matlab – Is there any way to obtain linearized state space model from set of differential equations in SIMULINK?

I should linearize my model around points. It seems that linmod function can linearize the system, but to run this code, we have a plant in SIMULINK. I don’t have a plant in SIMULNK, but i have 15 differential equations of my model.

Is there any toolbox to linearize my nonlinear state space?

Thanks a lot,

EDIT: In my opinion, i should implement my diff. eqs. in SIMULINK and use blocks. After that, using of linmod will be effective for my operation.

ssh – I set permitrootlogin to yes but still not working debian

What am i doing wrong

#LoginGraceTime 2m
#PermitRootLogin yes-password
#StrictModes yes
#MaxAuthTries 6
#MaxSessions 10

#PubkeyAuthentication yes

#AuthorizedKeysFile .ssh/authorized_keys .ssh/authorized_keys2

#AuthorizedPrincipalsFile none

#AuthorizedKeysCommand none
#AuthorizedKeysCommandUser nobody

#HostbasedAuthentication no

#IgnoreUserKnownHosts no

#IgnoreRhosts yes

#PasswordAuthentication yes
#PermitEmptyPasswords no

ChallengeResponseAuthentication no

#KerberosAuthentication no
#KerberosOrLocalPasswd yes
#KerberosTicketCleanup yes
#KerberosGetAFSToken no

#GSSAPIAuthentication no
#GSSAPICleanupCredentials yes
#GSSAPIStrictAcceptorCheck yes
#GSSAPIKeyExchange no

UsePAM yes

#AllowAgentForwarding yes
#AllowTcpForwarding yes
#GatewayPorts no
X11Forwarding yes
#X11DisplayOffset 10
#X11UseLocalhost yes
#PermitTTY yes
PrintMotd no
#PrintLastLog yes
#TCPKeepAlive yes
#PermitUserEnvironment no
#Compression delayed
#ClientAliveInterval 0
#ClientAliveCountMax 3
#UseDNS no
#PidFile /var/run/sshd.pid
#MaxStartups 10:30:100
#PermitTunnel no
#ChrootDirectory none
#VersionAddendum none

#Banner none

AcceptEnv LANG LC_*

Subsystem sftp /usr/lib/openssh/sftp-server

#Match User anoncvs

PasswordAuthentication yes

Any price comparison for car rental that send alerts when price drop at a certain amount set by user, without needing a reservation?

Do you know Any price comparison sites for car rental that send alerts when price drop at a certain amount set by user, so not just cents change or 5%, without needing a reservation to receive alerts?

Ideally would be to receive alerts for a destination when price per day, for a week long rental, reach X amount, without having to set the 100 alerts with different dates.

Don’t tell me Autoslash.

set theory – Definability up to isomorphism versus definability of an isomorphic copy

Question: Is it provable in ZFC that every structure ordinal definable up to isomorphism has an ordinal definable isomorphic copy? If not, what are some counterexamples? All structures are set-sized.

A positive answer would likely generalize to a definable procedure for the following: Given a nonempty set $S$ of isomorphic structures, choose a structure, possibly outside of $S$, that is isomorphic to an element of $S$.

Here is an illustration of some of the subtleties. Assuming GCH, up to isomorphism, there is a unique $ω_2$-saturated elementary extension of second order arithmetic (equivalently, $(ℝ,ℕ,+,⋅,=)$) of cardinality $ω_2$. But defining a specific example of the extension seems problematic — every nonstandard integer in real analysis gives a nonprincipal ultrafilter on $ℕ$, and consistently with ZFC, no such ultrafilters are definable. Still, A definable nonstandard model of the reals unconditionally gives a definable countably saturated elementary extension.

We can also consider restricting the domain of the definable isomorphic copy:

  • If the copy must be in HOD, then there are counterexamples, such as the second order arithmetic (assuming $ℝ∉text{HOD}$).
  • If the domain of the copy must consist of sets of ordinals, then the copy still has an ordinal definable (OD) linear ordering, so under appropriate assumptions, third order arithmetic would be a counterexample. I think there is even a symmetric generic extension of $V$ with an OD non-linearly-orderable countable set of countable sets of reals.
  • Requiring the domain of the copy to consist of sets of sets of ordinals does not affect existence of a definable copy.

set theory – Suslin trees at the successor of a large cardinal

Suppose $kappa$ is supercompact. Does there there exist a $kappa^+$-Suslin tree?

Here’s some motivation. Since $kappa^{<kappa} = kappa$, there is a $kappa^+$-Aronszajn tree. An argument of Todorcevic shows that adding a $kappa$-Cohen set adds a $kappa^+$-Suslin tree. So the universe is already “close” to having such a tree, and maybe some large cardinal property implies it’s close enough. To prevent the existence of such a tree, we might have to generalize the forcings for SH+CH.

graphs – Is the maximum independent set problem on a subgraph NP-hard?

