prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: What is the scaling form for the alternative order parameter O?

Read the following text and answer briefly.

Context 1: \section*{Dynamical Behaviour of $O$ in Lattice Gases}

The dynamical behaviour of the anisotropic order parameter  $m$ [see Eq ~\eqref{eq:def-m} in the Letter] following a quench to the critical point is well described by
the Gaussian theory for all the three lattice gas models studied, $i e ,$ driven lattice gas with either constant (IDLG) or random (RDLG) infinite drive and equilibrium lattice gas (LG)  In other words, in the short-time regime, $m \sim t^{1/2}$ [see Eq  \eqref{eq:mt}] and the Binder cumulant $g$ of the lowest transverse mode [defined in Eq  \eqref{eq:binder}] is zero in this regime  The alternative order parameter $O,$ however, distinguishes between the driven (IDLG, RDLG) and the equilibrium (LG) lattice gases  

In order to understand  this, we first write the phenomenological scaling form for $O$,  analogous to Eq  \eqref{eq:scalingass} in  the Letter,
\begin{eqnarray}
O (t, L_{\parallel} ; S_\Delta) = L_{\parallel}^{-\beta/[\nu(1+\Delta)]} \tilde f_O (t/L_{\parallel}^{z/(1+\Delta)} ; S_\Delta) \quad
\label{eq:Oscalingass}
\end{eqnarray}
We already remarked that, in the LG, this scaling form is not compatible with the prediction $O \sim t^{1/8}  L_{\parallel}^{-1/2}$ of the Gaussian theory   However, following Ref  \cite{AS2002}, it can be argued that, at short times, the only dependence of $O$ on the system size $L_{\parallel}$ is of the form $O \sim L_\parallel^{-1/2}$ which is very well confirmed by numerical simulations  Accordingly,  the generic behaviour of $O$ can be assumed to be
\begin{eqnarray}
O \sim t^{\alpha} L_\parallel^{-1/2}, \label{eq:O}
\end{eqnarray}
where $\alpha$ is a phenomenological exponent to be determined  This, along with Eq  \eqref{eq:Oscalingass}, implies $\tilde f_O(x) \sim x^{\alpha} $ Comparing the finite-size behaviour in Eq ~\eqref{eq:O} with Eq ~\eqref{eq:Oscalingass} one actually infers,
\begin{eqnarray}
\alpha &=& \frac{1+ \Delta -2 \beta/\nu}{2 \, (4- \eta)}  \label{eq:alpha}
\end{eqnarray}
This equation, together with the hyperscaling relation $\Delta - 2 \beta/\nu= - \eta$ in two spatial dimensions, shows that the prediction $\alpha = 1/8$ of the Gaussian theory [see Eq  \eqref{eq:Ot}] can be obtained only when $\eta=0,$ which is the case for the IDLG (exactly) and the RDLG (approximately) but not for the LG  

On the other hand,  Eq ~\eqref{eq:alpha} predicts $\alpha = 1/10$ upon substituting the values of the critical exponents corresponding to the Ising  universality class (LG)  This is consistent with the numerical simulation results presented in the main text, see Fig  \ref{fig:ising}(b) therein 

\begin{figure}[th]
\vspace*{0 2 cm}
 \centering
 \includegraphics[width=10 cm]{ /compare_binder pdf}

\caption{Comparison between the temporal evolution of the Binder cumulants $g$ corresponding to the $12^{th}$ transverse mode, $i e ,$ with $n_\perp =12,$ in the LG (lowest curve), IDLG and RDLG (two upper curves) on a $32 \times 32$ lattice  \label{fig:b}}
 \label{fig:binder}
\end{figure}


The emergence of this new value $1/10$ of the exponent $\alpha$ must be traced back to the non-Gaussian nature of higher fluctuating modes in the LG  In fact, even though the lowest mode behaves identically in all the three models we considered,  characterized by the same behaviour of $m$, higher modes show a significant difference in the non-driven case   


To illustrate this, we measured the Binder cumulants of higher modes which is defined  analogously to Eq ~(11), using transverse modes other than the first, i e , with $\mu=\tilde \sigma(0,2 \pi n_\bot/L_\bot)$ and $n_\bot>1 $  
 Figure \ref{fig:b} compares the same for all the three lattice gases for the mode with $n_\perp =12$ on a $32 \times 32$ lattice  Clearly, the curve corresponding to the LG (lowest, blue) departs from Gaussian behaviour $g=0$ (in practice, $e g ,$ $|g| \lesssim 0 005,$ corresponding to the shaded gray area) much earlier than it does for the IDLG  or RDLG (two upper curves, red and green respectively) 

Accordingly, the different dynamical behaviour of $O$, which involves a sum over all modes, can be attributed to the non-Gaussian nature of the higher modes in the LG  
Such a departure is not entirely surprising  In fact, for higher modes, mesoscopic descriptions such as the ones in Eqs  \eqref{eq:L-DLG} or \eqref{eq:g_evol} are not expected to hold, while the anisotropy at the microscopic level could be the mechanism leading to the Gaussianity of higher modes in the driven models 


