MF, Paraskevas, MF, Dimopoulos, MF, Karagiannides, FW, Baltas, FW, Milas, FW, Iliades, FW, Georgiades. AEK played its first match against Aias Athinon in November 1924, not possessing a football ground, AEK played most of its early matches at various locations around Athens, including the grounds of the Temple of Olympian Zeus and the Leoforos Alexandras Stadium. In 1926, land in Nea Filadelfeia that was set aside for refugee housing, was donated as a training ground for the refugees sports activities. AEK began using the ground for training and by 1930, the property was signed over to the club, venizelos soon approved the plans to build what was to become AEKs home ground for the next 70 years, the Nikos Goumas Stadium. The first home game, in November 1930, was a match against Olympiakos that ended in a 2–2 draw. In 1928, Panathinaikos, Olympiakos, and AEK, began a dispute with the fledgling Hellenic Football Federation, decided to break away from the Athens regional league, during the dispute, POK organised friendly matches against each other and several continental European clubs

2.
Panathinaikos F.C.
–
Panathinaikos F. C. also known simply as Panathinaikos, or with its full name Panathinaikos A. O. are a Greek professional football club based in the City of Athens. Panathinaikos can literally be translated as Panathenaic, which means of all Athens, today a part of Panathinaikos A. O. they are the oldest active football club in Greece, initially founded only to practice this sport. Amongst their major titles are twenty-six Greek Championships, twenty-one Greek Cups, achieving eight times the Double, and five official Greek Super Cups. They are also the club that won a championship undefeated, going without a loss in a top-flight campaign. Panathinaikos is also the most successful Greek club in terms of achievements in the European competitions and it is the only Greek team that has reached the European Cup final in 1971, and also the semi-finals twice, in 1985 and 1996. It is also the only Greek team that has played for the Intercontinental Cup, furthermore, they have reached the quarter-finals of the Champions League on another two occasions, as well as the quarter-finals of the UEFA Cup twice. They have also won the Balkans Cup in 1977, Panathinaikos is a member of the European Club Association. Panathinaikos became professional and independent in 1979 and they have played their home games in the Apostolos Nikolaidis Stadium, considered their traditional home ground, and the Athens Olympic Stadium. The club has million of fans inside Greece and millions of others in the Greek communities all over the world and they hold a long-term rivalry with Olympiacos, the clash between the two teams being referred to as the Derby of the eternal enemies. The name of the new club was Podosferikos Omilos Athinon and it was founded with the aim of spreading and making more known this new sport to the Athenian and Greek public in general. Also, intension of the founders was to create a team for all of Athens and to be connected with the rest of the European football movement, the first president elected was Alexandros Kalafatis, brother of Giorgos. The ground of the team was in Patission Street, oxford University athlete John Cyril Campbell was brought in as coach, the first time that a foreigner was appointed as the coach of a Greek team. Konstantinos Tsiklitiras, the great Greek athlete of the early 20th century, in 1910, after a dispute among a number of board members, Kalafatis with most of the players—also followed by Campbell—decided to pull out of POA and secured a new ground in Amerikis Square. Subsequently, the name of the changed to Panellinios Podosferikos Omilos and its colours to green. By 1914, Campbell had returned to England but the club was already at the top of Greek football with such as Michalis Papazoglou, Michalis Rokkos. In 1918, the team adopted the trifolium as its emblem, in 1921 and 1922, the Athens-Piraeus FCA organized the first two post-WWI championships, in both of which PPO was declared champion. After long discussions with the Municipality of Athens, an agreement was finally reached, the move to a permanent home ground also heralded another—final—name change to Panathinaikos Athlitikos Omilos, Panathenaic Athletic Club, on 15 March 1924, from now on a multi-sport club. However, the decision was taken by 1922

3.
Olympiacos F.C.
–
Olympiacos dominating success can be further evidenced by the fact that all other Greek clubs have won a combined total of 37 League titles. They are also one of three clubs to have never been relegated from the top flight of Greek football. They have also won the Balkans Cup in 1963, becoming the first ever Greek club to win an international, Olympiacos is one of the founding members of the European Club Association in 2008. The clubs home ground is the Karaiskakis Stadium in Piraeus, Olympiacos is the most popular Greek club with around four million fans inside Greece and millions of others in the Greek communities all over the world. Olympiacos was placed ninth on the 2006 list of clubs with the largest number of paying members, in 2014, that figure increased and the team boasts 98,000 registered members. They share a great and long-standing rivalry with Panathinaikos, with whom they contest the derby of the eternal enemies, Olympiacos was founded on 10 March 1925, in the port of Piraeus. Notis Kamperos, a officer of the Hellenic Navy, proposed the name Olympiacos. Michalis Manouskos, a prominent Piraeus industrialist, expanded the name to its complete and current status, Andrianopoulos, a family of well-established Piraeus merchants, played a pivotal role in the founding of Olympiacos. The five brothers, Yiannis, Dinos, Giorgos, Vassilis and Leonidas Andrianopoulos raised the reputation of the club and brought it to its current glory. Yiannis, Dinos, Giorgos and Vassilis were the first to play, while Leonidas, back then, their fan base consisted mainly of the working class, with the teams home ground at Neo Phaliron Velodrome, before moving to its current Karaiskakis Stadium. They became Piraeus Champions in 1925 and 1926, in 1926, the Hellenic Football Federation was founded and organized the Panhellenic Championship in the 1927–1928 season. The Panhellenic Championship was organized in this manner up until 1958–59, during the course of that season, the three of them played friendly games with each other and formed a group called P. O. K. Those results ignited an enthusiastic reception from the Greek press, who called Olympiacos Thrylos for the first time in history, Olympiacos put in a great performance during the competition and won the title very convincingly with 11 wins,2 draws and only one game lost. They managed to score 7 wins in 7 matches at home, beating Panathinaikos, AEK Athens, Aris, Iraklis and PAOK with the same score, the sole exception was the match against Ethnikos, where Olympiacos netted 4 goals and won with 4–1. The rise of the new decade marked a rise in Panhellenic Championships popularity throughout Greece. In October 1931, Giorgos and Yiannis Andrianopoulos, emblematic players and founding members of Olympiacos, especially Giannis Vazos, Christoforos Raggos and Theologos Symeonidis composed a formidable trio of attacking players, scoring numerous goals and became nothing short of legendary. In addition, the managed to win the 1936–37 and 1937–38 Championship titles undefeated. On 28 October 1940, Fascist Italy invaded Greece, and several Olympiacos players joined the Hellenic Army to fight against the Axis invaders, chistoforos Raggos was heavily injured in his left leg in January 1941, and wasnt able to play football again

4.
Apollon Smyrni F.C.
–
Apollon Smyrni F. C. or in its full name Gymnasticos Syllogos Apollon Smyrnis is a Greek football club based in the city of Athens, that plays in the Super League. It was founded in Smyrna in 1891 and is one of the oldest sports clubs in Greece, Apollon has departments in football, basketball, volleyball, water polo and other sports. Apollon Smyrna was founded in 1891 by former members of club Orpheus, Orpheus had been founded one year earlier in 1890. Among the founders of Apollon were prominent residents of Smyrna such as Chrysostomos of Smyrna, roughly in the year of 1893, the athletic department was organised. The first games of Smyrna took place in 1894, organized by the English sports fans of Bornova, in these games the athletes of Apollon achieved a lot of first victories. The person with the most wins was Theologos Anastasoglou, an athlete who later became Olympic champion. The Games were always organized by English sports fans until 1903, the third anniversary of the foundation of Apollon was celebrated joyously. Chairman N. Koulmasis gave the speech of the day, while the famous S. Pittakis spoke of Delphi and recited the anthem to the god Apollo. There was a pedestal on which had been set up an altar to praise the god Apollo. In 1894, with the election of its new presiding board, of the first excursions that were organized, one was to Ephesus and another to Aidini, in which the Russian scholar and historical Frigkol took part. In 1894, the council of the Gymnastic Association of Apollon was composed of chairman Mathaios Provatopoulos, sofianopoulos, G. Oikonomidis, A. Koulampidis and C. During this season the team acquired a privately owned ground, initially, only its members fought on these. Later, however it organized games in other associations could also take part. Apollon acquired its own stadium in 1894, at this point we should examine a little the background of the foundation of the first ground of Apollon. Fourteen years before, in 1880, Ioannis Damvergis with Apostolos Psaltof, Stefanos Papamihalis, makroulidis, all students of the Evangelic Faculty of Smyrni, created an off-hand gym in some open space, known with the name love arena. After they opened the ground, they set up a perimeter using ropes because of a lack of money, then, with hard economising, they bought a horizontal bar and other gymnastic equipment. The youth of Smyrni exercised there paying a symbolic price and this primitive gym constituted the precursor of the gym of Apollo, but was also the fountain for the later great athletes of the association. For this reason, the creator of this gym, Apostolos Psaltof, was called the grandfather of Apollon