I’m working on an optimization problem which can be modelled using a graph $G=(V,E)$. This graph can be split into two subgraphs $G_1=(V_1,E_1)$ and $G_2=(V_2,E_2)$. The two subgraphs are non-overlapping, i.e., $V_{1}cap V_{2}=phi$ and $E_{1}cap E_{2}=phi$, with $V_{1}cup V_{2}=V$ and $E_{1}cup E_{2}=E$. In other words, the two subgraphs are not connected (although the vertices in $G_2$ are connected).

Crucially, I’ve been able to establish that the finding the optimal solution of the problem corresponds to finding the maximum independent set on $G_2$. My question is simple: given that finding the maximum independent set on a graph is NP-hard, does this imply that the problem I’m working with is NP-hard too (although we are dealing with a subgraph)?

dnd 5e – How should I set up and execute air battles in my session to avoid easy encounters?

Admittedly, Hypnotic Pattern is an unusually powerful spell and one that can tip a combat, especially if the PC’s outnumber the monsters. Before you resort to changing the fundamentals of that spell, though, or “giving immunity” to monsters, make sure you are running the PC’s spells RAW. If you are not paying attention to things like range and timing, but just allowing the players to use spells because they have them, spells like Hypnotic Pattern are going to come off as even more powerful than they already are.

The sky is big – have you checked RAW range?

Unlike a “dungeon” or indoor setting, where most of the participants remain in spell range for the entire combat, the sky is a big, open space.

Mind Sliver has a range of 60 feet.
Polymorph has a range of 60 feet.
Hypnotic Pattern, for some reason, has a range of 120 feet.

But the roc has a flying movement of 120 feet! This means that it has a reasonable chance of remaining out of spell range until its turn, and then moving into range and making its attack, so long as its target is not immediately adjacent to the caster. For example, consider a Hypnotic Pattern caster and an allied PC standing on deck 20 feet away. If the roc approaches from the direction of the ally, it can start its turn at 140 feet from the caster (out of range of the Pattern) and still reach the ally to attack by the end of its turn. If it is a big ship and the PC’s aren’t clustered together, that may even give the roc the opportunity to both attack a PC and get back over the rail before the caster can respond. With a +13 to hit and an automatic grapple, the roc should be taking a PC with it. That should give the players pause – once their companion is over the rail in the roc’s talons, hypnotizing or polymorphing it may mean that a PC will be joining the roc in plummeting a thousand feet.

Casters can, of course, ready actions to cast spells when the roc comes within range. But remember that readying a spell requires casting the spell and then holding the energy, which dissipates at the end of the round. You can have the roc circle the ship a few times before it moves in. Once the casters have burned through a few third and fourth level slots readying spells that are never cast, they may reconsider.

Also, is the ship moving? If it is not hovering in place, but moving at a certain speed and direction, the roc may be able to use that. By grappling the aftmost PC, for example, the ship might move ‘out from under’ the PC on its turn.

Flying combat takes place in three dimensions

Currently 5e movement rules largely indicate two dimensional thinking. But the roc is a creature of the air. What is to prevent it from approaching the ship from underneath, so that the casters cannot see it until right before it bursts on deck and grabs someone? What is to prevent it (besides masts – I’m not familiar with the design of the airship) from approaching the ship from above, and dropping from outside of spell range to the deck, taking some fall damage itself but possibly doing considerable damage to everyone it lands on?

Finally, not RAW but pretty reasonable and supported in earlier editions – the roc could start its turn at a higher elevation than the ship and gain speed by dropping in elevation as it traveled toward the deck, allowing it to move from outside of spell range into its attack range and back off the ship in one turn.

The GM describes the environment

In general, you should avoid changing the details of player’s spells when you find them challenging to deal with. Players often feel a GM is being antagonistic rather than fair if they ‘nerf’ the player abilities – the one thing the players have going for them and can count on. However, it should be expected that the GM describes both the environment and its effects on the combat. Is the airship noisy and the roc a silent glider? Then it can likely sneak up on the ship at night, in a storm, or in a cloud – getting within striking range perhaps in a surprise round. When a roc falls, is it being buffeted by winds or just the air resistance of its massive wings? That could reasonably be considered something that would “shake the creature out of its (hypnotic) stupor” before it hit the ground. Have the players polymorphed an enemy flier into a chicken and thrown it off the ship? Chickens can fly – perhaps not well enough to glide a thousand feet to the ground – but certainly well enough to spiral, collide with the hull, take a point of damage, and resume their original form long before they hit the ground.

Rather than trying to change rules to limit the characters’ spells, try to rigorously enforce pre-existing RAW limits, expand the strategic options of the monsters, and describe the consequences of the environment in ways that don’t favor the players.

blockchain – Could a miner set a maximium transaction fee

Yes, miners can choose exactly what transactions to include in their candidate blocks, including the choice to not include anything at all.