Context 2: Hey folks! Here is the shiny new Changelog thread  We're including the archived patch notes from the old forums, so that they are preserved for anyone that would like to reference back to them  We will continue to update this thread with new notes as the patches are released 
Chat is now accessible from the quest board, upgrade screen, and many other menus 
Tapping on objects and menus may reveal helpful hints about that object 
Team PI is now colored red if lower than recommended for the quest 
Many text fixes and consistency improvements 
• A new Basic Catalyst found in Special Events is used in every recipe!
Several heroes have received improvements to their base stats 
The abilities of all Champions have increased in effectiveness 
A new Critical Boost buff has been introduced 
Iron Fist and Spiderman now have the ability to Armor Break with their Critical Hits 
Deadpool’s ability to Regenerate is more powerful, but only triggers once per fight 
Scarlet Witch now has a chance to trigger Nullify off of any Critical Hit 
Juggernaut and Rhino now have a layer of Armor 
Punisher and Winter Solider now may also trigger Fury in addition to Bleed 
Colossus now further increases his base Armor with the Armor Up ability 
Thor and Ronan no longer Armor Break; instead, base stats and Stun durations have improved 
We reduced the effectiveness of the Revive items in order to give away more as rewards 
A bonus of 50% for using ISO-8 matching your Champion’s Class can now be previewed on the Upgrade screen 
It’s now possible sell Champions in exchange for ISO-8 and Gold  The amount received increases proportionately to the Rank and Level of the sold Champion 
-You can now skip dialogue on the quest map by pressing ‘SKIP’ 
-Added a ‘Quit’ button directly on the quest interface 
-The Back button on the Top Bar now returns the player to the Home screen 
-Various game balance and cosmetic improvements to the available quests 
• PVP energy has been replaced with Hero Stamina  Each Hero has their own Stamina values, meaning the more Heroes you have the more you can play in PVP 
• Each Hero has 1 Stamina and takes 2 hours to recharge 
We have removed the Next Quest button for a much more favorable and flavorful approach to teaching and informing people about Marvel : Contest of Champions  In the Main Menu(Bottom Right Corner) you will now see an image of the Collector showing you what the best or recommended actions that you should preform  This can be anything from opening Crystals, Continuing a Quest, Ranking Up Champions if the difficulty is too hard, Tips where to obtain items, and Playing Versus/Arenas 
• Adjusted the PI calculation for Power Burn and Power Drain abilities to improve accuracy 
• Significantly increased the Power Burn multiplier as well as the amount of Power burned  Prior to this change, Vision's Special Attack damage output was far below the curve  Vision's Special Damage is distinct from other heroes in that the dependency on opponents' Power levels cause the damage dealt to be highly variable, and sometimes quite low; however, when striking an opponent with high Power levels, Vision has the potential to deal very high amounts of direct, Armor-ignoring damage 
• Slightly adjusted the Armor Break trigger to be less punishing to opponents with the Armor Up ability without sacrificing PI or damage output 
• Slightly increased his base Health and, in turn, the amount of Health recovered by Regeneration  This improvement is reflected by an increase to PI of about 1% 
• Slightly reduced the damage from Bleeding, but slightly increased the amount of Power drained by E M P  Arrow to compensate  This added utility strengthens the choice between whether to offensively Bleed the enemy or defensively drain their Power  These changes may modify PI by +/-1% 
• Slightly reduced the frequency of Nullify for basic attacks, but slightly increased the chance a Special Attack is critical  Chaotic Bombardment no longer has a chance to critical, and instead has a 100% chance to Nullify the target  This is less punishing to opponents with beneficial effects, while providing a more reliable source of Nullify  Overall, her PI has decreased by about 2% 
• Decreased base Health and Attack by 2% each to bring his PI in line with other Champions without compromising Special Attack effectiveness 
• Slightly increased base Health by 2% to bring his PI in line with other Champions  This change may result in a PI increase of up to 1% 
• Fixed a bug with her Bleed ability scaling incorrectly  This has no effect on PI 
• User's on iPhone 4 devices will no longer encounter a progression blocker after fighting Iron Man in the tutorial 
• Fixed an issue where player's Hero would disappear after using a special move 
• Fixed an issue where very rarely a character would lose all functionality when dashing 
• Added additional Network support to better diagnose disconnects  The game should resolve and recover much more gracefully than in previous updates 
• Adjusted some of the touch sensitivity while fighting  Heroes moves should feel more responsive  This is something that is going to be an ongoing process  Please let us know how you think it feels 
• Fixed various issues with Chat 
• We have updated Open GL versions/drivers for iOS devices that support Open GL 3 0 
• User's will no longer receive delayed Game Center notifications  This caused some weirdness to occur while opening Crystals in the Crystal Vault 
• The Crystal Vault has received another polish pass and should now feel much more responsive, thank you for all your feedback on this feature!
• Many more minor bug fixes were included in this update 
• Special Attack 1 base damage increased by +25% Attack Rating 
• Heavy Attack base Power gained reduced to 63 points 
We recently improved the functionality of Heavy Attacks, so they’re easier to use  Their base Power has been reduced to normal levels – previously, they generated Power at a higher rate to compensate for their difficult execution  Special Attacks have been adjusted to give the unlucky recipients more of a fighting chance  These changes bring these attacks in line with existing damage-to-power ratios 
*NOTE: Special Attacks only generate Power for the target struck, not for the user; this prevents infinite loops and helps serve as a comeback mechanic 
Versus Crystal prizes have been adjusted due to the Champion Stamina changes 
Arena Crystal prizes have been increased to help balance the adjustments to the Versus Crystal 
Payouts have significantly increased when receiving a duplicate Champion with a Star rating of two or more  The boosted amount increases based on Star rating  We apologize for any inconvenience caused by delivering each reward individually, and are working to get a fix to you as soon as possible  In the meantime, using the “Skip” button avoids the inconvenience 
• We fixed a bug where finding a new match could cost a player Units 
• Spending Units to find a new opponent will now return opponents with lower ratings 
• Chapters 3 and 4 of Act 2 Story Quests are now available  A mysterious opponent awaits you at the end of Act 2!
*NOTE: This caused some players' progress to reset for a brief time, but that issue should now be corrected 
• Event Quest difficulty has been adjusted to match Catalyst availability 
• Rank-Up Recipes have been adjusted to be more accessible across all ranks 
• Bosses for the Monday through Saturday Daily Events now have a small chance to drop a Class Catalyst  This is in addition to the drop chance from Chests 
• Ambush Rates have been adjusted on all Event Quests 
• Increased Catalyst drops for the Collector Free-For-All Event Quest 
• Alpha Catalysts now have a chance to drop from Chests in Medium and Hard difficulties of The Collector Free-For-All event 
• The unobtainable chest in Act 1, Chapter 1, Quest 6 has been removed from the Battlerealm 
Increased the amount of Gold awarded by the Arena Crystal 
Slightly reduced the cost to level-up a 3-Star Champion at Rank 1 to cleanly align with ISO-8 chunk values 
Fixed a bug with Billion-Dollar Punch not triggering Armor Break 
• Duplicate 2-Star, 3-Star, and 4-Star Champions now awaken a brand new ability unique to that Champion in addition to the rare ISO8 they currently give  Duplicates thereafter continue to level-up this ability to make it stronger  When a Champion is awakened, their Stars turn bright and glow, making them easy to identify (and look pretty cool too)  These new abilities can be quite powerful, so please fight responsibly!
• Various other improvements, including rank and level information for opponents, find match options in team select, and animation tuning 
• There is now a chance to encounter the elusive Treasure Adaptoid, who divulges his hoard of ISO8 and Gold to those able to defeat him in battle 
• Class Relationships can be viewed by tapping “Enemy Classes” before entering a quest, and preview the number of enemies in that quest for each class type 
• You can also now see rewards for completion and exploration on the Edit Team screen 
• Opponents are more aware of the distance between you and them, improving their interaction with knockback effects, such as that from Heavy Attacks 
Mutant Champions are now effective against Skill Champions 
• The high Special Attack damage and regenerative abilities of Mutant Champions are effective against Skill Champions, which typically rely on Bleed damage from their weaponry  We think of this relationship as if the X-Gene grants Mutant Champions superpowers that evolved to be stronger than Champions that are merely “Skilled” 
Skill Champions are now effective against Science Champions 
• While scientists fiddle in their cute little laboratories to create flasks full of serums to turn even frail young men into super-soldiers, Skill Champions were just born that way baby  Often donning sharp weaponry to make their opponents Bleed, Skill Champions enjoy watching the high base attributes of Science Champions just melt away 
Cosmic Champions are now effective against Tech Champions 
• Tech Champions construct durable robots and thick suits of Armor to outlast their opponents in battles of tank-the-nuke   which gives Cosmic Champions extra time to build up stacks of beneficial effects to overrun Tech Champions using their peculiar alien enhancements 
• Tech Champions are still effective against Mutant Champions 
Tech Champions typically excel at Armor, Resistance, and Power manipulation, which is effective against the high Special Attack damage of Mutant Champions  Think of the robotic Sentinels adapting for tactical advantages in the war against Mutantkind!
Science Champions are still effective against Mystic Champions 
• Science Champions – a Class of behemoths like Hulk and super-soldiers like Captain America – typically have above average base attributes like Health, Attack, and Armor  These raw stats cannot be affected by pesky Mystics and their removal abilities: Nullify and Purge 
Mystic Champions are still effective against Cosmic Champions 
• Cosmic Champions explore strange new beneficial effects to seek out new power and new abilities, to boldly take their attributes where no class has gone before  Well, not if Mystic Champions – who are fully capable of stripping Cosmic Champions of their beneficial effects – have anything to say about it! Maybe it’s the Mystic Agenda to protect the secrets of the universe?
These changes ensure that having a Class Bonus always gives you the advantage it promises, as it now also reflects ability trends for a particular Class  Please keep in mind that these are generalizations, and some Champions abilities may not always strictly align with these relationships  Learn more about Champions’ abilities by viewing their profiles and tapping on features for detailed information 
• When you attack someone, you charge up their Power in addition to yours  This meant they would reach a full three bars while you only reached one and a half  We've reduced the amount defenders receive such that you'll be at two bars when they're at three  This change maintains the underdog functionality to give defenders a chance to comeback while being less punishing to players earning high Combos 
New damage types for attacks now play a larger role in the abilities of Champions  For example, some heroes power-up by successfully blocking magical damage, while others’ abilities may harm anyone that makes physical contact with them 
New Resistances and Immunities have found their way to the Battlerealm  Some heroes are completely immune to specific status effects based on either lore from the comics or logic  For example, the android Vision has no blood, and is therefore fully immune to Bleed conditions  We’ve also strengthened the effectiveness of certain status effects, so be careful who you choose to bring into battle! Could you guess who might be immune to the new “Poison” condition?
• Poison: Inflicts damage over time and reduces healing and regeneration effectiveness 
• Unstoppable: A buff to shrug off the impact from attacks, but still take the damage 
• Weakness: A debuff that reduces Attack attributes 
• Heal Block: Fully prevents the target from gaining health in any way 
• Power Lock: Seals the target, preventing them from gaining any Power 
• When fighting, you may notice that many status effects are now able to stack  This also changes how certain beneficial “buffs” and detrimental “debuffs” interact with one another  For example, it's now possible to have both Armor Up and Armor Break effects on you simultaneously  Let the tug-o-war begin, and may the strongest effects win!
• Black Bolt's Corkscrew: +25% damage, but at the cost of minor recoil damage 
• Punisher's “Wrath” has been replaced by "Payback"  Payback deals additional damage based on the total damage dealt to Frank 
• Colossus' “Unbreakable” now deal bonus damage based on his armor level at the time of activation 
• All of Black Panther’s special attacks now deal bonus damage based on the number of Bleeds on the target 
• Spider-Man’s Web-Slinger now has a chance to inflict Weakness 
• Vision’s Physical Disruption: Added a minor Power Burn effect due to “his” use of his Infrared Beam  “He” also now purges all status effects while phasing through the ground 
• Scarlet Witch: Increased the Critical Hit Chance for Hex Bolt and Hex Sphere 
• Many knockback effects have been adjusted to improve consistency 
We’ve tested the Signature Abilities quite extensively before releasing them, but there have been a few abilities that we have been keeping an eye on  We’ve compared our notes with the feedback you’ve been sending us and are making some balance changes to them  Thanks for your feedback!
Slightly reduced the frequency and duration of Juggernaut’s “Unstoppable” ability 
• He was indeed a bit too   unstoppable  We’ve toned down the frequency this ability triggers, as well as reduced the duration it’s active for when it does trigger  We feel Juggernaut is still a powerful Champion despite these revisions  Take care!
Slightly reduced the starting values of Wolverine's “Cellular Regeneration” 
• We found that Cellular Regeneration was too strong at lower levels where fewer counters to Regeneration exist 
Re-scaled Gamora's “Assassination” to start higher but scale slower 
• At lower levels, Special Attacks were used too infrequently, giving this powerful ability little visibility  We’ve adjusted the scaling to better match Special Attack usage at all levels 
Increased the frequency that Black Bolt’s “Provocation” triggers 
• Due to the varying Critical Hit rates across all Champions, in some cases Provocation would trigger rarely or not at all within a fight  We’ve increased the frequency to ensure you’ll see it every match – but especially so against opponents with high Critical Hit rates 
We’ll continue to follow the effect of these new abilities on gameplay  Please keep your feedback coming!
Hey everyone! We have been hard at work on improving the game and have prepared a big update inspired in part by your great community feedback  Please keep letting us know what you think!
• Fixed many Dash, Medium, Heavy and Special Attacks missing or failing to execute 
• Added Alliances and a new Alliance Crystal 
• Rocket Raccoon and Unstoppable Colossus join The Contest 
• Temporary Boosts to Attack, Health, and XP are now available from the Alliance Crystal 
• Rewards for completing and exploring Chapters and Acts  Earn a guaranteed 3-Star hero crystal for each fully explored Act! This is retroactive, just complete any quest to claim them 
• A new Fight Menu combines The Arenas, Story Quests and Event Quest menus 
• Updated Summoner Profiles with new information  Inspect other players’ Profiles and brag about your achievements!
• A list of blocked users has been added to Chat windows  The option to unblock these users is found in this new menu  The power is in your hands now!
• We fixed Dash and Medium Attack issues for many heroes that sometimes missed or did not activate 
• We fixed issues to Drax and Colossus Light and Medium Attacks where they would not connect 
• Fixed an issue where the camera would stop moving after a level 3 special sequence 
• Fixed an issue where the player’s heavy attack would get stuck in charge even after the player has released input 
• Fixed a rare bug where Champions were still able to deal damage after they died, resulting in tied fights 
Form Alliances with your Friends!
What is better than playing? Playing with your friends! Create a new Alliance or join an existing one through the new Alliance Menu 
• Invite other players to your Alliance 
• Search for an Alliance by name or join a Recommended Alliance 
• Receive rewards for entering your first Alliance 
• Alliance News Feed  The news feed celebrates your Alliance member’s achievements 
• Alliance Chat  Chat with other members of your Alliance in a private channel all to yourself



ground_truth: O(t, L_{\parallel}; S_\Delta) = L_{\parallel}^{-\beta/[\nu(1+\Delta)]} \tilde f_O(t/L_{\parallel}^{z/(1+\Delta)}; S_\Delta).

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: How can players skip dialogue on the quest map?

Read the following text and answer briefly.