5.
Greek Football Cup
–
The Greek Football Cup, commonly known as the Greek Cup or for sponsorship reasons the Football Cup OPAP, is a Greek football competition, run by the Hellenic Football Federation. The holders of the Greek Cup are AEK Athens, who beat Olympiacos 2–1 in the 2016 final held on May 17,2016, the Greek Cup under EPO began in 1931. In its early years, entry was optional, Teams were paired against each other by the football associations, without a draw taking place. Later on, for years, a proper draw took place. In the 90s, the matches were played in groups. The winners of the played against each other up to the final in two-leg matches. Until 1964, if the score was a draw, the two teams played another match, while penalties didnt exist. The next year a new rule was applied, to determine that, if the game was undecided even after extra time and that rule was abolished in 1969, when the penalty shootout was applied. Until 1971, teams all over the country, professional. Each team first played against clubs from its own association and the winners continued in a nationwide competition, since 1971, only teams from the three professional divisions are allowed entry, while amateur clubs take part in the Amateur Cup. Over the years, the competition has played under various formats. In the initial format, one-legged ties were played at the ground of the team as determined by the draw, if the final result between two teams was a draw, the match was replayed at the opponents ground. There was extra time but no penalty shootout, if teams were still level after extra time, the winner was nominated by drawing lots or toss of coin. From 1969, the penalty shootout was established and the matches were concluded without the need for replays, for some years of the decades of 1980 and 1990, the First Round was played in preliminary groups, from which 16 teams qualified. These teams continued in knockout format with two-leg ties until the final match. For two seasons, the Final was also held as a tie, but then this rule was discarded. The current format is in effect from 2005, excluding 2009–10 season, for 2011–12, only to Semi-finals will be double matches. This is because the start of the tournament will delay because of court decisions pending for several teams, First Round, The teams of two groups of Football League 2 participate

6.
Pierikos F.C.
–
Pierikos or Pierikos Syndesmos Filathlon Katerinis is a Greek football club based in Katerini, Greece. The club was founded on 11 April 1961 from the merger between Megas Alexandros Katerinis and Olympos Katerinis, unification of the two clubs has seen as the only way for the city of Katerini to have a team in the 1st Division. In its first season Pierikos took the place of Megas Alexandros in the 2nd Division and it played in the Group of Western and Central Macedonia and finished 1st. Therefore, it was able to play in the 2nd Division play-offs, in the final Pierikos won 2–0 in a match against Olympiakos Kozanis and gained promotion to the 1st Division. In this season Pierikos scored 108 goals and conceded 28. In its first season in the 1st division Pierikos finished in the 9th position scoring 36 goals and his biggest win was a 4–0 against Aris Thessaloniki F. C. Pierikos also played in the Greek Cup final this season. The club suffered a 3–0 defeat by Olympiacos CFP, in the 1963–64 season Pierikos finished in the 7th position. Its biggest wins were, a 5–1 against Doxa Dramas and a 4–0 against Ethnikos Piraeus. The club scored 34, Pierikos also played in the Greek Cup Semi-Final this season where was suffered a 3–1 defeat by AEK Athens FC. This was as Final because the other Semi-Final between Olympiacos CFP and Panathinaikos FC never ended and therefore AEK Athens FC was awarded the Greek Cup by E. P. O, the 1964–65 season is, probably, the best season in the History of Pierikos. Pierikos finished in the 5th position scoring 39 and conceding 39 and its biggest win was a 4–0 against Niki Volou. In the 1965–66 season Pierikos finished in the 8th position and its biggest win was a 5–1 against AO Trikala. The club scored 40 and conceded 40 goals, in the 1966–67 season Pierikos finished in the 14th position. Its biggest win was a 4–1 against Vyzas Megaron, the club scored 36 and conceded 51 goals. In the 1967–68 season Pierikos finished in the 5th position and its biggest win was a 9–1 against Olympiakos Nicosia. This is the biggest victory of the club, in the 1st Division, ever. The club scored 42 and conceded 46 goals, in the 1968–69 season Pierikos finished in the 9th position. Its biggest win was a 5–1 against Apollon Smyrnis, the club scored 31 and conceded 37 goals. In the 1969–70 season Pierikos finished in the 7th position and its biggest win was a 3–0 against Olympiakos Nicosia. The club scored 45 and conceded 44 goals, in the 1970–71 season Pierikos finished in the 14th position. The club didnt manage to win any game by more than one goal

7.
Atromitos F.C.
–
Atromitos Athens Football Club is an association football club based in Peristeri, Athens that plays in the Superleague Greece. It was founded in 1923 and its ground is Peristeri Stadium. In recent years, Atromitos has been established itself as one of the most competitive and strong clubs in Greece. They were runners-up of the Greek Cup in 2011 and 2012 and have had breakthrough runs in the league, finishing 4th in 2011–12, 3rd in 2012–13, 4th in 2013–14 and 4th as well in 2014–15 season. Their best performance in the league has been the third place, in 1924, Atromitos was accepted into the Greek football league. At the time, Atromitos played at Aris Park, which was the ground of Panellinios and Panathinaikos. During their first season in the leagues first division, they ended in third place behind Panathinaikos, in 1928, they defeated Goudi 4–3 in the final game at Rouf Stadium to become champions of Athens. That same year, they part in the first Panhellenic Championship as Athens champions. On 24 May 1928, they were beaten 3–1 by Aris Thessaloniki in an away game, on 10 June, they managed a draw at home against Ethnikos, before losing again to Aris 3–1 seven days later. Overall in the championship, Atromitos finished third. During the following two years, Atromitos stayed in the part of the first division of Athens, and in 1929, they finished third behind Panathinaikos. They repeated the feat in 1930 but they were relegated from the first division of Athens in 1931, in 1932, Ioseph Chourouktsoglou and Nikolaos Epioglou decided to move Atromitos to Peristeri. Earlier, it was located in the area as Panathinaikos. There, they formed a merger with the team of Astir Peristeriou, from which comes the crest of Atromitos. Before occupation of Greece, they played again in Panhellenic championship in the season of 1938–39, Atromitos played in second division until May 1972 when, under the coaching of Savva Papazoulou, they were re-promoted to the first level. It proved a change too hard to handle, and they were demoted the following year, in 1975, a better-prepared Atromitos returned to the first division with a large fanbase, and ended the year in 13th place, securing their spot in the top flight. In 1976 they improved to end the season in 9th place, by 1981, Atromitos had succeeded in attracting renowned players such as Stylianopoulos, Álvarez, Toskas and Athanasopoulos. However, despite expectations, the club played for the last time in the top flight

8.
Vyzas F.C.
–
Vyzas F. C. is a football club based in Megara, Greece. Vyzas Megaron was founded in 1928 by students and named after the ancient Megara hero Byzas, in 1960, the club was promoted to Greeces Beta Ethniki, where it stayed for seven years. Vyzas was later promoted to Greeces top league, Alpha Ethniki, between 1970 and 1975 and between 1979 and 1983, Vyzas played in Beta Ethniki. The team played for four years in Gamma Ethniki from 1983 to 1987, after 12 years in Amateur championships and four years in Delta Ethniki, the team moved to Gamma Ethniki in the summer of 2002 which they would remain until 2011. During that season, the team finished 14th along with Larissa, later in the 2009–10 season, Vyzas played with Trikala, the 2nd team of the North group to the neutral stadium of Panionios at Nea Smyrni. Vyzas was losing 1–0 till 90th minute where the Megara team had a chance, which was stopped by a handball, as Megarians said. Trikala won the game by 2–0 and the season took part at Beta Ethniki. In 2011, the team finished 2nd in the South Group, as a historical team Vyzas has its big rivalries with other teams such as Korinthos, Panachaiki, the Patras-based team, and Aentas Salaminas which is based at an island nearby Megara called Salamina. At the 2009–2010 season Vyzas and Panachaiki were the two first teams of the South Group and was fighting for the first and the promotion to Beta ethniki and they played an extremely important match very late in the season, in the crowded Megara stadium. About 3000 Megarians made a fantastic atmosphere supporting their team but finally game ended 0–0, Vyzas didnt make it to gain promotion that season. The Stadium of Megara, the home of Megara team is located in the centre of the city, players may hold more than one non-FIFA nationality. Owners, Theodoros Michalaros Chairmen, Theodoros Michalaros Managers, Vasilis Stasinopoulos For details on former players, see Category, Vyzas F. C. players

9.
Proodeftiki F.C.
–
Proodeftiki F. C. also known simply as Proodeftiki, Proodeftiki Nikaia, Proodeftiki Piraeus or with its full name as A. O. Proodeftiki Neolea, is a football club, part of the major multi-sport club A. O. Proodeftiki Neolea, based in Nikaia, Piraeus - Attica, the club has a longstanding presence in Super League. Have participated so far in the Super League 15 times, founded in 1927, in Palea Kokkinia, which is the older name of Nikaia. Club founded after idea of D. Korrai, N. Vertzopoulos and I. Metaxas, Palea Kokkinia, the older name of Nikaia, inhabited mainly by Greeks and Armenians refugees who inhabited the coast of Asia Minor. The motto of the emblem is the mythical long-lived bird. The colours of the club are crimson and white, the 2006-2007 was one of the worst seasons in the clubs history and would be relegated to the Football League 2. However, due to bankruptcy, relegated to the Greek Fourth Division for first time in clubs history, the stadium was complete in 1937 and its latest refresh done in 2000. It currently has a capacity of 5,500. The football matches between Proodeftiki F. C. and Ionikos F. C. are called «The Derby of Kokkinia» or «The Derby of Nikaia», note, Flags indicate national team as defined under FIFA eligibility rules. Players may hold more than one non-FIFA nationality, oliver Makor Oleh Protasov Stepan Atayan John Yaw Rush Proodeftiki Fansite


Q:

What does one use a saw for?