Of course, if a high fee paying transaction is available, and one miner chooses to not include it, other miners still can. This is only untrue if an entire cartel with sufficient hashrate that is actively performing a 51% attack chooses not to include a transaction – in that case, it can be censored as long as the attack lasts.

domains – I would like to set up a subdomain for my website that redirects to my discord invite link

If I correctly understand this you would need to set up a subdomains to point to a link that you own, and then either do a redirect to the invite link or embed it in an iframe.

I’ve only skimmed their terms and conditions but I see nothing therein preventing you from doing a redirect. Their terms may preclude you from legally going the iframe route.

dnd 5e – How should I set up and execute air battles in my session to avoid easy encounters?

Combat balance is always tricky, and airship-related elements can make it harder. I’ll try to focus on the novel environment of the airship, since that’s the meat of the question. But for completeness, a few issues about combat balance generally:

  • Combat difficulty estimates (like a hard encounter, deadly encounter,
    etc.) are just that– estimates. And not very precise ones. Further,
    the difficulty of an encounter is mostly defined around the
    likelihood of PC KOs. Even a deadly encounter is one that PC party is
    expected to win
  • Powerful parties are powerful. They have lots of options to deal with
    a variety of situations, and one manifestation of that is that they
    can approach a given encounter in many ways. Some of those ways will
    make certain combats pretty easy for them, such as gaining access to
    Polymorph. With options like that available, an encounter may need to be much harder to suit those powerful options
  • You are running a game for a pretty large party. 5 to 6 party members (and even up to 8!)
    gives a big edge in terms of action economy, and allows for lots of
    synergies between PCs (which tends to make combats easier).
    If you have that many PCs, you likely need to include more enemies
    per combat in order to keep things challenging
  • 3 to 5 hard combats per day is below the number assumed in a typical
    adventuring day, and consequently it’s not surprising if the party
    overperforms

Tweaks to ordinary combat-balance issues are covered pretty well in answers to other questions, and are not quite in scope here.


Airship combat between individual characters and enemies can be tricky to balance

As you’ve discovered! If you can get enemies onto the deck of the ship you can have a pretty typical combat encounter, plus an obvious terrain feature that allows shoving enemies over the side to plummet to the ground.

But if you have flying enemies that menace the ship by flying around it you can start to lose terrain features and tactics that add variety and challenge to combats. For an easy example, consider cover: outside of using the body of the ship, cover is probably going to be hard to come by. This favors spellcasters and ranged fighters, who get to act like fixed turrets.

My preferred approach to combat between PCs on or in a vehicle and enemies that move around that vehicle (this includes airships, regular ships, wagons, mine carts, and so on) tend to focus on treating the vehicle as a unique environment which is a part of the fight(s):

  • A rollable table of ship-related effects is a great tool to have, and
    can really alter player tactics. For example, if the airship suddenly
    rolls to the side PCs may need DEX saves to keep their footing or
    risk falling prone/taking damage/pitching over the side. Rolling a d6
    every round or two to impose environmental effects like that can make
    a combat harder without fiddling with enemy composition, as well as
    adding variety to combats generally
  • Flying hundreds of feet in the air offers unique opportunities and
    dangers. Does the airship have to fly through a thunderstorm,
    possibly creating a risk of lightning damage or driving winds? Can
    the PCs defeat the enemies and survive the harsh environment? Does the environment make certain strategies more or less attractive, by adjusting the potential risks and rewards? Can enemies weave in and out of clouds, breaking line-of-sight and attacking from unexpected angles?
  • What are the enemies’ goals? If they want to kill or otherwise impede
    the PCs, they might as well focus on damaging the airship itself.
    This can change combat from an HP-reduction grind into a race against
    time, and can also keep enemies out of easy reach of spells and
    ranged attacks. If the enemies want something other than slaughter, the fight being relatively easy for the PCs may not be enough to truly “win” the combat encounter
  • Some condition exists that means things get worse until that
    condition is fixed. In one combat I ran, my players were in a small
    ship trying to escape from a massive Orcish warship, which had shot a
    large hauser-connected harpoon into their deck. As long as the ships
    stayed attached, orcs kept climbing across the rope to board the
    ship. The PCs had to fight the boarders and cut through the hauser
    or rip out the harpoon, or else the fight would (effectively) never
    end and they would eventually be overwhelmed

Adventure-day design is a different beast than single-encounter design

Encounter design is always an art, and designing a challenging combat is different from designing a difficult adventuring day. A combat might be tough, but with lots of resources a party might be able to prevail. An adventuring day being tough, in contrast, means more questions about whether or not it’s worth spending resources right now (for an easier current combat) versus keeping something in reserve for potential future combats, and surviving those later combats when the resources are gone.

And however easily your players dispatch threats in a given fight, if they have more fights they will eventually run low on resources and face much greater danger. More combat encounters per day, with fewer opportunities for rest, lead to much greater challenges for the party.