Context 2: 
• Help Allies  Players can ask for help when out of Energy or Stamina  Alliance members help each other as much as they can to earn Loyalty Points  Loyalty points have a daily limit to how many can be earned 
• Alliance Crystal  Access a new Alliance Crystal while part of any Alliance  Use new Loyalty Points for purchasing Alliance Crystals 
He may start out slow, but watch out for his immense power at high ranks!
• Adjusted the range of many Heavy Attacks, including Hulk and Drax, to ensure they correctly connect with enemies 
• Many Special Attacks, including those for Wolverine, Iron Fist, Winter Soldier, Punisher, Black Panther, and many others have had their range adjusted to ensure they correctly connect with enemies even if activated immediately after a combo that knocked the enemy back 
• Payback and Unbreakable now display their maximum potential damage bonus 
• Added detailed descriptions for Bleed Immunity and Poison Immunity 
• Gamora: We’ve adjusted the scaling of her base Special Attack damage to ensure they scale up more similarly to other heroes  This also makes Gamora more reliant on her high Bleed damage, and improves the chances of opponents able to deal with her high Bleed 
Vital Strike and Jade Assassin damage decreased by 10% 
Godslayer damage increased by 10% 
• Magik: Rewind is a game-changer for Magik that allows her to go up against foes like Gamora and Rewind off big Critical Hits and Bleed damage; however, the frequency of Rewind triggering was too low to be there when she needed it 
Increased the likelihood Rewind triggers by +20% at all levels 
Rewind now heals over one second instead of instantly 
Fixed a bug allowing Magik to break out of an enemy combo using Rewind  It now only removes Status Effects 
• Hulk: Given the riskiness of losing Health in certain game modes, Hulk’s anger-management provided too little help too late in the game  We’ve increased the Attack boost to ensure he’s appropriately scary in all game modes – as long as he’s angry!
Increased Hulk Rage by +20% Attack at all ability levels 
Arc Overload no longer causes Armor Break when it expires 
• Vision: Added Poison Immunity to our robot friend 
Arena tuning is an ongoing process  The team is continually making adjustments to Arenas to improve the experience 
Ultron has infected The Contest!
Many new Champions join the battle against Ultron 
Quest through the new Ultron’s Assault Event 
Wield new power with Summoner Masteries 
Grow your Friend’s List with the new Social Hub 
Team up with your Alliance in new Events, Arenas, and more!
Filter and sort your Stash 
Fights have been optimized for performance improvements on all devices 
Users can now filter through the items in their Stash 
Fixed several issues where Hero Rating would fluctuate 
Fixed a bug with Rhino and Juggernaut having 11-20% more Armor than intended 
Fixed a bug with Rocket Raccoon’s Dash attack being slower than intended 
Added a confirmation popup when spending Units on stamina recharges and unlocking arenas 
Regeneration no longer displays green Health values if you’re at full Health 
Several new improvements to how status effects are displayed 
AI opponents are no longer able to perform one unavoidable attack in response to a Special Attack 3 
A new and improved look for all Health Potions in the Battlerealm 
All Revive Potions now revive your Champions with +10% more Health 
We’re adding so many new Champions, they could form their own Alliance!
Some of your favourite heroes of the Marvel Cinematic Universe join The Contest!
Summoner Mastery is on the horizon!
Masteries provide beneficial effects for your Champions 
Access Masteries through your Summoner Profile 
Earn Mastery Points when you level up 
Choose your Masteries wisely and strategically customize your benefits 
Recover your points to try a new specialization as often as you’d like 
Keep an eye on in-game messaging for more information 
The daily loyalty limit has been set to refresh at 08:00UTC for all players 
A timer has been added to show when the daily loyalty limit resets 
Loyalty balance is now displayed in the Alliance menus 
Ask for Versus help with a single tap on the ‘Help’ icon in Team Select 
New Alliance Events are coming very soon!
Work together with your Alliance to complete objectives and receive rewards!
Muster your might, Alliance Arenas will soon open their gates!
Competing in Alliance Arenas shares your points across your whole Alliance; work together to reach milestones and top ranks!
Work together to amass a huge score, and defeat your competition in classic Arena combat! No slackers here either - if you don’t contribute to win the competition, you’re not eligible for the goods!
All social features (Chat, Mail, and Friends) can now be accessed through the new Social Hub 
Search for and add friends, and send private messages to Summoners on your Friends List 
Redesigned chat and mail screens 
Take on other Summoners’ top Champions for bragging rights and prizes in 1-on-1 Duels!
A new series of special Ultron quests are available, starting with the first Chapter  Fight back against Ultron’s infection alongside the Summoner, and team up with some of Marvel’s finest! New quests unlock each week!
The Spider-Man Champion gate has been removed from Act 1, Chapter 1, Quest 5 
• Fixed an issue where chat snapped to the most recent message 
• Fixed several issues where Hero Rating would fluctuate 
• Various improvements to the Summoner Mastery screens and descriptions 
• Increased the ISO8 awarded by duplicate 2-Star Champions 
Quest through the new single-player campaign, Ant-Man’s Adventure!
In addition to Ant-Man and Yellowjacket feuding throughout the Battlerealm, additional new Champions will be joining The Contest!
Access more Masteries in the new Utility Mastery tree!
Please note, these changes may result in a loss of Hero Rating as incorrect effects are restored back to normal levels 
Improved and polished combat mechanics to reduce the amount of stutters and lost input 
Fixed and optimized rendering related issues with Metal enabled devices 
Team up with Ant-Man, and put a stop to Yellowjacket’s mysterious mission!
All Alliance Quests only last for a specified amount of time, defeat the boss with your Alliance before it expires!
New Prestige System - A dynamic difficulty and score setting that adjusts as you and your Alliance succeed in harder quests  The better you do and the tougher your Alliance is, the higher the prestige  The higher the prestige, the better the rewards!
Choose your teams carefully as Champions within Alliance Quests cannot be used in other Story or Event Quests 
Act 4 has been released! Play Chapter 1 now!
Summoner level maximum has been increased to level 60!
5-Star Champions are coΩming to The Contest! These are the most powerful Champions yet!
Additional improvements have been made to the UI, Versus Arenas, Synergy Bonuses, the Stash & Items Store 
Act 4 - Chapter 1 released!
New challenges - more path variation and features to challenge the strongest Summoners!
Greater challenge means greater rewards! Earn 4 Star Crystals and Mastery Points!
The Summoner Level cap has been increased by ten levels to level 60!
Champion Items will be coming soon! These allow you to apply items and buffs to a specific Champion, keep an eye out for updates on these new Champion Items!
Synergy Bonuses have updated iconography and the calculation has been updated to a distinct, additive bonus - What you see is what you get!
Alliance class distribution is now displayed on team select - Choose the right class!
Your Catalysts now have their own inventory, and will no longer appear in the Upgrade Item inventory 
The Stash is now separated into three tabs: Catalysts, Rewards and ISO, allowing you to sort and view your Stash much faster!
The UI flow for both Quests and Arenas have been greatly improved  You can now skip through fight victory and reward animations!
Here is the rundown of patch 5 1 0, filled with various bug fixes and optimizations  The important ones to note are below 
New Champions, new theme, and a new arena!
To celebrate our one year anniversary AND the holidays, we’ll be running a special event quest! Battle through the history of The Contest, and test your mettle against familiar faces both old and new!
A special reward will be available to those who master every quest!
Our Anniversary Celebration will be happening very soon; stay tuned for more info!
More Act 4 quests are coming very soon!
Opponents in Story Quests now have the ability to use their Special 3 attack! Note that we are not changing previous quest opponents to have this special attack (Act 1-3, Proving Grounds, Realm of Legends will not change); this will be in effect starting with the soon-to-be-released Act 4 content 
As with our previous major build releases (3 0’s Ultron, 4 0’s Ant Man, and 5 0’s Battlerealm), the Contest has been reskinned with a new theme!
The Road to Knowhere map is here! Fight in a new level inspired by Guardians of the Galaxy!
A new button in your Alliance Chat to take you directly to Alliance Quests!
You can now collect Catalyst Fragments in Event Quests, Proving Grounds, and Alliance Quests; these can be pieced together into a Catalyst!
Selling Items is now a thing! Sell any items in your inventory for gold!
Level 3 and Level 4 Health Potions have arrived! These are powerful instruments to help you tackle all the new Act 4 content!
Over 400 bugs were fixed in this patch!
This patch is a fix for the missing Champions during the Special 3 animation on Android devices 
This issue occurred during our upload process to the Google Play Store  This was an odd edge case scenario that we could not have caught during our internal tests, as it began appearing once we uploaded to the Google Play Store  This hotfix will be out by tomorrow, and will put Android at version 6 0 1  As this issue does not occur on iOS devices, iOS will remain at version 6 0 
3:30pm PST: We have started slow-rolling this patch out to Android devices, beginning with about 20% of users  We expect this to be available for 100% of users within the next 24 hours 
We have a few new Champions that you will see within the next couple of months (including one of my personal favorites)!
Over 200 total bugs squashed in this patch!
An artifact left over from the early days of the contest was Black Panther’s ability to gain a Critical Hit Rate boost during Special 3 attacks  As many might know, Critical Hits aren’t possible during a Special 3 anymore, making this effect   unhelpful  We’ve switched it out with a new ability to stack up even more Bleed effects on the opponent based on how many Bleeds are already active 
Example: The opponent has 4 stacks (instances) of Bleed on them when you launch a Special 3  With this new ability, you have a chance to add an additional 0 - 4 more stacks (instances) of Bleed 
Previously, a bug existed that allowed champions with Evade to continue to dodge Black Widow’s attacks, even if her Signature Ability was maxed out  This issue has been fixed 
Captain America WW2 has started to become outpaced by his non-WW2 counterpart and while we want the two to feel different and each have their own specific uses, we also want to ensure they are kept within range of each other in terms of balance  To accomplish this, we’ve given WW2 Cap the ability to Stun with his Special 1 and Special 3 attacks, but kept his Bleed on Special 2 the same, giving him options during combat against non-bleeding champions 
A bug that prevented Daredevil from triggering Armor Breaks from Heavy Attacks has been fixed and is now working as intended 
Against non-bleeding champions: Critical Hits have a chance to Armor Break on Special Attacks 
Increase range of Signature to 25% from 20% 
Many players found Elektra’s signature ability lacked enough opportunities to use it  To remedy this, we’ve increased the range from 20% to 25%  Additionally, to help make Elektra unique from other skill champions, we’ve given her the ability to deal with naturally Bleed Immune champions  Note: This Armor Break only applies to champions naturally immune to bleed, such as Colossus and Ultron, and not to champions granted Bleed Immunity from Local or Link Nodes 
Guillotine’s Bleed effect used to have a chance to activate from any given attack, meaning that it had to be kept quite weak to compensate for the frequency of triggers  We’ve made the switch to have her Bleed behave closer to existing champions, and in doing so have boosted the strength of the Bleed and have allowed it to stack 
Norman Osborn overloads the Arc Reactor in his chest if Health drops below 10%, granting a large burst of power, with (18% - 48% ) Armor, Regeneration, and Power Gain  After that, his suit burns out and cannot trigger Armor Up, Armor Break or Stun and loses all base Armor 
Many players didn’t like Iron Patriot’s old signature ability, feeling that due to the lack of Regeneration, it was considerably weaker than Iron Man’s  While we agreed, we didn’t want to just copy and paste his signature ability, but rather give him his own unique twist on the ability  This “all or nothing version” feels more like Norman Osborn, pushing his suit to the limit to get a larger boost but at the cost of damaging the suit  The addition of Power Gain allows Iron Patriot a large attack before the suit burns out, if timed correctly 
Heavy Attacks: 90% chance to Stagger the enemy for 8 seconds  A Staggered enemy cannot gain their next beneficial effect 
All versions of Juggernaut, even those who haven’t been awakened, now gain the 2 second Unstoppable ability at the start of the fight when they hit Rank 2 
We wanted to add some new functionality to Juggernaut, while also keeping him true to his Mystic class assignment  To accomplish this, we added this “buff smasher” effect which keeps an opponent from gaining their next beneficial effect  Additionally, we wanted to make non-awakened versions of Juggernaut more fun to play, without adding more power to the awakened variations  As a result, we gave all versions of Juggernaut the ability to become Unstoppable at the start of the fight 
While many players liked the new functionality of Star-Lord’s Element Gun effect, they found it to be a little too random, specifically when it would Heal Block a champion incapable of Healing  We’ve now added in some contingencies that will make Heal Block appear less unless the opposing champion shows that he / she can Heal during the fight  This includes both activated healing effects, such as Wolverine or Ultron’s Heal, or passive healing effects gained from Masteries, such as Salve or Willpower 
It’s been a bit weird that Bucky wasn’t friends with his most famous friend  Well, he is now  This affects 3 Star and above versions 
We’ve increased the overall speed of this attack, allowing quick players to use this ability after a four or five hit combo 
It seems the Marvel’s have gotten tired of their beams being dodged so easily and have decided to angle it a little better, increasing the overall range of the attack and making it harder to dodge away from  We’ve also increased the speed of both special attacks to allow them to better flow into combat 
In order to allow this attack to better flow in combat, we’ve shaved off a few frames from the beginning, allowing players to chain this attack into 4 and 5 hit combos 
Alliance Wars have arrived! It’s Alliance versus Alliance in a war for Battlerealm supremacy!
Enter the NEW Loyalty Store to buy Alliance Potions, Mastery items, or other EXCLUSIVE items 
Gain Power back from Special Attacks, enhance or defend against Special Attacks, OR gain a temporary Arena Point Boosts with hoards of new Summoner Boost items!
Additional changes and improvements are listed below 
This patch will be released February 24th 
A new area of the Battlerealm has been opened! Compete with your Alliance-mates for pride, glory, and PRIZES!
Matchmake to find a rival Alliance, then combine strategy and teamwork to dominate them 
Setup the ultimate defensive team to fortify your Battlerealm, then take your offensive team on the assault!
Watch your War Rating skyrocket as your Alliance works together to defeat rivals!
Load up on Crystal Shards, Loyalty, and brand new exclusive rewards!
Note that this will be slow-rolled to Alliances in phases, similar to the introduction of Alliance Quests (to ensure server stability and gather your feedback on the new mode)  Expect tuning changes throughout these phases, as well as into Season 1 
Use Loyalty instead of Units to obtain items for Alliance Quests & Wars!
Items will rotate daily, similar to how the Mastery cores in the current Store change 
Store contents will be randomly chosen from a pool of categories/items; a select few items will be persistent and always be available for purchase 
A 5-Star version of Unstoppable Colossus will be available in the Loyalty Store (keep in mind, this is an expensive Champion due to his exclusivity; this will require winning quite a few Alliance Wars and saving up!) 
This is accessible from the “Store” section of the pop-down menu, and will be available at a later date after the initial 7 0 launch; there will be advance notice through forums and in-game before we release the Loyalty Store 
New Summoner Boosts have arrived in the Loyalty Store; NEW Boost types, purchasable with Loyalty Points 
Class specific Boosts, such as Mystic Champions restoring power after using Special Attacks 2 and 3, or Skill Champions boosting their Special Attack Damage 
Defensive Boosts, where your Champions take reduced incoming Special 3 Attack Damage 
Gain a temporary Arena Point boost with new Arena Boost items!
Fixed an issue where, after Parrying certain Champion’s Special Attacks, your Champion would be stuck in a blocking state until the Special Attack finished 
Fixed an issue where 90s Cyclops’ Armor Breaks would not remove Armor Ups 
Fixed an issue with Scarlet Witch’s Signature Ability proc rate (previously, the % chance displayed did not match in-game functionality; this is now fixed) 
(Netflix) Daredevil’s Heavy Attack now has a chance to apply 2 stacks of Armor Break, instead of the previous 1 stack 
When spending Battlechips to enter an Arena (such as the Tier 4 Basic or Alpha Catalyst Arena), there is now a confirmation popup 
The Alliance Crystal now has a purchase limit that resets daily 
Permanently increased the Alliance Crystal’s points in Summoner Advancement (from 30 to 300) 
Updates to Champion Special Attack animations, flow, and timing 
7 0 1 will be released within the next few days 
A celebration message is sent to the War Room when an Alliance War battlegroup is cleared 
Players can now tap directly on another node icon while the tile info popup is open (previously, the popup had to be closed before selecting another node) 
Alliance’s reward tier position is now highlighted in the Alliance War tier breakdown 
In Attack Phase, players can view the score breakdown for both the battlegroup and overall 
The “Place Your Defenders” text now disappears much faster after tapping on the screen 
Mail messages now display the date they were sent 
It should be much harder to accidentally tap the Units Store when closing a screen 
Players can tap to skip the point animation in Versus mode again 
Resolved an issue with Class Masteries (specifically Mystic Dispersion) not functioning 
The Juggernaut issue with his linked nodes not appearing in Act 4, Chapter 3, Quest 3 (4 3 3) has been fixed 
Fixed a crash that occurs when a player who is not in an Alliance enters Alliance Wars through an outside link 
Fixed a text issue where Alliance War specific descriptions would appear on the Alliance Quest “Select a Battlegroup” screen 
Resolved ~20 various rare crashes and additional minor issues in different game modes 
Fixed and optimized performance on the new Samsung S7 
Fixed an Unknown Error that occurred rarely after a device was woken after going to sleep 
Improved Performance(Frames Per Second) tracking per fight to help diagnose hitches/pauses/lag spikes during gameplay 
Improved gesture tracking(Swipe, Tap, Hold) during low performance moments in combat 
Fixed a rare crash that would sometimes occur when receiving a phone call while in combat 
Tuned and updated many Champion Special Attack animations to improve timing and combat flow  Please see the expanded forum post HERE for a full list 
Fixed She-Hulk’s Special Attacks being marked as a projectile (allowing Daredevil to evade them) 
Fixed an issue where the player would be stuck in place after parrying Captain America’s Special 1 
Fixed an issue where chaining 2 medium attacks into Old Man Logan’s Special 2 would cause the first 2 strikes to miss opponents 
Fixed an issue with Daredevil or Spider-man missing with a dash attack if Vision charges a heavy attack during the dash 
Fixed an issue where some hidden information in Alliance Wars was visible 
Fixed a display issue where Defender Placement percentage was not displaying all placed Alliance members 
Resolved minor issue with the total Alliance’s score being displayed on the War Progress widget (now only displays the score of the battlegroup being viewed) 
Multiple minor Alliance War issues have also been fixed in this patch 
Fixed a display issue where Shard amounts provided by defeating a boss displayed as double 
Fixed a display issue where opponent PI values would display differently between the map, prefight screen, and in combat 
Boss power is now correctly displayed after removing Global and Linked boosts 
Fixed an issue where a player in Alliance Quests would lose input ability on the quest board after sleeping the device 
Fixed an issue where a player enters Alliance Quests and gets stuck after viewing the linked node or buff node tutorial 
Fixed an issue where sending an Alliance invite to a player would cause the “Add Friend” button to become greyed out 
Fixed a text issue that appears when viewing Featured Hero information from the Home Screen 
Join The Iron or fight for The Blue with new events, quests, Champions, and special Shards; inspired by Marvel’s Captain America: Civil War!
Solo Events: constantly-evolving events that vary in length, requirements, and prizes!
Compare statistics against other players and Alliances with the new Leaderboards!