In the 1939 illustrated book Madeline is a kitchen scene. On the counter are plates (or bowls), a colander, a ladle, a saucepan, a large knife — and a hand saw. Is a hand saw a kitchen implement? If so, what's it for?

A:

Any Kitchen I worked in –that does a bit of butchering– has one (any butcher also). It's for sawing bones.
At the time you would not throw anything out of an animal, and a lot of people would make their stock or put a piece of bone in a stew or soup for taste. But, as far as I know, they usually look like a hacksaw not like a the one you're showing.
Maybe the illustrator did not know what a kitchen saw looked like. He's been asked to draw one and did a hand saw by mistake.
This type of saw could be also used in a pastry shop. At some stage (and still, apparently according to @divi) wedding and other momumental cakes, but also smaller ones, were consolidated with pieces of wood or other non comestible material.

A:

In addition to cutting up bones, I've also found the hand saw handy when layering cakes. I've used it for cutting woden and plastic dowels to specific length for cake layering.


[Functional heterogeneity of polymorphonuclear leukocytes population in peripheral blood of patients with acute dysentery].
To study chemiluminescence (CL) of polymorphonuclear neutrophils (PMNL) in peripheral blood of patients with acute mild and moderate dysentery caused by Shig. Flexneri in response to Re- and S-chemotype lipopolysaccharide (LPS) Sh. Flexneri and agonists fMLP, PMA and OZ. PMNL population proved functionally heterogeneic, correlating with acute dysentery severity. Subgroups of PMNL varied by CL amplitude, reserve ability to additional stimulation. LPS rather modulated CL of PMNL than stimulated it. CL intensity depended on LPS structure and concentration. Mild acute dysentery was characterized by pool of primed PMNL which had higher functional reserves. CL analysis can be used for raising accuracy of dysentery prognosis and severity, assessment of implications of functional state of neutrophil granulocytes for support of antiendotoxin immunity in acute dysentery.


Q:

Android: How to set time gap in methods, when sleep or wait is not working

I built a TicTacToe game for android. And i want that there should be some time gap or time difference between User's turn and Computer's turn. Mean i want like a sleep() or any other method should be invoked between User's turn and Computer's turn. But when i call Sleep() before cpuPlay() method or after userPlay() it makes sleep to both user and Android and both wake up together. I really tried very hard to find why it is making sleep() to both method together but i am unable to find. Please help me with this.
Thanks in advance.
Here's my code
public class Game extends Activity
  {
private final int GAME_VICTORY = 0x1;
private final int GAME_DEFEAT = 0x2;
private final int GAME_TIE = 0x3;
private final int GAME_CONTINUES = 0x4;
private final float UNIQUE_MAX_WEIGHT=0.85f;
static final int ACTIVITY_SELECTION = 1;
private int x_Player_win_counter;
private int o_Player_win_counter;
public static TextView textlevel=null;
public static TextView textlevel1=null;
public double startTime;
double userDuration;
double cpuDuration;
private float[] w;
private int[] c;
private int[][] PosTable;
private Button[] buttons;
private int lineH = -1;
private int lineV = -1;
private int lineD = -1;

public void onCreate(Bundle savedInstanceState) {
    super.onCreate(savedInstanceState);
    setContentView(R.layout.game);

    buttons = new Button[9];

    buttons[0] = (Button) findViewById(R.id.Button01);
    buttons[0].setOnClickListener(new View.OnClickListener() {
        public void onClick(View v) {
            btnClicked(0);
        }
    });
    buttons[1] = (Button) findViewById(R.id.Button02);
    buttons[1].setOnClickListener(new View.OnClickListener() {
        public void onClick(View v) {
            btnClicked(1);
        }
    });
    buttons[2] = (Button) findViewById(R.id.Button03);
    buttons[2].setOnClickListener(new View.OnClickListener() {
        public void onClick(View v) {
            btnClicked(2);
        }
    });
    buttons[3] = (Button) findViewById(R.id.Button04);
    buttons[3].setOnClickListener(new View.OnClickListener() {
        public void onClick(View v) {
            btnClicked(3);
        }
    });
    buttons[4] = (Button) findViewById(R.id.Button05);
    buttons[4].setOnClickListener(new View.OnClickListener() {
        public void onClick(View v) {
            btnClicked(4);
        }
    });
    buttons[5] = (Button) findViewById(R.id.Button06);
    buttons[5].setOnClickListener(new View.OnClickListener() {
        public void onClick(View v) {
            btnClicked(5);
        }

    });
    buttons[6] = (Button) findViewById(R.id.Button07);
    buttons[6].setOnClickListener(new View.OnClickListener() {
        public void onClick(View v) {
            btnClicked(6);
        }
    });
    buttons[7] = (Button) findViewById(R.id.Button08);
    buttons[7].setOnClickListener(new View.OnClickListener() {
        public void onClick(View v) {
            btnClicked(7);
        }
    });
    buttons[8] = (Button) findViewById(R.id.Button09);
    buttons[8].setOnClickListener(new View.OnClickListener() {
        public void onClick(View v) {
            btnClicked(8);
        }
    });

  startActivityForResult(new Intent(Game.this, Game.class), ACTIVITY_SELECTION);

    DisplayMetrics dm = getApplicationContext().getResources().getDisplayMetrics();
    float h = (float) (dm.heightPixels - (100.0)*dm.density);
    float w = dm.widthPixels;
    for(int i=0;i<9;i++) {
        buttons[i].setHeight((int) (h/3));
        buttons[i].setWidth((int) (w/3));
    }
}
protected void onActivityResult(int requestCode, int resultCode, Intent data) {
    beginPlay();
    if (requestCode == ACTIVITY_SELECTION) {
        if (resultCode == RESULT_OK) {
            Bundle extras = data.getExtras();
            if (extras.getString("result").equals("CPU")) cpuPlay();
        }
    }
}
public void userGame() {
    new AlertDialog.Builder(this)
    .setTitle("User Won!!!")
    .setMessage("want to start another game")
    .setIcon(android.R.drawable.ic_dialog_alert)
    .setPositiveButton("Yes", new DialogInterface.OnClickListener() {
        public void onClick(DialogInterface dialog, int which)
        {

            buttonsEnable(true);
            beginPlay();
        }
    })
    .setNegativeButton("No", new DialogInterface.OnClickListener() {
        public void onClick(DialogInterface dialog, int which)
        {
            finish();
        }
    })
    .show();
}

public void cpuGame() {
    new AlertDialog.Builder(this)
    .setTitle("Android Won!!!")
    .setMessage("want to start another game")
    .setIcon(android.R.drawable.ic_dialog_alert)
    .setPositiveButton("Yes", new DialogInterface.OnClickListener() {
        public void onClick(DialogInterface dialog, int which)
        {

            buttonsEnable(true);
            beginPlay();
        }
    })
    .setNegativeButton("No", new DialogInterface.OnClickListener() {
        public void onClick(DialogInterface dialog, int which)
        {
            finish();
        }
    })
    .show();
}

public void tieGame() {
    new AlertDialog.Builder(this)
    .setTitle("TIE!!!")
    .setMessage("want to start another game")
    .setIcon(android.R.drawable.ic_dialog_alert)
    .setPositiveButton("Yes", new DialogInterface.OnClickListener() {
        public void onClick(DialogInterface dialog, int which)
        {

            buttonsEnable(true);
            beginPlay();
        }
    })
    .setNegativeButton("No", new DialogInterface.OnClickListener() {
        public void onClick(DialogInterface dialog, int which)
        {
            finish();
        }
    })
    .show();
}

private void beginPlay() {
    //initializations start
    w=new float[9];
    c=new int[9];
    InitTable();
    w[0]=0.7f;
    w[1]=0.4f;
    w[2]=0.7f;
    w[3]=0.4f;
    w[4]=0.7f;
    w[5]=0.4f;
    w[6]=0.7f;
    w[7]=0.4f;
    w[8]=0.7f;
    //c[i] : 0 for empty, 1 for cpu, 2 for user
    for(int i=0;i<9;i++)
        c[i]=0;
    //initializations done