Context 3: Bare Acts Live
Himachal Pradesh Town and Country Planning Act, 1977
Himachal Pradesh Town And Country Planning Rules, 1978
3  Form of Notice 
4  Manner of publication of notice 
5  Manner of publication of Regional Plan 
6  Notice of Modifications in Regional Plan 
7  Manner of publication of existing land-use map 
8  Manner of publication of approved Interim Development Plan 
9  Manner of publication of draft development plan 
10  Manner of publication of approved development plan 
11  Intention of development undertaken on behalf of Union or State Government 
12  Form of application for permission for development of land by others 
13  Form of permission 
14  Manner of communication of order under sub-section (4) of Section 31 
16  Notice by owner to purchase interest in land 
17  Manner of communication of revocation and modification permission to development 
20  Preparation of town development scheme 
21  Acquisition of land 
22  Mode of levy 
23  Power to borrow money 
24  Terms and conditions subject to which loans may be raised by the Special area Development Authority 
1  Short title, extent, commencement and application 
3  Director and other officers 
4  Establishment of regions 
5  Director to prepare regional plan 
6  Survey 
7  Contents of regional plan 
8  Preparation of regional plan 
9  Finalisation of regional plan 
10  Restriction on use of land or development thereof 
11  Exclusion from claims of amount in certain cases 
12  Review of regional plan 
13  Planning area 
14  Director to prepare development plans 
15  Existing land use maps 
16  Freezing of land use 
17  Interim development plans 
18  Development plan 
19  Publication of draft development plan 
20  Sanction of development plans 
21  Director to prepare sectoral plan 
22  Contents of sectoral plan 
23  Provisions of sections 19 and 20 to apply to sectoral plan 
24  Review of development plan and sectoral plan 
25  Director to control land use 
26  Conformity with development plan 
27  Prohibition of development without permission 
28  Development undertaken on behalf of Union or State Government 
29  Development by local authority or by any authority constituted under this Act 
30  Application for permission for development by others 
30A  Exemption from development permission in rural areas falling within Planning or Special Area 
30B  Exemption in respect of development of certain lands or buildings 
31  Grant or refusal of permission 
34  Lapse of permission 
35  Obligation to acquire land 
36  Deletion of reservation of designated land from draft or final development plan 
37  Power of revocation and modification or permission to development 
38  Penalty for unauthorised development or for use otherwise than in conformity with development plan 
39  Power to require removal of unauthorised development 
40  Establishment of Town and Country Development Authority 
41  Incorporation of Town and Country Development Authority 
42  Constitution of Town and Country Development Authority 
42A  Constitution of Town and Country Development Authority for the Capital Town of Himachal Pradesh 
43  Term of office of Chairman and other members 
44  Resignation of members and filling of casual vacancy 
45  Remuneration of Chairman 
46  Leave of absence and appointment etc  of acting Chairman 
47  Meeting of Town and Country Development Authority 
48  Chief Executive Officer 
49  Other officers and servants 
50  Conditions of service of Chief Executive Officer and other officers and servants 
51  Town development schemes 
53  Power to revise the development schemes 
54  Power of State Government to give Directions 
55  Restriction on land use and development 
56  Lapse of scheme 
57  Town development scheme public purpose 
58  Acquisition of land for Town and Country Development Authority 
59  Developments 
60  Disposal of land, buildings and other development works 
61  Development charges 
63  Fund of Town and Country Development Authority 
64  Annual budget 
66  Constitution of special areas 
67  Special area Development Authority 
68  Incorporation of Special Area Development Authority 
70  Functions 
71  Powers 
72  Fund of Special Area Development Authority 
73  Annual estimates 
74  Power of State Government of supervision and control 
76  Power of Government to review plans etc  for ensuring conformity 
78  Dissolution of authorities 
79  Right of entry 
80  Jurisdiction of Court 
82  Member and officers to be public servants 
83  Suit and other proceedings 
84  Vacancy not to invalidate proceedings 
85  Member to continue till successor enters upon office 
86  Interpretation of regional plan etc 
87  Powers to moke rules 
89  Power to lay the rules and regulations 
The Himachal Pradesh Town and Country Planning Act, 1977
(as amended by Amendment Act No  22 of 1983)
Amended by Act No  8 of 2009
Act published in the Rajpatra, Extraordinary, dated the 30th September, 1977 vide Law Department Notification No  LLR-D(6)5/77, dated the 22nd September, 1977 
An Act to make provision for planning and development and use of land; to make better provision for the preparation of development plans and sectoral plans with a view to ensuring that town planning schemes are made in a proper manner and their execution is made effective; to constitute the Town and Country and Development Authority for proper implementation of town and country development plan; to provide for the development and administration of special areas through the Special Area Development Authority; to make provision for the compulsory acquisition of land required for the purpose of the development plans and for purposes connected with the matters aforesaid 
Be it enacted by the Himachal Pradesh Legislative Assembly in the Twenty-eighth Year of the Republic of India as follows:-
1  Short title, extent, commencement and application  - (1) This Act may be called the Himachal Pradesh Town and Country Planning Act, 1977 
(3) It shall come into force on such date as the State Government may, by notification, appoint and different dates may be appointed for different areas and for different provisions of this Act 
(4) Nothing in this Act shall apply to-
(a) lands comprised within a cantonment under the Cantonments Act, 1924; (2 of 1924) 
(b) lands owned, hired or requisitioned by the Central Government for the purpose of naval, military and air force works;
(c) lands under the control of railway administration for the purpose of construction and maintenance of works under Chapter III of the Indian Railways Act, 1890; (9 of 1890) and
(d) lands owned by any department of the Central Government where operational constructions are going on 
(a) "agriculture" includes horticulture, farming, raising of annual or periodical crops, fruits, vegetables, flowers, grass, fodder, trees or any kind of cultivation of soil, the reserving of land for fodder, grazing or thatching areas, breeding and keeping of livestock including cattle, horses, donkeys, mules, pigs, breeding of fish and keeping of bees, and the use of land ancillary to the farming of land, but does not include-
(i) keeping of cattle purely for the purpose of milking and selling the milk and milk products,
(ii) a garden which is an appendage of buildings, and the expression "agricultural" shall be construed accordingly;
(b) "amenity" includes roads and streets, water and electric supply, open spaces, parks, recreational area, natural feature, playgrounds, street lighting, drainage, sewerage and other utilities, services and conveniences;
(c) "building" includes any structure or erection, or part of a structure or erection, which is intended to be used for residential, industrial, commercial or other purposes, whether in actual use or not;
(d) "building operation" includes-
(i) erection or re-erection of a building or any part thereof,
(ii) roofing or re-roofing of any part of building or an open space,
(iii) any material alteration or enlargement of a building,
(iv) any such alteration of a building as is likely to alter its drainage or sanitary arrangements, or materially affect its security,
(v) the construction of a door opening on any street or land not belonging to the owner;
(e) "commercial use" means the use of any land or building or part thereof for the purpose of carrying on any trade, business or profession, or sale or exchange of goods of any type whatsoever and includes running of with a view to make profit hospitals, nursing homes, infirmaries, educational institutions, hostels, restaurants and boarding houses not being attached to any educational institutions, sarais and also includes the use of any land or building for storage of goods or as buildings for storage of goods or as an office whether attached to an industry or otherwise;
(f) "court" means the principal civil court of original jurisdiction in the district;
(g) "development" with its grammatical variations means the carrying out of a building, engineering, mining or other operations in, on, over or under land, or the making of any material change in any building or land or in the use of either, and includes sub-division of any land;
(h) "development plan" means interim development plan or development plan prepared under this Act;
(i) "director" means the Director of Town and Country Planning appointed under this Act;
(j) "existing land use map� means a map indicating the use to which lands in any specified area are put at the time of preparing the map, and includes the register prepared, with the map giving details of land-use;
(k) "land" includes benefits to arise out of land and things attached to the earth or permanently fastened to anything attached to the earth;
(l) "member" means a member of a Town and Country Development Authority or a Special Area Development Authority, as the case may be, and includes a Chairman thereof;
(m) "occupier" includes-
(i) a tenant,
(ii) an owner in occupation of or otherwise using his land,
(iii) a rent free tenant,
(iv) a licensee, and
(v) any person liable to pay to the owner, damages for the use and occupation of the land;
(n) "owner" includes a mortgagee in possession, a person who for the time being is receiving or is entitled to receive, or has received, the rent or premium for any land whether on his own account or on behalf of or for the further benefit of any other person or as an agent, trustee, guardian or receiver for any other person or for religious or charitable institutions or who would receive the rent or be entitled to receive the rent or premium if the land were to be let and includes a head of a Government department, General Manager of a Railway and the Chief Executive Officer, by whatever name designated, or a local authority, statutory authority, company, corporation or undertaking in respect of properties under their control;
(o) "planning area" means any area declared to be planning area under this Act;
(p) "region" means any area established to be a region under this Act;
(q) "regional plan" means a plan for the region prepared under this Act and approved by the State Government;
(r) "sector" means any sector of a planning area for which, under the development plan, a detailed sectoral plan is prepared;
(s) "slum area" means any predominantly residential area, where the dwellings which by reason of dilapidation, over-crowding, faulty arrangement of design, lack of ventilation, light or sanitary facilities or any combination of these factors are detrimental to safety, health or moral and which is defined by a development plan as a slum area;
(t) "special area" means a special area designated as such under section 66;
(u) "Special Area Development Authority� means an authority constituted under section 67;
(v) "Town Development Scheme" means a scheme prepared for the implementation of the provisions of a development plan by the Town and Country Development Authority; and
(w) "Town and Country Development Authority" means an authority established under section 40 
Director of Town and Country Planning
3  Director and other officers  - (1) After the commencement of this Act the State Government shall, by notification in the Official Gazette, appoint an officer for the purpose of carrying out functions assigned to him under this Act, as the Director of Town and Country Planning for the State and may appoint such other categories of officers as it may deem fit 
(2) The Director shall exercise such powers and perform such duties as are conferred or imposed upon him by or under this Act and the officers appointed to assist the Director shall, within such area as the State Government may specify, exercise such powers and perform such duties conferred and imposed on the Director by or under this Act as the State Government may, by special or general order, direct 
(3) The officers appointed to assist the Director shall be subordinate to him and shall work under his guidance, supervision and control 
4  Establishment of regions  - (1) The State Government may, by notification,-
(a) declare any area in the State to be a region for the purposes of this Act;
(b) define the limits of such area; and
(c) specify the name by which such region shall be known 
(2) The State Government may, by notification, alter the name of any such region and on such alteration, any reference in any law or instrument or other document to the region shall be deemed to be a reference to the region as re-named unless expressly otherwise provided or the context so requires 
(3) The State Government may, by notification,-
(a) alter the limits of a region so as to include therein or exclude therefrom Such area as may be specified in the notification;
(b) amalgamate two or more regions so as to form one region;
(c) divide any region into two or more region; or
(d) declare that the whole or part of the area comprising a region shall cease to be a region or part thereof 
5  Director to prepare regional plan  - Subject to the provisions of this Act and the rules made thereunder, it shall be the duty of the Director-
(i) to carry out a survey of the regions;
(ii) to prepare an existing land use map; and
(iii) to prepare a regional plan 
6  Survey  - (1) The Director shall, with a view to prepare the existing land use map, and other maps as are necessary for the purpose of regional plan,-
(a) carry out such surveys as may be necessary;
(b) obtain from any department of Government and any local authority such maps, survey reports and land records as may be necessary for the purpose 
(2) It shall be the duty of every Government department and local authority to furnish, as soon as may be possible, maps, reports and record, as may be required by the Director 
7  Contents of regional plan  - The regional plan shall indicate the manner in which land in the region should be used, the phasing of development, the net work of communications and transport, the proposals for conservation and development of natural resources, and in particular-
(a) allocation of land to such purposes as residential, industrial; agricultural or as forests or for mineral exploitation;
(b) reservation of open spaces for recreational purposes, gardens, tree belts, and animal sanctuaries;
(c) access or development of transport and communication facilities such as roads, railways, water ways, and the allocation and development of airports;
(d) requirements and suggestions for development of public utilities such as water supply, drainage and electricity;
(e) allocation of areas to be developed as "Special Areas� wherein new towns, townships, large industrial estates or any other type of large development projects may be established;
(f) landscaping and the preservation of areas in their natural state,
(g) measures relating to the prevention of erosion, including rejuvenation of forest areas;
(h) proposals relating to irrigation, water supply or flood control works 
8  Preparation of regional plan  - (1) After preparation of the existing land use map, the Director shall cause to be prepared a draft regional plan and publish it by making a copy thereof available for inspection and publishing a notice in such form and manner as may be prescribed inviting objections and suggestions from any person with respect to the draft plan before such date as may be specified in the notice, such date not being earlier than sixty days from the publication of the notice  Such notice shall specify in regard to the draft plan the following particulars, namely-
(a) the existing land use map and the narrative report thereon;
(b) a narrative report supported by necessary map and charts explaining the provisions of the draft plan;
(c) a note indicating the priorities assigned to works included in the draft plan and the phasing of the programme of development as such;
(d) a notice on the role being assigned to different departments of Government, the Town and Country Development Authorities; the Special Area Development Authorities, and the Local Authorities in the enforcement and implementation of draft plan 
(2) The Director shall consider all the objections and suggestions received by him within the period specified in the notice under sub-section (1) and shall, after giving a reasonable opportunity to all persons affected thereby of being heard, prepare the regional plan containing such modifications, if any, as he considers necessary and submit it to the State Government for approval together with all connected documents, plans, maps and charts 
9  Finalisation of regional plan  - (1) The State Government may approve the draft regional plan submitted under section 8 with or without modification or reject or return the same to the Director for reconsideration 
(2) Immediately after the draft regional plan is approved under sub-section (1) the State Government shall publish in such manner, as may be prescribed, a notice stating that the regional plan has been approved and mentioning a place where a copy of the plan may be inspected at all reasonable hours and shall specify therein a date on which the regional plan shall come into operation:
Provided that where the State Government approves the draft regional plan with modifications, it shall not be published, unless the State Government having published such modifications in the Official Gazette along with a notice inviting objections and suggestions thereon, within a period of not less than thirty days from the date of publication of such notice have considered the objections and suggestions after giving a reasonable opportunity of being heard to persons affected thereby 
10  Restriction on use of land or development thereof  - (1) Notwithstanding anything contained in any other law for the time being in force, on or after the date of publication of the draft regional plan, no person, authority, department of Government or any other person shall change the use of land for any purpose other than agriculture, or carry out any development in respect of any land contrary to the provisions of the draft plan, without the prior approval of the Director or any officer next to him authorised by the Director, in this behalf 
(2) Notwithstanding anything contained in any law for the time being in force, the permission referred to in sub-section (1) shall not be granted otherwise than in conformity with the provision of the draft or final plan and no permission, if granted, shall be construed to confer any legal right whatsoever on the person seeking the permission 
(3) If any work is carried out in contravention of the provisions of this section, the Municipal Corporation or Municipal Committee within its local area, and the Collector in area outside such local areas, may cause such work to be removed or demolished at the cost of the defaulter, which shall be recovered from him in the same manner as an arrear of land revenue:
Provided that no action shall be taken under this sub-section unless the person concerned is given a reasonable opportunity of being heard and a notice calling upon him to remove or demolish the work within a time specified therein 
(4) Any person aggrieved by the order of the Municipal Corporation, Municipal Committee or Collector, as the case may be, calling upon to remove or demolish the work may prefer an appeal to the Director within fifteen days of the receipt of the notice under sub-section (3) and the order of the Director in such appeal shall be final 
11  Exclusion from claims of amount in certain cases  - Where the regional plan assigns a particular land use to a certain areas and any land situate therein is already put to such use, subject to substantially similar restrictions in force under any other law which was in force on the date on which restrictions were imposed by or under this Act and if amount in respect of such restrictions have already been paid under any such other law which was in force for the time being in respect of the property or any right or interest therein to the claimant, or any predecessor in interest of the claimant, the owner shall not be entitled to any further amount on account of injury or damage caused to his rights by reasons of the restrictions placed on the use of the land under the provisions of this Act 
12  Review of regional plan  - (1) The Director may, on his own motion or if so required by the State Government, at any time after a regional plan has come into operation, undertake the review and evaluation of the regional plan and make such modification in it as may be justified by the circumstances 
(2) The foregoing provisions of this Chapter shall, so far as they can be made applicable, apply to the modifications under sub-section (1) as these provisions apply in relation to the preparation, publication and approval of a regional plan 
Planning Area and Development Plans
13  Planning area  - (1) The State Government may, by notification, constitute planning areas for the purposes of this Act and define the limits thereof 
(2) The State Government may, by notification -
(a) alter the limits of a planning area so as to include therein or excluse therefrom such area as may be specified in the notification;
(b) amalgamate two or more planning areas so as to constitute one planning area;
(c) divide any planning area into two or more planning areas;
(d) declare that the whole or part of the area constituting the planning area shall cease to be a planning area or part thereof 
14  Director to prepare development plans  - Subject to the provisions of this Act and the rules made thereunder, the Director shall-
(a) prepare an existing land use map;
(b) prepare an interim development plan;
(c) prepare a development plan;
(d) prepare a sectoral plan;
(e) carry such surveys and inspections and obtain such pertinent reports from government departments, local authorities and public institutions as may be necessary for the preparation of the plans;
(f) perform such duties and functions as are supplemental, incidental, and consequential to any of the foregoing functions or as may be assigned by the State Government for the purpose of carrying out the provisions of this Act 
15  Existing land use maps  - (1 )The Director shall carryout the survey and prepare an existing land use map and, forthwith publish the same in such manner as may be prescribed together with public notice of the preparation of the map and of the place or places where the copies may be inspected, inviting objections and suggestions in writing from any person with respect thereto within thirty days from the date of publication of such notice 
(2) After the expiry of the period specified in the notice published under sub-section (1), the Director may, after allowing a reasonable opportunity of being heard to all such persons who have filed the objections or suggestions, make such modifications therein as may be considered desirable 
(3) As soon as may be after the map is adopted with or without modifications the Director shall publish a public notice of the adoption of the map and the place or places where the copies of the same may be inspected 
(4) A copy of the notice shall also be published in the Official Gazette and it shall be conclusive evidence of the fact that the map has been duly prepared and adopted 
16  Freezing of land use  - On the publication of the existing land use map under section 15-
(a) no person shall institute or change the use of any land or carry out any development of land for any purpose other than that indicated in the existing land use map without the permission in writing of the Director;
Provided that the Director shall not refuse permission if the change is for the purpose of agriculture;
(b) no local authority or any officer or other authority shall, not withstanding anything contained in any other law for the time being in force, grant permission for the change in use of land otherwise than as indicated in the existing land use map without the permission in writing of the Director;
[(c) no Registrar or the Sub-Registrar, appointed under the Indian Registration Act, 1908, shall, in any planning area constituted under section 13, register any deed or document of transfer of any sub-division of land by way of sale, gift, exchange, lease or mortgage with possession, unless the sub-division of land is duly approved by the Director, subject to such rules as may be framed in this behalf by the State Government:]
Provided that the Registrar or the Sub-Registrar may register any transfer,-
(i) where the land is owned by a person and the transfer is made without involving any further divisions;
(ii) where the partition/sub-division of land is made in a Joint Hindu Family;
(iii) where the lease is made in relation to a part or whole of a building;
(iv) where the mortgage is made for procuring the loans for construction or improvements over the land either from the Government or from any other financial institution constituted or established under any law for the time being in force or recognised by the State Government 
17  Interim development plans  - As soon as may be, after the declaration of a planning area, the Director shall, within such time as may be necessary, prepare, after consultation with local authorities concerned, if any, and submit to the State Government an interim development plan for the planning area or any of its parts and such other area or areas contiguous or adjacent to the planning areas as the State Government may direct to be included in the interim development plan 
(2) The interim development plan shall-
(a) indicate broadly the land use proposed in the planning area;
(b) allocate broadly areas or sector of land for-
(i) residential, industrial, commercial or agricultural purposes,
(ii) open spaces, parks and gardens, green belts, zoological gardens and play-grounds,
(iii) public institutions and offices,
(iv) such special purposes as the Director may deem fit;
(c) lay down the pattern of National and State Highways connecting the planning area with the rest of the region, ring roads, arterial roads and the major roads within the planning areas;
(d) provide for the location of airports, railway stations, bus termini and indicate the proposed extension and development of railways and canals;
(e) make proposals for general land scaping and preservation of natural areas;
(f) project the requirement of the planning area of such amenities and utilities as water, drainage, electricity and suggest their fulfilment;
(g) propose broad based regulations for sectoral development, by way of guide-lines, within each sector of the location, height, size of buildings and structures, open spaces, court-yards and the use to which such buildings and structures and land may be put;
(h) lay down the board-based traffic circulation patterns in a city;
(i) suggest architectural control features, elevation and frontage of buildings and structures;
(j) indicate measures for flood control, prevention of air and water pollution, disposal of garbage and general environmental control 
(3) Subject to provisions of the rules made under this Act for regulating the form and contents of the interim development plan any such plan shall include such maps and such descriptive matter as may be necessary to explain and illustrate the proposals in the interim development plan 
(4) As soon as may be, after the submission of the interim development plan, under sub-section (1) the State Government may either approve the interim development plan or may approve it with such modification as it may consider necessary 