    //now we play!

        startTime = System.currentTimeMillis();
        textlevel=(TextView)findViewById(R.id.userInfo);
        textlevel.setText(String.valueOf(x_Player_win_counter));

        textlevel1=(TextView)findViewById(R.id.cpuInfo);
        textlevel1.setText(String.valueOf(o_Player_win_counter));

    for(int i=0;i<9;i++)
        {
        updateBtn(i);
        buttons[i].setTextColor(Color.BLACK);
        }
    String PlayerName="User";
    updateGameInfo(PlayerName + " turn.");
}

private void cpuPlay()
{
    int cpos=getDecision();
    if (cpos == -1)
    {
        Toast toast = Toast.makeText(getApplicationContext(), "GAME OVER", Toast.LENGTH_SHORT);
        toast.show();
        return;
    }
    else
    {
    c[cpos]=1;
    updateBtn(cpos);
    String name= "user";
    updateGameInfo(name + " turn");
    int gstatus = CheckGameStatus();
    if (gstatus == GAME_VICTORY)
    {
        userDuration = (System.currentTimeMillis() - startTime)/1000;
        Toast toast = Toast.makeText(getApplicationContext(), "Congrts You Won in " + userDuration + " seconds", Toast.LENGTH_SHORT);
        toast.show();
        ++x_Player_win_counter;
        userGame();
    }
    else if (gstatus == GAME_DEFEAT) {
        cpuDuration = (System.currentTimeMillis() - startTime)/1000;
        Toast toast = Toast.makeText(getApplicationContext(), "Sorry, Android Won in "  + cpuDuration + " seconds", Toast.LENGTH_SHORT);
        toast.show();
        ++o_Player_win_counter;
        cpuGame();
    }
    else if (gstatus == GAME_TIE) {
        Toast toast = Toast.makeText(getApplicationContext(), "Its a TIE", Toast.LENGTH_SHORT);
        toast.show();
        tieGame();
    }
    else if (gstatus == GAME_CONTINUES) {
        //user plays
    }
    }
}
private void updateBtn(int i) {
    if(c[i]==0)
    {
        buttons[i].setText(" ");
    }
    else if(c[i]==1)
    {

        buttons[i].setText("O");
        buttons[i].setTextColor(Color.RED);
    }
    else
    {
        buttons[i].setText("X");
    }
}

private int CheckGameStatus() {
    int s = 0;
    //check horizontal
    if(c[0]==2&&c[1]==2&&c[2]==2)
    {
        s = GAME_VICTORY;
    }
    if(c[3]==2&&c[4]==2&&c[5]==2)
    {
        s = GAME_VICTORY;
    }
    if(c[6]==2&&c[7]==2&&c[8]==2)
    {
        s = GAME_VICTORY;
    }
    if(c[0]==1&&c[1]==1&&c[2]==1)
    {
        s = GAME_DEFEAT;
    }
    if(c[3]==1&&c[4]==1&&c[5]==1)
    {
        s = GAME_DEFEAT;
    }
    if(c[6]==1&&c[7]==1&&c[8]==1)
    {
        s = GAME_DEFEAT;
    }
    //check vertical
    if(c[0]==2&&c[3]==2&&c[6]==2)
    {
        s = GAME_VICTORY;
    }
    if(c[1]==2&&c[4]==2&&c[7]==2)
    {
        s = GAME_VICTORY;
    }
    if(c[2]==2&&c[5]==2&&c[8]==2)
    {
        s = GAME_VICTORY;
    }
    if(c[0]==1&&c[3]==1&&c[6]==1)
    {
        s = GAME_DEFEAT;
    }
    if(c[1]==1&&c[4]==1&&c[7]==1)
    {
        s = GAME_DEFEAT;
    }
    if(c[2]==1&&c[5]==1&&c[8]==1)
    {
        s = GAME_DEFEAT;
    }
    //check diagonal
    if(c[0]==2&&c[4]==2&&c[8]==2) {s = GAME_VICTORY;}
    if(c[2]==2&&c[4]==2&&c[6]==2) {s = GAME_VICTORY;}
    if(c[0]==1&&c[4]==1&&c[8]==1) {s = GAME_DEFEAT;}
    if(c[2]==1&&c[4]==1&&c[6]==1) {s = GAME_DEFEAT;}

    if (s != 0) {
        buttonsEnable(false);
        return s;
    }

    boolean box_empty = false;
    for(int i=0;i<9;i++) {
        if (c[i] == 0) box_empty = true;
    }
    if (box_empty) {    //if any box is empty -> game continues
        return GAME_CONTINUES;
    }
    else {  //else there is tie
        buttonsEnable(false);
        return GAME_TIE;
    }
}

private void buttonsEnable(boolean b) {
    for(int i=0;i<9;i++)
        buttons[i].setEnabled(b);
}

private void btnClicked(int i)
{
    if(c[i]!=0) {
        Toast toast = Toast.makeText(getApplicationContext(), "Position occupied", Toast.LENGTH_SHORT);
        toast.show();
    }
    else
    {
        //all OK
        c[i] = 2;
        updateBtn(i);
        String name= "Android";
    //  updateGameInfo(name + " turn");

        int gstatus = CheckGameStatus();
        if (gstatus == GAME_VICTORY) {
            userDuration = (System.currentTimeMillis() - startTime)/1000;
            Toast toast = Toast.makeText(getApplicationContext(), "Congrats You Won in "  + userDuration + " seconds", Toast.LENGTH_SHORT);
            toast.show();
            ++x_Player_win_counter;
            userGame();
        }
        else if (gstatus == GAME_DEFEAT) {
            cpuDuration = (System.currentTimeMillis() - startTime)/1000;
            Toast toast = Toast.makeText(getApplicationContext(), "Sorry, Android Won in "  + cpuDuration + " seconds", Toast.LENGTH_SHORT);
            toast.show();
            ++o_Player_win_counter;
            cpuGame();
        }
        else if (gstatus == GAME_TIE) {
            Toast toast = Toast.makeText(getApplicationContext(), "Its a TIE", Toast.LENGTH_SHORT);
            toast.show();
            tieGame();
        }
        else if (gstatus == GAME_CONTINUES) {
            try {
                Thread.sleep(1000);
            } catch (InterruptedException e) {
                // TODO Auto-generated catch block
                e.printStackTrace();
            }
            cpuPlay();
        }
    }
}

private int getDecision()
{
    for(int i=0;i<9;i++)
        for(int j=0;j<9;j++) {
            if(c[i]==1&&c[j]==1)    //place 'o' to win
                if(PosTable[i][j]!=-1)  //if we have 3 in a row
                    if(c[PosTable[i][j]]==0)    //if position is free
                        return PosTable[i][j];
            if(c[i]==2&&c[j]==2)    //place 'o' to prevent user's victory
                if(PosTable[i][j]!=-1)  //if we have 3 in a row
                    if(c[PosTable[i][j]]==0)    //if position is free
                        return PosTable[i][j];
        }

    if(c[0]==1&&c[8]==0) return 8;
    if(c[2]==1&&c[6]==0) return 6;
    if(c[8]==1&&c[0]==0) return 0;
    if(c[6]==1&&c[2]==0) return 2;
    Random r=new Random();
    boolean exist07=false;
    boolean[] free=new boolean[9]; //will hold the free positions
    for(int i=0;i<9;i++)
        free[i]=false;
    for(int i=0;i<9;i++)
        if(c[i]==0) {   //free ??
            free[i]=true;   //add position to free
            if(w[i]==UNIQUE_MAX_WEIGHT) return i;
        }
    //more than 1 positions with same weight
    for(int i=0;i<9;i++)
        if(free[i]) //if position is free
            if(w[i]==0.7f) exist07=true;
    if(exist07)
        for(int i=0;i<9;i++)
            if(free[i]) //if position is free
                if(w[i]==0.4f) free[i]=false;

    int j=0;
    int rn=0;
    int[] tmp;
    for(int i=0;i<9;i++)
        if(free[i]) j++;
    if(j!=0) {
        tmp=new int[j];
        rn=r.nextInt(j);
        j=0;
        for(int i=0;i<9;i++)
            if(free[i]) tmp[j++]=i;
        return tmp[rn];
    }
    else {
        return -1; //else GAME OVER
    }
}
private void InitTable() {

    PosTable=new int[9][9];
    for(int i=0;i<9;i++)
        for(int j=0;j<9;j++)
            PosTable[i][j]=-1;
    PosTable[0][1]=2;
    PosTable[0][2]=1;
    PosTable[0][3]=6;
    PosTable[0][4]=8;
    PosTable[0][6]=3;
    PosTable[0][8]=4;
    PosTable[1][2]=0;
    PosTable[1][4]=7;
    PosTable[1][7]=4;
    PosTable[2][4]=6;
    PosTable[2][5]=8;
    PosTable[2][6]=4;
    PosTable[2][8]=5;
    PosTable[3][4]=5;
    PosTable[3][5]=4;
    PosTable[3][6]=0;
    PosTable[4][5]=3;
    PosTable[4][6]=2;
    PosTable[4][7]=1;
    PosTable[4][8]=0;
    PosTable[5][8]=2;
    PosTable[6][7]=8;
    PosTable[6][8]=7;
    PosTable[7][8]=6;
}

private void updateGameInfo(String info)
{
    Toast.makeText(this, info, Toast.LENGTH_SHORT).show();
    TextView infoView =(TextView) findViewById(R.id.gameInfo);
    infoView.setText(info);
}

}

A:

If you want to delay some code, you should post it in a handler with a delay time.
This way the handler will wait the given time and then execute the given runnable.
    new Handler().postDelayed(new Runnable() {

        @Override
        public void run() {
            cpuPlay();
        }
    }, TIME_TO_WAIT_IN_MS);


The success of any wearable technology lies in its immediacy and usefulness, and specialised apps for Google Glass are trying hard to bring information to our eye level.

The Spanish online travel portal Destinia.com is trialling an app that will work on GPS and alert the wearer of any hotel rooms nearby.

For the business traveller – and Google Glass wearer – it means they can step off the plane without a hotel booking and can instantly find, book and filter places to stay by price or category.

Users of the gadget must select the app called Hotel Near Me by tapping on the side of the Google Glass and say “go Glass”. Google Glass, which picks up sound from the vibrations in the ear bone, activates the app, which then searches the available options nearby. The user can then tap on the side of the Glass or even nod their head to activate, select and browse the results.

The Google Glass app will be free but Destinia will earn money from hotel bookings. But surely it will also raise its fees that it charges the hotels it is helping to promote? Not immediately, says Ian Webber, the development director at Madrid-based Destinia.com.

Its success, in fact the success of Google Glass itself, remains to seen. Google Glass will launch in the United States next year and only a few thousand of the prototypes are available to app developers such as the Destinia team.

As someone who normally wears glasses, I found the tiny screen distracting and difficult to read. No matter how close it was to my eye, it felt like an ant was crawling across the Google Glass.

Moreover, the gadget itself is still under trial and needs development before it can seamlessly merge with our daily life in the same way a smartphone does. The battery life is short and can be used up in half an hour. Plus the Glass is tuned to the head of the wearer, so if someone else dons it, the screen does not go live immediately. It takes at least a few minutes of adjusting.

However, that has not deterred app developers.

The Glass has already encouraged several new applications – from Glassnost, which shares and rates Google Glass photos and videos, to Glass Eats, which searches for restaurants nearby.

Q&A: Travel takes a new direction

Ian Webber, the development director at Madrid-based Destinia.com, talks about the future of travel apps.

Is the Destinia.com app for Google Glass going to disrupt the travel industry?

Not right now since it is not going to be launched right now. But it can be important in the future. It is going to disrupt the communication industry in general. There are some great ideas out there. We are working on an app on augmented reality. When you visit the Colosseum in Rome, you can, for instance, see how it used to be with this app. We are working on another app that would help you make an itinerary as you move around and share photos and videos as you go.

So, as this app suggests, is the travel industry adapting to new technology?

It is coming up with new ideas. When we started a hotel directory in 1995 [which eventually gave rise to Destinia.com], we thought why not have online travel reservations? At that time, you phoned in, and the call went to the booking people. The process is much more sophisticated now.

How many hotels does Destinia.com feature?

Destinia.com, through the Amadeus travel technology provider, offers access to 250,000 hotels around the world and 450 flights in 25 languages. It has 100 employees.

Are you developing anything for the mobile?

We should have an app out in a month. It took us a week to go from the idea to the actual app.

Top five apps for Google Glass

1 Strava, a fitness app

2 Word Lens, translates signs and maps and more real time

3 Kitchme, teaches recipes

4 Preview for Glass, plays movie previews

5 Glassentation, puts flashcards into the glass

– Source: heavy.com

ssahoo@thenational.ae

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It seems increasingly likely that we will one day build machines that possess superhuman intelligence. We need only continue to produce better computers—which we will, unless we destroy ourselves or meet our end some other way. We already know that it is possible for mere matter to acquire "general intelligence"—the ability to learn new concepts and employ them in unfamiliar contexts—because the 1,200 cc of salty porridge inside our heads has managed it. There is no reason to believe that a suitably advanced digital computer couldn't do the same.

It is often said that the near-term goal is to build a machine that possesses "human level" intelligence. But unless we specifically emulate a human brain—with all its limitations—this is a false goal. The computer on which I am writing these words already possesses superhuman powers of memory and calculation. It also has potential access to most of the world's information. Unless we take extraordinary steps to hobble it, any future artificial general intelligence (AGI) will exceed human performance on every task for which it is considered a source of "intelligence" in the first place. Whether such a machine would necessarily be conscious is an open question. But conscious or not, an AGI might very well develop goals incompatible with our own. Just how sudden and lethal this parting of the ways might be is now the subject of much colorful speculation.

One way of glimpsing the coming risk is to imagine what might happen if we accomplished our aims and built a superhuman AGI that behaved exactly as intended. Such a machine would quickly free us from drudgery and even from the inconvenience of doing most intellectual work. What would follow under our current political order? There is no law of economics that guarantees that human beings will find jobs in the presence of every possible technological advance. Once we built the perfect labor-saving device, the cost of manufacturing new devices would approach the cost of raw materials. Absent a willingness to immediately put this new capital at the service of all humanity, a few of us would enjoy unimaginable wealth, and the rest would be free to starve. Even in the presence of a truly benign AGI, we could find ourselves slipping back to a state of nature, policed by drones.

And what would the Russians or the Chinese do if they learned that some company in Silicon Valley was about to develop a superintelligent AGI? This machine would, by definition, be capable of waging war—terrestrial and cyber—with unprecedented power. How would our adversaries behave on the brink of such a winner-take-all scenario? Mere rumors of an AGI might cause our species to go berserk.

It is sobering to admit that chaos seems a probable outcome even in the best-case scenario, in which the AGI remained perfectly obedient. But of course we cannot assume the best-case scenario. In fact, "the control problem"—the solution to which would guarantee obedience in any advanced AGI—appears quite difficult to solve.

Imagine, for instance, that we build a computer that is no more intelligent than the average team of researchers at Stanford or MIT—but, because it functions on a digital timescale, it runs a million times faster than the minds that built it. Set it humming for a week, and it would perform 20,000 years of human-level intellectual work. What are the chances that such an entity would remain content to take direction from us? And how could we confidently predict the thoughts and actions of an autonomous agent that sees more deeply into the past, present, and future than we do?

The fact that we seem to be hastening toward some sort of digital apocalypse poses several intellectual and ethical challenges. For instance, in order to have any hope that a superintelligent AGI would have values commensurate with our own, we would have to instill those values in it (or otherwise get it to emulate us). But whose values should count? Should everyone get a vote in creating the utility function of our new colossus? If nothing else, the invention of an AGI would force us to resolve some very old (and boring) arguments in moral philosophy.

However, a true AGI would probably acquire new values, or at least develop novel—and perhaps dangerous—near-term goals. What steps might a superintelligence take to ensure its continued survival or access to computational resources? Whether the behavior of such a machine would remain compatible with human flourishing might be the most important question our species ever asks.

The problem, however, is that only a few of us seem to be in a position to think this question through. Indeed, the moment of truth might arrive amid circumstances that are disconcertingly informal and inauspicious: Picture ten young men in a room—several of them with undiagnosed Asperger's—drinking Red Bull and wondering whether to flip a switch. Should any single company or research group be able to decide the fate of humanity? The question nearly answers itself.

And yet it is beginning to seem likely that some small number of smart people will one day roll these dice. And the temptation will be understandable. We confront problems—Alzheimer's disease, climate change, economic instability—for which superhuman intelligence could offer a solution. In fact, the only thing nearly as scary as building an AGI is the prospect of not building one. Nevertheless, those who are closest to doing this work have the greatest responsibility to anticipate its dangers. Yes, other fields pose extraordinary risks—but the difference between AGI and something like synthetic biology is that, in the latter, the most dangerous innovations (such as germline mutation) are not the most tempting, commercially or ethically. With AGI the most powerful methods (such as recursive self-improvement) are precisely those that entail the most risk.