(5) The State Government shall publish the interim development plan as approved under sub-section (4) in the Official Gazette  The interim development plan shall come into operation from the date of its publication in the Official Gazette and shall be binding on all local authorities functioning within the planning areas 
18  Development plan  - A development plan shall -
(a) indicate broadly the land use proposed in the planning areas;
(b) allocate broadly areas or sector of land for,-
(c) lay down the pattern of National and State Highways connecting the planning area with the rest of the region, ring roads, arterial roads, and the major roads within the planning area;
(d) provide for the location of airports, railway stations, bus termini and indicate the proposed extension and development of railways;
(g) propose broad-based regulations for sectoral development, by way of guide-line, within each sector of the location, height, size of buildings and structures, open spaces, court-yards and the use to which such buildings and structures and land may be put;
(h) lay down the broad-based traffic circulation patterns in a city;
19  Publication of draft development plan  - (1) The Director shall forthwith publish the draft development plan prepared under section 18 in such manner as may be prescribed together with a notice of the preparation of the draft development plan and the place or places where the copies may be inspected, inviting objections and suggestions in writing from any person with respect thereto, within thirty days from the date of publication of such notice Such notice shall specify in regard to the draff development plan the following particulars, namely:-
(i) the existing land use maps;
(ii) a narrative report, supported by maps and charts, explaining the provisions of the draft development plan;
(iii) the phasing of implementation of the draft development plan as suggested by the Director,
(iv) the provisions for enforcing the draft development plan and stating the manner in which permission to development may be obtained;
(v) an approximate estimate of the cost of land acquisition for public purposes and the cost of works involved in the implementation of the plan 
(2) The Director shall, not later than ninety days after the date of expiry of the notice period under sub-section (1), consider all the objections and suggestions as may be received within the period specified in the notice under sub-section (1)and shall, after giving reasonable opportunity to all persons affected thereby of being heard, make such modifications in the draft development plans as he may consider necessary, and submit, not later than six months after the publication of the draft development plan, the plan so modified, to the State Government for approval together with all connected documents, plans, maps and charts 
20  Sanction of development plans  - (1) As soon as may be after the submission of the development plan under section 19 the State Government may either approve the development plan or may approve it with such modifications as it may consider necessary or may return it to the Director to modify the same or to prepare a fresh plan in accordance with such directions as it may issue in this behalf 
(2) Where the State Government approves the development plan with modifications, the State Government shall, by a notice, published in the Official Gazette, invite objections and suggestions in respect of such modifications within a period of not less than thirty days from the date of publication of the notice in the Official Gazette 
(3) After considering objections and suggestions and after giving a hearing to the persons desirous of being heard the State Government may confirm the modification in the development plan 
(4) The State Government shall publish the development plan as approved, under the foregoing provisions in the Official Gazette and shall along with the plan publish a public notice, in such manner as may be prescribed, of the approval of the development plan and the place or places where the copies of the approved development plan may be inspected 
(5) The development plan shall come into operation from the date of publication thereof in the Official Gazette and as from such date shall be binding on all Development Authorities constituted under this Act and all local authorities functioning within the planning area 
(6) After the coming into operation of the development plan, the interim development plan shall stand modified or altered to the extent the proposals in the development plan are at variance with the interim development plan 
Sectoral Plan
21  Director to prepare sectoral plan  - The Director may, on his own motion, at any time after the publication of the development plan, or thereafter if so required by the State Government shall, within six months of such requisition, prepare a sectoral plan 
22  Contents of sectoral plan  - (1) The sectoral plan shall enlarge the details of land use as indicated in the development plan and shall -
(a) indicate the land liable to acquisition for public purpose or the purposes of the Union Government, the State Government, the Town and Country Development Authority, the Special Area Development Authority, the local authority or any other authority established by or under any enactment for the time being in force 
Provided that no land shall be so designated unless the acquisition proceedings are likely to be completed within ten years of the preparation of the plan;
(b) define in detail and provide for areas reserved for agriculture, public and semi-public open spaces, parks, playgrounds, gardens, recreational areas, green belts and natural reserves;
(c) allocate in detail areas or sectors for residential, commercial, industrial, agricultural and other purposes;
(d) define and provide for the complete road and street pattern for the present and in the future and indicate the traffic circulation;
(e) lay down in detail the projected road and street improvement;
(f) indicate and provide for areas reserved for public buildings, institutions and civic developments;
(g) assess, make projections for and provide for the future requirements of amenities, services and utilities such as municipal, transport, electricity, water and drainage;
(h) prescribe in detail the sectoral regulations for each sector, with a view to facilitating on individual layout and regulating the location, height, number of storeys and the size of buildings and other structures, the size of the court-yards, courts and other open spaces and the use of the buildings, structures and land;
(i) define areas which have been badly laid out or areas which have developed so as to form slums, and provide for their proper development and/or relocation;
(j) designate areas for future development and expansion;
(k) indicate the phasing of the programme of development 
(2) The sectoral plan may and if possible shall, indicate -
(a) control over architectural features; elevation and frontage of buildings and structures; and
(b) the details of development of specific areas for housing, shopping centres, industrial areas, educational and cultural institutions and civic centres 
23  Provisions of sections 19 and 20 to apply to sectoral plan  - The provisions of sections 19 and 20 shall apply for the preparation, publication, approval and operation of sectoral plan as they apply in respect of the development plan 
24  Review of development plan and sectoral plan  - The Director may on his own motion or if so required by the State Government shall, at any time after the sectoral plan has come into operation, undertake a review and evaluation of the development plan and sectoral plan 
(2) The foregoing provisions of sections 19, 20 and 23 shall, so far as may be apply to the modification under sub-section (1) as those provisions apply in relation to the preparation, publication and approval of a development plan or a sectoral plan 
Control of Development And Use of Land
25  Director to control land use  - The overall control of development and the use of land in the planning area shall, as from the date of publication in the Official Gazette of a notification by the State Government, vest in the Director 
26  Conformity with development plan  - (1) After coming into force of the development plan, the use and development of land shall conform to the provisions of the development plan:
Provided that the Director may, at his discretion, permit the continued use of land for the purpose for which it was being used at the time of the coming into Operation of the development plan 
Provided further that such permission shall not be granted for a period exceeding seven years from the date of coming into operation of the development plan 
27  Prohibition of development without permission  - After coming into operation of the development plan, no person shall change the use of any land or carry out any development of land without the permission in writing of the Director 
Provided that no such permission shall be necessary -
(a) for carrying out works for the maintenance, repair or alteration of any building which does not materially alter the external appearance of the building;
(b) for carrying out work for the improvement or maintenance of a highway, road or public street by the Union or State Government or an authority established under this Act or by a local authority having jurisdiction, provided that such maintenance or improvement does not change the road alignment contrary to the provisions of the development plan;
(c) for the purpose of inspecting, repairing or renewing any drain, sewers, mains, pipes, cables, telephone or other apparatus including the breaking open of any street or other land for that purpose;
(d) for the excavation or soil shaping in the interest of agriculture;
(e) for restoration of land to its normal use where land has been used temporarily for any other purposes 
(f) for use for any purpose incidental to the use of building for human habitation, or any other building or land attached to such buildings;
(g) for the construction of a road intended to give access to land solely for agricultural purposes
28  Development undertaken on behalf of Union or State Government  - (1) When the Union Government or the State Government intends to carry out development of any land for the purpose of its departments or offices or authorities, the officer-in-charge thereof shall inform in writing to the Director the intention of the Government to do so, giving full particulars thereof, accompanied by such documents and plans as may be prescribed at least thirty days before undertaking such development 
(2) Where the Director raises any objection to the proposed development on the ground that the development is not in conformity with the provisions of the development plan, the officer shall,-
(i) make necessary modification in the proposals for development to meet the objections raised by the Director, or
(ii) submit the proposal for development together with the objections raised by the Director to the State Government for decision:
Provided that where no modification is proposed by the Director within thirty days of the receipt of the proposed plan by the Government, the plan will be presumed to have been approved 
(3) The State Government, on receipt of the proposals for development together with the objections of the Director shall, approve the proposals with or without modifications or direct the officer to make such modifications in the proposals as it considers necessary in the circumstances 
(4) The decision of the State Government under sub-section (3) shall be final and binding 
29  Development by local authority or by any authority constituted under this Act  - Where a local authority or any authority specially constituted under this Act intends to carry out development on any land for the purpose of that authority, the procedure applicable to the Union or State Government, under section 28 shall, mutatis' mutandis, apply in respect of such authority 
30  Application for permission for development by others  - (1) Any person, not being the Union Government, State Government, a local authority or a special authority constituted under this Act intending to carry out any development on any land, shall make an application in writing to the Director for permission, in such form and containing such particulars and accompanied by such documents as may be prescribed 
(2) Such application shall also be accompanied by such fee as may be prescribed 
[30A  Exemption from development permission in rural areas falling within Planning or Special Area  - (1) Any person who owns land in rural areas, falling within Planning or Special Areas wherein neither Interim Development Plan nor Development Plan has been notified, shall be exempted from permission under this Act for the following development activities up to the limits as may be prescribed: -
(i) Residential activities such as farm-houses and residential houses up to three storeys, cattle shed, toilet, septic tank, kitchen, store, parking shed or garage and rain shelter;
(ii) Commercial activities such as basic commercial activities like shops of general merchandise, cobbler, barber, tailoring, fruit, vegetable, tea or sweet, eating places and dhabas, chemist and farm produce sale depot;
(iii) Service Industries such as cottage or house-hold, service industries like carpentry, knitting, weaving, blacksmith, goldsmith, atta-chakki with capacity up to five horse-power, water mill, agriculture equipments or machinery repair, electrical, electronic and house-hold appliances;
(iv) Public amenities such as public amenities like panchayat offices, schools, mahila mandals, yuvak mandals, community halls, post offices, dispensaries and clinics (including health, veterinary and Indian System of Medicines) information technology kiosks, patwar khanas, guard huts, anganwaries, electricity and telephone installations and connections, roads and paths, ropeways, water tanks, rain harvesting tanks, overhead or underground water tan 