We seem to be in the process of building a God. Now would be a good time to wonder whether it will (or even can) be a good one.


function prev_rng = seed_rand(seed)
% seed_rand - Set random number generator to a fixed seed.
%   prev_rng = seed_rand(seed)
%
%   Strategic use ensures that results are reproducible.
%
%   To restore the previous rng after calling this do:
%   rng(prev_rng);

% AUTORIGHTS
% ---------------------------------------------------------
% Copyright (c) 2014, Ross Girshick
%
% This file is part of the R-CNN code and is available
% under the terms of the Simplified BSD License provided in
% LICENSE. Please retain this notice and LICENSE if you use
% this file (or any portion of it) in your project.
% ---------------------------------------------------------

if nargin < 1
    % This value works best for me.
    seed = 3;
    % Just kidding, of course ;-).
end

prev_rng = rng;
rng(seed, 'twister')


(CNN) The Florida man accused of sending mail bombs to CNN offices and prominent Democrats pleaded guilty on Thursday in Manhattan federal court to 65 felony counts, including using weapons of mass destruction in an attempted domestic terrorist attack.

Cesar Sayoc, 57, admitted in court to having mailed 16 explosive devices to a variety of officials -- primarily Democrats, including former Presidents Barack Obama and Bill Clinton and Sens. Cory Booker and Kamala Harris; and major Democratic donors, including George Soros and Tom Steyer -- and to CNN's offices in October 2018.

None of the devices detonated and no one was injured. After a four-day nationwide hunt , FBI agents found and arrested Sayoc in Plantation, Florida.

A courtroom sketch shows Cesar Sayoc during a hearing in a New York federal court last November.

In addition to 16 counts of the use of weapons of mass destruction, Sayoc pleaded guilty to the interstate transport of explosives, the illegal mailing of explosives with the intent to kill or injure and the carrying of explosives during the commission of a felony, among other crimes.

He faces a maximum sentence of life imprisonment and is set to be sentenced on September 12.

Read More


List of United States Supreme Court cases, volume 281

This is a list of all the United States Supreme Court cases from volume 281 of the United States Reports:

 Kansas City Southern R. Co. v. Guardian Trust Co., 281 U.S. 1 (1930)
 Lucas v. North Tex. Lumber Co., 281 U.S. 11 (1930)
 Chicago & North Western R. Co. v. Lindell, 281 U.S. 14 (1930)
 Moore v. Mitchell, 281 U.S. 18 (1930)
 District of Columbia v. Thompson, 281 U.S. 25 (1931)
 United States Fidelity & Guaranty Co. v. Guenther, 281 U.S. 34 (1930)
 Lindgren v. United States, 281 U.S. 38 (1930)
 District of Columbia v. Fred, 281 U.S. 49 (1930)
 Collie v. Fergusson, 281 U.S. 52 (1930)
 Illinois Central R. Co. v. Crail, 281 U.S. 57 (1930)
 Carley & Hamilton, Inc. v. Snook, 281 U.S. 66 (1930)
 Ohio ex rel. Bryant v. Akron Metropolitan Park Dist., 281 U.S. 74 (1930)
 Railroad Comm'n of Wis. v. Maxcy, 281 U.S. 82 (1930) (per curiam)
 Early v. Federal Reserve Bank of Richmond, 281 U.S. 84 (1930)
 Gunning v. Cooley, 281 U.S. 90 (1930)
 Staten Island Rapid Transit R. Co. v. Phoenix Indemnity Co., 281 U.S. 98 (1930)
 Oklahoma v. Texas, 281 U.S. 109 (1930) (per curiam)
 Lucas v. Earl, 281 U.S. 111 (1930)
 Lucas v. Ox Fibre Brush Co., 281 U.S. 115 (1930)
 Henrietta Mills v. Rutherford County, 281 U.S. 121 (1930)
 Nogueira v. New York, N. H. & H. R. Co., 281 U.S. 128 (1930)
 United States v. Unzeuta, 281 U.S. 138 (1930)
 Ohio Oil Co. v. Conway, 281 U.S. 146 (1930)
 Kentucky v. Indiana, 281 U.S. 163 (1930)
 Wisconsin v. Illinois, 281 U.S. 179 (1930)
 United States v. Adams, 281 U.S. 202 (1930)
 Wilbur v. United States ex rel. Kadrie, 281 U.S. 206 (1930)
 John Baizley Iron Works v. Span, 281 U.S. 222 (1930)
 Employers' Liability Assurance Corp. v. Cook, 281 U.S. 233 (1930)
 May v. Heiner, 281 U.S. 238 (1930)
 Lucas v. Pilliod Lumber Co., 281 U.S. 245 (1930)
 Alexander Sprunt & Son, Inc. v. United States, 281 U.S. 249 (1930)
 Miller v. McLaughlin, 281 U.S. 261 (1930)
 Lucas v. Kansas City Structural Steel Co., 281 U.S. 264 (1930)
 Meadows v. United States, 281 U.S. 271 (1930)
 Patton v. United States, 281 U.S. 276 (1930)
 Missouri ex rel. Missouri Ins. Co. v. Gehner, 281 U.S. 313 (1930)
 National Fire Ins. Co. of Hartford v. Thompson, 281 U.S. 331 (1930)
 United States v. Worley, 281 U.S. 339 (1930)
 Jackson v. United States, 281 U.S. 344 (1930)
 New York Central R. Co. v. Marcone, 281 U.S. 345 (1930)
 Atchison, T. & S. F. R. Co. v. Toops, 281 U.S. 351 (1930)
 Niles Bement Pond Co. v. United States, 281 U.S. 357 (1930)
 Dohany v. Rogers, 281 U.S. 362 (1930)
 Cochran v. Louisiana Bd. of Ed., 281 U.S. 370 (1930)
 Corliss v. Bowers, 281 U.S. 376 (1930)
 Escher v. Woods, 281 U.S. 379 (1930)
 Chesapeake & Potomac Telephone Co. v. United States, 281 U.S. 385 (1930)
 Danovitz v. United States, 281 U.S. 389 (1930)
 Home Ins. Co. v. Dick, 281 U.S. 397 (1930)
 Board of Railroad Comm'rs of N. D. v. Great Northern R. Co., 281 U.S. 412 (1930)
 Corporation Comm'n of Okla. v. Lowe, 281 U.S. 431 (1930)
 Cincinnati v. Vester, 281 U.S. 439 (1930)
 Todok v. Union State Bank of Harvard, 281 U.S. 449 (1930)
 Eliason v. Wilborn, 281 U.S. 457 (1930)
 Barker Painting Co. v. Painters, 281 U.S. 462 (1930)
 Federal Radio Comm'n v. General Elec. Co., 281 U.S. 464 (1930)
 Grubb v. Public Util. Comm'n of Ohio, 281 U.S. 470 (1940)
 Pittsburgh & West Virginia R. Co. v. United States, 281 U.S. 479 (1930)
 United States v. Updike, 281 U.S. 489 (1930)
 Tyler v. United States, 281 U.S. 497 (1930)
 Georgia Power Co. v. Decatur, 281 U.S. 505 (1930)
 Western Cartridge Co. v. Emmerson, 281 U.S. 511 (1930)
 Charter Shipping Co. v. Bowring, Jones & Tidy, Ltd., 281 U.S. 515 (1930)
 United States Shipping Bd. Merchant Fleet Corporation v. Harwood, 281 U.S. 519 (1930)
 Richbourg Motor Co. v. United States, 281 U.S. 528 (1930)
 Broad River Power Co. v. South Carolina ex rel. Daniel, 281 U.S. 537 (1930)
 Texas & New Orleans R. Co. v. Railway Clerks, 281 U.S. 548 (1930)
 Wheeler Lumber Bridge & Supply Co. of Des Moines v. United States, 281 U.S. 572 (1930)
 Universal Battery Co. v. United States, 281 U.S. 580 (1930)
 Baldwin v. Missouri, 281 U.S. 586 (1930)
 Campbell Fed. Prohibition Administrator v. Galeno Chemical Co., 281 U.S. 599 (1930)
 Campbell v. W. H. Long & Co., 281 U.S. 610 (1930)
 United States v. Norris, 281 U.S. 619 (1930)
 United States v. Farrar, 281 U.S. 624 (1930)
 Jamison v. Encarnacion, 281 U.S. 635 (1930)
 Alpha S. S. Corp. v. Cain, 281 U.S. 642 (1930)
 Toombs v. Citizens Bank of Waynesboro, 281 U.S. 643 (1930)
 Surplus Trading Co. v. Cook, 281 U.S. 647 (1930)
 Ann Arbor R. Co. v. United States, 281 U.S. 658 (1930)
 Panama Mail S. S. Co. v. Vargas, 281 U.S. 670 (1930)
 Brinkerhoff-Faris Trust & Sav. Co. v. Hill, 281 U.S. 673 (1930)
 New Orleans Public Service, Inc. v. New Orleans, 281 U.S. 682 (1930)

External links

Volume 281
Category:1930 in United States case law


Q:

Verify client certificate using SSLServer in Ruby

Heres the code I'm using to setup the server:
require 'socket'
require 'openssl'

socket = TCPServer.new('127.0.0.1', 4433)

ssl_context = OpenSSL::SSL::SSLContext.new()
ssl_context.cert = OpenSSL::X509::Certificate.new(File.open("ssl/server/server.crt"))
ssl_context.key = OpenSSL::PKey::RSA.new(File.open("ssl/server/server.key"))

ca_cert = OpenSSL::X509::Certificate.new(File.open("ssl/ca/ca.crt"))

ssl_socket = OpenSSL::SSL::SSLServer.new(socket, ssl_context)

Thread.start(ssl_socket.accept) do |s|
    puts "Connected to #{s.peeraddr.last}"

    if s.peer_cert.verify(ca_cert.public_key)
        puts "Certificate verified"
    else
        puts "Certificate invalid"
    end
end

And the client:
require 'socket'
require 'openssl'

socket = TCPSocket.new('127.0.0.1', 4433)

ssl_context = OpenSSL::SSL::SSLContext.new
ssl_context.cert = OpenSSL::X509::Certificate.new(File.open("ssl/client1/client1.crt"))
ssl_context.key = OpenSSL::PKey::RSA.new(File.open("ssl/client1/client1.key"))

ssl_socket = OpenSSL::SSL::SSLSocket.new(socket, ssl_context)

ca_cert = OpenSSL::X509::Certificate.new(File.open("ssl/ca/ca.crt"))

ssl_socket.connect

if ssl_socket.peer_cert.verify(ca_cert.public_key)
    puts "Certificate checks out"
else
    puts "Certificate not verified"
end

However, the server throws an exception when it tries to get the peer_cert that it cannot find.  Is there a way to get the SSLServer to expect a client certificate?

A:

Have a look at test_client_auth and start_server in the tests for OpenSSL::SSL.
From the top of my head, the only thing I see missing in your code is that you forgot to explicitly require client authentication on the server side - it is important to set the flag combination
flags = OpenSSL::SSL::VERIFY_PEER|OpenSSL::SSL::VERIFY_FAIL_IF_NO_PEER_CERT
ctx.verify_mode = flags

so that the server will actually require client authentication and not silently accept requests that come unauthenticated. If you don't set these, the server will be happy without requesting client authentication and as a result there will also be no peer certificate available.


The Best Stories To Watch During Twitch's Absurdly Ginormous Classic Doctor Who Marathon

Today, Twitch begins a seven-week endurance run/celebration of all things old-school Doctor Who, live streaming over 500 episodes worth of adventures in Time and Space. Unless you happen to have seven weeks of free time starting imminently (in which case, I envy you), you likely can't sit down and watch all of it. So here's a few must-watch storylines to dive in for.

Given that 500-plus episodes is, well, a whole damn lot, in order to break this down into a more digestible format we'll be recommending a few choice selections for each of the first seven Doctors, as well as the times and dates they will be broadcasting on Twitch Presents over the next seven weeks. If you want to see the full schedule of stories that are airing and the time of each daily block they're in, you can check them out in both Pacific and GMT time-zone formats over at the official Doctor Who website here.

Where it all began, with 1963's "An Unearthly Child".Image: BBC

First Doctor

An Unearthly Child — The story that started it all is not actually that great — the first adventure, set in the stone age, is a bit plodding. But this is a piece of Doctor Who history that is delightful to experience if you've never done so before, and the actual first episode of mystery and setup in '60s London is majestic. (Air Date: May 29)

The Daleks — Speaking of history-defining: the Daleks' debut! They're creepy, they're shrill, and they're so utterly, utterly weird as the Doctor and his new friends find themselves on a strange world ravaged by terrible war. (Air Date: May 29)

The Time Meddler — The Meddling Monk is never going to be listed at the top of anyone's "best Who villains" list, but this story is one of the first that actually really engaged with the internal logic and morality of time travel in Doctor Who, and the dangers of trying to use it to change the past. (Air Date: June 4)

The Cybermen awaken from their cryo-slumber in "The Tomb of the Cybermen."Image: BBC

Second Doctor

Tomb of the Cybermen — One of the all-time great Cybermen stories, this creepy, icy expedition into the heart of an entire structure of sleeping cyber-monsters is a case study in why the Cybermen are such a chilling concept. (Air Date: June 5)

The Ice Warriors — Speaking of ice, the Ice Warriors' famous debut is definitely worth a revisit if you've been fond of their recent appearances in the Peter Capaldi and Matt Smith stories. They're less brutish, honour-bound warrior-aliens here than they are in recent Who, but still just as sinister. Or ssssssssinister, rather. (Air Date: June 5)

The Web of Fear — This story was famous for being among the missing serials of early Doctor Who until a few years ago, and its recovery means you can now experience the bizarre dichotomy of some genuinely scary action sequences set in the bleak tunnels of London's underground rail network, as well as the Yeti, monsters who are really not creepy but instead absurdly, absurdly fluffy and kind of cute? (Air Date: June 6)

The War Games — This epic-length saga is a bit of a slog at times, but it's Patrick Troughton's final story as the Doctor, and it's the first time we get to see his fellow Time Lords... and learn what absolute arseholes they are. (Air Date: June 7)

The Doctor meets a Silurian in "The Silurians."Image: BBC

Third Doctor

The Silurians — The Silurians as monsters are not just great as a concept — an "alien" race that lived on Earth before humanity even existed, lying in wait for eons — but their debut story grapples with some really interesting moral quandaries for the Doctor and his relationship with UNIT. It also features a truly chilling twist about halfway through that is one of Doctor Who's scariest scenes. (Air Date: June 8)

Inferno — The Third Doctor slips into a parallel reality where all his friends are jerks and the Brigadier has an eyepatch and is forced to consider the end of not just this reality, but his main one. What more could you want!? (Air Date: June 11)

Terror of the Autons — The Master makes a spectacular debut here, the second-go for the Autons in the Third Doctor's era. It's a much better story for the plastic terrors here too, epitomizing some of Doctor Who's best scifi twists on everyday life. (Air Date: June 12)

The benevolent faces of the Axons from "The Claws of Axos."Image: BBC

The Claws of Axos — Although this story is predominantly about handsome, gold-coated aliens who come to Earth in peace (only to turn out to be evil villains who are actually gross looking blobby-monsters), it's at its best focusing on the Doctor and the Master in a battle of wits with each other. (Air Date: June 12)

The Green Death — Most of this story about giant gross maggots and other bugs is a bit funky, especially if you're not too accustomed to old-school special effects work. But it's fondly remembered for the fact that it ends with an utterly heartbreaking farewell between the Doctor and his companion, Jo. (Air Date: June 19)

The Time Warrior — This story would be here even if it was simply just a great time-travel romp about an advanced Sontaran warrior being stuck in Medieval England. But it's also the debut of the dearly-missed Elisabeth Sladen as the one, the only, Sarah Jane Smith, one of Doctor Who's most beloved companions. And it's a damn good story for her to get going with. (Air Date: June 19)

The Doctor helps Sarah Jane out of a vent in "The Ark in Space."Image: BBC

Fourth Doctor

The Ark in Space — Tom Baker's debut story, "Robot," is a ton of fun, but he really gets going in this, his sophomore serial about the creepy Wirrn infesting a ship full of cryogenically frozen humans waiting out an apocalyptic event on Earth. (Air Date: June 21)

Genesis of the Daleks — If you've ever heard a thing about classic Doctor Who, you've probably heard about this, perhaps the greatest-ever story about the Daleks. The Doctor encounters the evil creator of his greatest foe, Davros, for the first time, but this entry excels for its moral core — sent back in time by his own people to prevent the Daleks from ever existing, does the Doctor have the right to do so? (Air Date: June 21)

Terror of the Zygons — Before they were brought back for modern Who, this was the only Zygon story, but it was the perfect example of why it was such a great injustice it took so long for the shapeshifting, sucker-covered aliens to come back... if you ignore the very dodgy Loch Ness Monster creature. (Air Date: June 22)

Pyramids of Mars — The Doctor and Sarah Jane confront the ancient evil god Sutekh, one of the show's best-ever one-off villains. This one also includes some genuinely creepy henchmen in the form of Sutekh's mummy-bots, who team up to crush a man between their ginormous chests in a genuinely grim scene. (Air Date: June 22)

The Doctor faces Time Lord drama in "The Deadly Assassin."Image: BBC

The Deadly Assassin — The story that shook up the Time Lord mythos again, this is primarily about the return of the Master and is known for being a story without companions. But it's full of delightful intrigue and Time Lord politics that let Tom Baker turn in a wild and wonderful performance. (Air Date: June 26)

The Robots of Death — The Doctor and his aggressive warrior-friend Leela find themselves caught up in a Robo-revolution. Worth it alone for the amazingly glam robot designs, but it helps that it's a cracking murder-mystery tale too. (Air Date: June 27)

The Horror of Fang Rock — Set entirely in a small, dark lighthouse, this grim tale features the blob-like Rutans, a long time foe of the Sontarans, slowly but surely picking off members of a small group of survivors as the Doctor races to defeat them. (Air Date: June 27)

City of Death — Douglas Adams' most famous story, this is an all-time Doctor Who classic. Delightful banter, time-hopping shenanigans, sumptuous location footage shot in Paris, and a great, hammy villain in the form of Julian Glover's Scaroth, last of the Jagaroth. One of the greatest Who stories ever. (Air Date: July 4)

The Cybermen overtake a ship destined to change the future in "Earthshock."Image: BBC

Fifth Doctor

Earthshock — The Cybermen of the '80s were a little more... bombastic than their chilling prior forms, but this excellent story is driven by the fact that it ends with one of the Doctor's companions, Adric, making the greatest sacrifice in order to save the day. Yes, Adric sucked, but it was still pretty sad! (Air Date: July 10)

Kinda and Snakedance — This pair of stories about a giant psychic snake called the Mara is let down by some rather dodgy snake effects (we don't know if Twitch will use the updated digital effects made for the stories' home releases), and the first story is a bit of a drag. It's on this list for the second Mara tale, "Snakedance," which sees the Doctor's companion Teagan forced to reckon with the trauma she went through thanks to the Mara's enthrallment of her in "Kinda," in a rare bit of follow-up storytelling. (Air Date: "Kinda" on July 9, "Snakedance" on July 11)

Enlightenment — A wonderfully weird costume drama set on solar-sailed spaceships — of the literal "ships in space" variety — filled with telepaths, creating some truly lush visuals that the actual story itself can never quite really live up to. (Air Date: July 11)

The Caves of Androzani — Often seen as one of the, if not the, best Doctor Who tales ever told. The final story of the Fifth Doctor's run sees him doomed to death from the get-go, and is all about the Doctor choosing to go down in his final hours doing what he does best — facing villains, saving lives, and giving everything he can to keep his best friend Peri safe. (Air Date: July 12)

Sixth Doctor

The Trial of a Timelord — Twitch isn't actually showing some of the better stories in Colin Baker's tumultuous reign as the Doctor; I have a soft spot for "Revelation of the Daleks," which is about the galaxy's greatest terror running a funeral home that's secretly converting corpses into fresh Daleks! But there is a whole day dedicated to one of classic Doctor Who's boldest experiments, season 23 — a series of four loosely interconnected separate stories revolving around the Doctor being put on trial by his own people (and, twist, an evil future version of himself). (Air Date: July 18)

The Doctor and Ace head to Victorian England to confront Ace's greatest fears in "Ghost Light."Image: BBC

Seventh Doctor

Ghost Light — The actual story of "Ghost Light" absolutely does not live up to its gorgeous Victorian horror house environs, but it's the relationship between Ace (often seen as a prototype for Modern Doctor Who's take on the companion role) and the Doctor that makes this excellent viewing, as the Doctor pushes Ace to confront her childhood fears. (Air Date: July 20)

The Curse of Fenric — Featuring not only some really creepy looking watery-vampires called the Haemovores, this serial is one of the defining moments in the Seventh Doctor's darker turn, revealing just how far he's willing to manipulate his closest friends to confront the terrible threat of the titular Fenric. (Air Date: July 23)

Survival — The very last story of classic Who is worth a watch simply for that historical footnote. It offers another great story for Ace, although it features some slightly off-looking furry cheetah-monsters that take the wind out of its sails a bit. (Air Date: July 23)

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Q:

Bounds on Size of Join of two Subgroups

Let $H$ and $K$ be two subgroups of a finite group $G$. Are there upper and lower bounds on the size of $H \vee K = \left<H \cup K\right>$ that depend on the size of the intersection $H \cap K$?
I believe that in case the intersection is trivial $(\left|H \cap K\right| = 1)$, then we have $\left|H \vee K\right| \geq \left|H\right|\left|K\right|$. Is this bound tight or even correct?
When the intersection is nontrivial there seem to be less elements in $H \vee K$, but I could not find a precise upper bound. Is there an upper bound in this case?

A:

Let $HK=\{hk\mid h\in H, k\in K\}$. Note that this is not necessarily a group, yet it is a basic exercise (found in most books) that $|HK|=\frac{|H||K|}{|H\cap K|}$.
Moreover, $HK\subseteq \langle H\cup K\rangle$, so $\frac{|H||K|}{|H\cap K|}\leq|\langle H\cup K\rangle|$.
In general, there is no meaningful upper bound on $|\langle H\cup K\rangle|$; $H$ and $K$ can both be very small but generate a large group.
On the other hand, if $HK$ is a group (which is always the case when one of $H$ or $K$ is normal in $G$, for example, or more generally, when one of them normalises the other) then $HK=\langle H\cup K\rangle$ and the previous inequality becomes an equality.


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Britain's May defies critics to back new US$22b Heathrow runway

Wednesday, October 26, 2016 - 07:31

Britain backed a US$22 billion expansion of London's Heathrow Airport on Tuesday, ending 25 years of indecision with an ambitious plan to boost global trade links following the vote to leave the European Union.

PHOTO: AFP

[LONDON] ritain backed a US$22 billion expansion of London's Heathrow Airport on Tuesday, ending 25 years of indecision with an ambitious plan to boost global trade links following the vote to leave the European Union.

Heathrow, Europe's busiest airport, defeated a proposal from smaller rival Gatwick to secure the first new full-length runway to be built near London in 70 years after environmental and political protests scuppered previous attempts.

The long-awaited decision put Prime Minister Theresa May on a collision course with several senior politicians including her own foreign secretary, Boris Johnson, and the plan is also likely to be challenged in the courts.

But with a promise of jobs and greater trade links after Britons opted in June for Brexit, Mrs May is likely to win parliament's approval, triumphing over an issue that has paralysed successive governments in the past.

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"After decades of delay we are showing that we will take the big decisions when they're the right decisions for Britain," Mrs May said of her Conservative government's backing for what will one of Europe's biggest infrastructure projects.

The decision in favour of a third runway at Heathrow, due to be built by 2025, is one of Mrs May's most significant acts since she took office in July. It follows her approval in September of a US$24 billion nuclear power plant at Hinkley Point.

With established links around the world, Heathrow always offered the greatest economic potential. However, its position to the west of London, near several affluent suburbs represented in parliament by Conservative lawmakers including Mr Johnson, drew a powerful coalition of opponents worried about noise and pollution.

A new runway will also require parts of the motorway circling the capital to be rebuilt, making it more expensive and complex than alternative options to extend an existing Heathrow runway or build a new one at Gatwick, south of London.

According to a three-year study by Britain's independent Airports Commission, a new runway at Heathrow would create 70,000 new jobs by 2050 and increase gross domestic product by between 0.65 and 0.75 per cent over the same period.

It will also enable Britain to keep pace with Europe's biggest airports in Paris, Amsterdam and Frankfurt, which have greater capacity.

But within hours of the decision, politicians were lining up to denounce it. Mr Johnson, a leading Brexit campaigner, said the plan was "undeliverable" and "very likely to be stopped" while London Mayor Sadiq Khan, alarmed by the potential impact on air quality, said he was exploring legal options.

Zac Goldsmith, a lawmaker in Mrs May's Conservative Party, resigned over the issue, meaning a by-election will be held in his constituency near the airport and potentially threatening to reduce Mrs May's already slim majority in parliament.

Mr Johnson, a former London mayor who once vowed to lie down in front of the bulldozers to prevent a new Heathrow runway being built, said he worried that a third would be followed by a fourth.

"You'd have New York, a city of beautiful skyscrapers, Paris the city of light, London the city of planes," he told reporters.

"Is that really what we want for our fantastic capital city?"

Wary of being damaged by the issue, Mrs May has allowed her ministers to criticise the plan but not campaign against it before a vote in parliament in a year's time. Surveys show a majority of lawmakers will back her.

Lawyers said opponents could delay the decision on the project in the courts but were unlikely to be able to block it.

Adam Marshall, director general of the British Chambers of Commerce, said governments had prevaricated for too long.

"Put simply, it's about time," he said.

"Businesses will now want assurances that the final approval process for Heathrow's new runway will be smooth and swift, so that construction can begin as soon as possible."

"The time for playing politics with our national connectivity is over."

Heathrow is owned by Spanish infrastructure company Ferrovial, Qatar Holding, China Investment Corp and other investors, and the bill for expansion will be paid for by the private sector, with the government expected to pay for some of the additional road and rail costs.

Engineering firms Arup, US-headquartered CH2M, British construction company Mace and construction and project management firm Turner & Townsend are already working on the early stages of the project.

The government said the UK aviation regulator would work with Heathrow and airlines to ensure the new runway was affordable and keep landing charges paid by the carriers close to current levels.

The government also proposed legally binding noise targets to provide respite for local residents while Heathrow will need to meet air quality rules as a condition of planning approval.

"Heathrow stands ready to work with government, businesses, airlines and our local communities to deliver an airport that is fair, affordable and secures the benefits of expansion for the whole of the UK," the airport said.