ground_truth: Players can skip dialogue on the quest map by pressing the 'SKIP' button.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: Who is responsible for carrying out the functions assigned under the act?

Read the following text and answer briefly.

Context 4:  The process is repeated for all the couplings obtaining then a fully connected adjacency matrix  The results here presented are obtained with $\lambda = 0 01$ 
   For the minimization we have used the MATLAB routine \emph{minFunc\_2012}\cite{min_func}  
      
      \begin{figure}[t!]
    	\centering
    	\includegraphics[width=1\linewidth]{Jor11_2D_l2_JR_soJR_TPJR}
    	\caption{Top panels: instances of single site coupling reconstruction for the case of $N=64$ XY spins on a 2D lattice with ordered $J$ (left column) and bimodal distributed $J$ (right column)  
    	
    	Bottom panels: sorted couplings }
    	\label{PL-Jor1}
    \end{figure}

   
To produce the data by means of numerical Monte Carlo simulations a system with $N=64$  spin variables  is considered on a deterministic 2D lattice with periodic boundary conditions  
Each spin has then connectivity $4$, i e , we expect to infer an adjacency matrix with $N c = 256$ couplings different from zero  
The dynamics of the simulated model is based on the Metropolis algorithm and parallel tempering\cite{earl05} is used to speed up the thermalization of the system 
The thermalization is tested looking at the average energy over logarithmic time windows and
the acquisition of independent configurations
starts only after the system is well thermalized 

   For the values of the couplings we considered two cases: an ordered case, indicated in the figure as  $J$ ordered (e g , left column of Fig  \ref{PL-Jor1}) where the couplings can take values $J_{ij}=0,J$, with $J=1$, 
   and a quenched disordered case, indicated in the figures as  $J$ disordered (e g , right column of Fig  \ref{PL-Jor1})
   where the couplings can take also  negative values, i e , 
    $J_{ij}=0,J,-J$, with a certain probability   The results here presented were obtained with bimodal distributed $J$s: 
   
    $P(J_{ij}=J)=P(J_{ij}=-J)=1/2$   The performances of the PLM have shown not to depend on $P(J)$  
   
    We recall that in Sec  \ref{sec:plm} we used the temperature-rescaled notation, i e , $J_{ij}$ stands for $J_{ij}/T$  
   
    To analyze the performances of the PLM, in Fig  \ref{PL-Jor1} the inferred couplings, $\mathbb{J}^R_{\rm inf}$, are shown on top of the original couplings,  $\mathbb{J}^R_{\rm true}$ 
     The first figure (from top) in the left column shows  the $\mathbb{J}^R_{\rm inf}$ (black) and the $\mathbb{J}^R_{\rm tru}$ (green) for a given spin
     at temperature $T/J=0 7$ and number of samples  $M=1024$  PLM appears to reconstruct the correct couplings, though zero couplings are always given a small inferred non-zero value  
     In the left column of Fig   \ref{PL-Jor1},  both the $\mathbb{J}^R_{\rm{inf}}$ and the $\mathbb{J}^R_{\rm{tru}}$ are sorted in decreasing order and plotted on top of each other  
     We can clearly see that $\mathbb{J}^R_{\rm inf}$ reproduces the expected step function  Even though the jump is smeared, the difference between inferred couplings corresponding to the set of non-zero couplings 
     and to the set of zero couplings can be clearly appreciated 
     Similarly, the plots in the right column of Fig  \ref{PL-Jor1} show the results obtained for the case with  bimodal disordered couplings, for the same working temperature and number of samples  
     In particular, note that the algorithm infers half positive and half negative couplings, as expected 
     
     
\begin{figure}
\centering
\includegraphics[width=1\linewidth]{Jor11_2D_l2_errJ_varT_varM}
\caption{Reconstruction error $\mbox{err}_J$, cf  Eq  (\ref{eq:errj}), plotted as a function of temperature (left) for three values of the number of samples $M$ and  as a function $M$ (right) for three values of temperature in the ordered system, i e , $J_{ij}=0,1$  
The system size is $N=64$ }
\label{PL-err-Jor1}
\end{figure}

In order to analyze the effects of the number of samples and of the temperature regimes, we plot in Fig  \ref{PL-err-Jor1} the reconstruction error, Eq  (\ref{err}), as a function of temperature for three different sample sizes $M=64,128$ and $512$  
The error is seen to sharply rise al low temperature, incidentally, in the ordered case, for  $T<T_c \sim 0 893$, which is the Kosterlitz-Thouless transition temperature of the 2XY model\cite{Olsson92}  
 However, we can see that if only $M=64$ samples are considered, $\mbox{err}_J$ remains high independently on the working temperature  
 In the right plot of Fig  \ref{PL-err-Jor1},  $\mbox{err}_J$ is plotted as a function of $M$ for three different working temperatures $T/J=0 4,0 7$ and $1 3$  As we expect, 
 $\mbox{err}_J$  decreases as $M$ increases  This effect was observed also with mean-field inference techniques on the same model\cite{Tyagi15} 

To better understand the performances of the algorithms, in Fig  \ref{PL-varTP-Jor1} we show several True Positive (TP) curves obtained for various values of $M$ at three different temperatures $T$  As $M$ is large and/or temperature is not too small,  we are able to reconstruct correctly all the couplings present in the system (see bottom plots) 
The True Positive curve displays how many times the inference method finds a true link of the original network  as a function of the index of the vector of sorted absolute value of reconstructed couplings $J_{ij}^{\rm inf}$  
The index $n_{(ij)}$ represents the related spin couples $(ij)$  The TP curve is obtained as follows: 
first  the values $|J^{\rm inf}_{ij}|$ are sorted in descending order and  the spin pairs $(ij)$ are ordered according to the sorting position of $|J^{\rm inf}_{ij}|$  Then,
     	a cycle over the ordered set of pairs $(ij)$, indexed by $n_{(ij)}$, is performed, comparing with the original network coupling $J^{\rm true}_{ij}$ and verifying whether it is zero or not  The true positive curve is computed as
\begin{equation}
\mbox{TP}[n_{(ij)}]= \frac{\mbox{TP}\left[n_{(ij)}-1\right] (n_{ij}-1)+ 1 -\delta_{J^{\rm true}_{ij},0}}{n_{(ij)}}
\end{equation}
As far as $J^{\rm true}_{ij} \neq 0$, TP$=1$  As soon as the true coupling of a given $(ij)$ couple in the sorted list is zero, the TP curve departs from one  
In our case, where the connectivity per spin of the original system is  $c=4$ and there are $N=64$ spins, we know that we will have  $256$ non-zero couplings   
     	If the inverse problem is successful, hence, we expect a steep decrease of the TP curve when  $n_{ij}=256$ is overcome 

In Fig  \ref{PL-varTP-Jor1}
it is  shown that,  almost independently of $T/J$, the TP score improves as $M$ increases  Results are plotted for three different temperatures, $T=0 4,1$ and $2 2$, with increasing number of samples $M = 64, 128,512$ and $1024$ (clockwise)  
We can clearly appreciate the improvement in temperature if the size of the data-set is not very large: for small $M$, $T=0 4$ performs better  
When $M$ is high enough (e g , $M=1024$), instead, the TP curves do not appear to be strongly influenced by the temperature 

\begin{figure}[t!]
	\centering
	\includegraphics[width=1\linewidth]{Jor11_2D_l2_TPJR_varT_varM}
	\caption{TP  curves  for 2D short-range ordered $XY$ model with $N=64$ spins at three different values of $T/J$ with increasing - clockwise from top - $M$ }
	\label{PL-varTP-Jor1} 
\end{figure} 

\subsection{$XY$ model with complex-valued couplings}
For the complex $XY$ we have to contemporary  infer $2$ apart coupling matrices,  $J^R_{i j}$ and $J^I_{i j}$   As before, a system of $N=64$ spins is considered on a 2D lattice 
For the couplings we have considered both ordered and bimodal disordered cases 
In Fig  \ref{PL-Jor3}, a single row of the matrix $J$ (top) and the whole sorted couplings (bottom) are displayed for the ordered model (same legend as in Fig  \ref{PL-Jor1}) for the real, $J^R$ (left column), and the imaginary part, $J^I$   

\begin{figure}[t!]
	\centering
\includegraphics[width=1\linewidth]{Jor3_l2_JRJI_soJRJI_TPJRJI}
	\caption{Results related to the ordered complex XY model with $N=64$ spins on a  2D lattice  Top: instances of  single site reconstruction for the real, JR (left column), and
		the imaginary, JI (right column), part of $J_{ij}$  Bottom: sorted values of JR (left) and JI (right) }
		
	\label{PL-Jor3}
\end{figure}
 
 
  \section{PLM with Decimation}
 \label{sec:res_dec}
 

\begin{figure}[t!]
   	\centering
   	\includegraphics[width=1\linewidth]{Jor1_dec_tPLF_varT_varM}
    	\caption{Tilted Pseudolikelyhood, ${\cal L}_t$, plotted as a function of decimated couplings  Top: Different ${\cal L}_t$ curves obtained for different values of $M$ plotted on top of each other  Here $T=1 3$  The black line indicates the expected number of decimated couplings, $x^*=(N (N-1) - N c)/2=1888$  As we can see, as $M$ increases, the maximum point of ${\cal L}_t$ approaches $x^*$  Bottom: Different ${\cal L}_t$ curves obtained for different values of T with $M=2048$  We can see that, with this value of $M$, no differences can be appreciated on the maximum points of the different  ${\cal L}_t$ curves }
   	\label{var-$t$PLF}
   \end{figure}

\begin{figure}[t!]
    \centering
    \includegraphics[width=1\linewidth]{Jor1_dec_tPLF_peak_statistics_varM_prob eps}
    	\caption{Number of most likely decimated couplings, estimated by the maximum point of $\mathcal{L}_t$, as a function of the number of samples $M$  We can clearly see that the maximum point of $\mathcal{L}_t$ tends toward $x^*$, which is the right expected number of zero couplings in the system }  
    	\label{PLF_peak_statistics}
    \end{figure}
      
      For the ordered real-valued XY model we show in Fig  \ref{var-$t$PLF}, top panel, the outcome on the tilted pseudolikelyhood, $\mathcal{L}_t$ Eq  \eqref{$t$PLF}, of the progressive decimation: from a fully connected lattice  down to an empty lattice  The figure shows the behaviour of $\mathcal{L}_t$ for three different data sizes $M$  A clear data size dependence of the maximum point of  $\mathcal{L}_t$, signalling the most likely value for decimation, is shown  For small $M$ the most likely number of  couplings is overestimated and for increasing $M$ it tends to the true value, as displayed in Fig  \ref{PLF_peak_statistics}   In the bottom panel of Fig  \ref{var-$t$PLF} we display instead different 
 $\mathcal{L}_t$ curves obtained for three different values of $T$ 
  Even though the values of $\mathcal{L}_t$ decrease with increasing temperature, the value of the most likely number of decimated couplings appears to be quite independent on $T$ with $M=2048$ number of samples 
In Fig  \ref{fig:Lt_complex} we eventually display the tilted pseudolikelyhood for a 2D network with complex valued ordered couplings, where the decimation of the real and imaginary coupling matrices proceeds in parallel, that is, 
when a real coupling is small enough to be decimated its imaginary part is also decimated, and vice versa 
One can see that though the apart errors for the real and imaginary parts are different in absolute values, they display the same dip, to be compared with the maximum point of $\mathcal{L}_t$ 
     
       \begin{figure}[t!]
    	\centering
      	\includegraphics[width=1\linewidth]{Jor3_dec_tPLF_new}
      	\caption{Tilted Pseudolikelyhood, ${\cal L}_t$, plotted with the reconstruction errors for the XY model with $N=64$ spins on a 2D lattice  These results refer to the case of  ordered and complex valued couplings  The full (red) line indicates ${\cal L}_t$  The dashed (green) 
      		and the dotted (blue) lines show the reconstruction errors (Eq  \eqref{eq:errj}) obtained for the real and the imaginary couplings respectively  We can see that both ${\rm err_{JR}}$ and ${\rm err_{JI}}$ have a minimum at $x^*$ }
          	\label{fig:Lt_complex}
    \end{figure}

\begin{figure}[t!]
   	\centering
   	\includegraphics[width=1\linewidth]{Jor1_dec_JR_soJR_TPJR}
   	\caption{XY model on a 2D lattice with $N=64$ sites and real valued couplings  The graphs show the inferred (dashed black lines) and true couplings (full green lines) plotted on top of each other  The left and right columns refer to the
   		 cases of ordered and bimodal disordered couplings, respectively  Top figures: single site reconstruction, i e , one row of the matrix $J$  Bottom figures: couplings are plotted sorted in descending order }  
   	\label{Jor1_dec}
   \end{figure}
   
\begin{figure}[t!]
    	\centering
    	\includegraphics[width=1\linewidth]{Jor3_dec_JRJI_soJRJI_TPJRJI}
    	\caption{XY model on a 2D lattice with $N=64$ sites and ordered complex-valued couplings 
    		The inferred and true couplings are plotted on top of each other  The left and right columns show the real and imaginary parts, respectively, of the couplings  Top figures refer to a single site reconstruction, i e , one row of the matrix $J$  Bottom figures report the couplings sorted in descending order }
    	\label{Jor3_dec}
    \end{figure}
    
       







       \begin{figure}[t!]
     	\centering
     	\includegraphics[width=1\linewidth]{MF_PL_Jor1_2D_TPJR_varT}
     	\caption{True Positive curves obtained with the three techniques: PLM with decimation, (blue) dotted line,  PLM with $l_2$ regularization, (greed) dashed line, and mean-field, (red) full line   These results refer to real valued ordered couplings with $N=64$ spins on a 2D lattice  The temperature is here $T=0 7$ while the four graphs refer to different sample sizes: $M$ increases clockwise }
     	\label{MF_PL_TP}
     \end{figure}
    
    \begin{figure}[t!]
    	\centering
    	\includegraphics[width=1\linewidth]{MF_PL_Jor1_2D_errJ_varT_varM}
    	\caption{Variation of reconstruction error, ${\rm err_J}$, with respect to temperature as obtained with the three different techniques, see Fig  \ref{MF_PL_TP}, for four different sample size:  clockwise from top   $M=512,1024, 2048$ and $4096$ } 
    	\label{MF_PL_err}
    \end{figure}
    
     Once the most likely network has been identified through the decimation procedure, we perform the same analysis displayed in Fig  \ref{Jor1_dec}  for ordered and then quenched disordered real-valued couplings
and in Fig  \ref{Jor3_dec} for  complex-valued ordered couplings   In comparison to the results shown in Sec  \ref{sec:res_reg},
  the PLM with decimation leads to rather cleaner results  In Figs  \ref{MF_PL_err} and \ref{MF_PL_TP} we compare the performances of the PLM with decimation in respect to ones of the PLM with $l_2$-regularization  These two techniques are also analysed in respect to a mean-field technique previously implemented on the same XY systems\cite{Tyagi15} 
  
    For what concerns the network of connecting links, in Fig  \ref{MF_PL_TP} we compare the TP curves obtained with the three techniques  The results refer to the case of ordered and real valued couplings, but similar behaviours were obtained for the other cases analysed  
  The four graphs are related to different sample sizes, with $M$ increasing clockwise  When $M$ is high enough, all techniques reproduce the true network  
  However, for lower values of $M$ the performances of the PLM with $l_2$ regularization and with decimation drastically overcome those ones of the previous mean field technique  
  In particular, for $M=256$ the PLM techniques still reproduce the original network while the mean-field method fails to find more than half of the couplings  
  When $M=128$, the network is clearly reconstructed only through the PLM with decimation while the PLM with $l_2$ regularization underestimates the couplings  
  Furthermore, we notice that the PLM method with decimation is able to clearly infer the network of interaction even when $M=N$ signalling that it could be considered also in the under-sampling regime $M<N$   
 
 
In Fig  \ref{MF_PL_err} we compare the temperature behaviour of the reconstruction error 
In can be observed that for all temperatures and for all sample sizes  the reconstruction error, ${\rm err_J}$, (plotted here in log-scale) obtained with the PLM+decimation is always smaller than 
that one obtained with the other techniques  The temperature behaviour of ${\rm err_J}$ agrees with the one already observed for Ising spins in \cite{Nguyen12b} and for XY spins  in \cite{Tyagi15} with a mean-field approach:  ${\rm err_J}$ displays a minimum around $T\simeq 1$ and then it increases for very lower $T$; however,
 the error obtained with the PLM with decimation is several times smaller  than the error estimated by the other methods 



 
 

     
     \section{Conclusions}
     \label{sec:conc}


Different statistical inference methods have been applied to the inverse problem of the XY model 
After a short review of techniques based on pseudo-likelihood and their formal generalization to the model we have tested their performances against data generated by means of Monte Carlo numerical simulations of known instances
with diluted, sparse, interactions 

The main outcome is that the best performances are obtained by means of the  pseudo-likelihood method combined with decimation  Putting to zero (i e , decimating) very weak bonds, this technique turns out to be very precise for  problems whose real underlying interaction network is sparse, i e , the number of couplings per variable does not scale with number of variables 
The PLM + decimation method is compared to the PLM + regularization method, with $\ell_2$ regularization and to a mean-field-based method  The behavior of the quality of the network reconstruction is analyzed by looking at the overall sorted couplings and at the single site couplings, comparing them with the real network, and at the true positive curves in all three approaches  In the PLM +decimation method, moreover, the identification of the number of decimated bonds at which the tilted pseudo-likelihood is maximum allows for a precise estimate of the total number of bonds  Concerning this technique, it is also shown that the network with the most likely number of bonds is also the one of least reconstruction error, where not only the prediction of the presence of a bond is estimated but also its value 

The behavior of the inference quality in temperature and in the size of data samples is also investigated, basically confirming the low $T$ behavior hinted by Nguyen and Berg \cite{Nguyen12b} for the Ising model  In temperature, in particular, the reconstruction error curve displays a minimum at a low temperature, close to the critical point in those cases in which a critical behavior occurs, and a sharp increase as temperature goes to zero  The decimation method, once again, appears to enhance this minimum of the reconstruction error of almost an order of magnitude with respect to other methods 
 
The techniques displayed and the results obtained in this work can be of use in any of the many systems whose theoretical representation is given by Eq  \eqref{eq:HXY} or Eq  \eqref{eq:h_im}, some of which are recalled in Sec  \ref{sec:model}  In particular, a possible application can be the field of light waves propagation through random media and the corresponding problem of the  reconstruction of an object seen through an opaque medium or a disordered optical fiber \cite{Vellekoop07,Vellekoop08a,Vellekoop08b, Popoff10a,Akbulut11,Popoff11,Yilmaz13,Riboli14} 

 	



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