text:
December 22, 2021 / Article
Something Old, Something New: The Halo Infinite Story Review
Watch the video version of this article on Youtube here.
Even allowing for variation in how you count it, the 343 Industries-helmed era of Halo has now eclipsed that of the original developers at Bungie.1 The studio focused solely on the franchise has overseen the production of more than a decade's worth of spinoff and franchise media and three main in-house games—Halo 4, Halo 5: Guardians, and now Halo Infinite.
Whatever you consider the strengths and weaknesses of their games, 343 Industries' biggest problem during their tenure is arguably being too reactive to criticism. Halo 4 was lambasted for requiring too much background knowledge to understand, so 343 Industries responded by jettisoning a bunch of characters and backstory and moved in what seemed a completely different direction for Halo 5 with the Created conflict. Halo 5 in turn was criticized for making Cortana "evil" and focusing on newcomers Team Osiris to the detriment of fan favorites Blue Team, so 343 promised to "double down" on Chief going forward.2 Rather than merely adjusting their trajectory, 343 seemed to be shooting for entirely new targets with each outing, leaving story fans with a sense of whiplash. Especially if you liked some of the storytelling or story choices in Halo 4 or 5, there was good reason to be worried that Halo Infinite's status as a "spiritual successor" to Combat Evolved would mean that, once again, existing plot lines would be jettisoned in favor of rehashing the familiar and the safe.
While it's possible to squint at Infinite and make that argument, fans of 343's work should be left heartened by the approach the game takes. While it has its storytelling flaws, it does not shrink from the franchise's past—and in fact, wholeheartedly embraces it. The Created conflict and Cortana's turn to antagonist are (possibly) fully resolved (more on that later), but it is not simply tossed aside. The Covenant replacements in this game, the Banished, keep the familiar rhythms of Halo's gameplay unchanged, but the story sets up new antagonists. Infinite doesn't feel like a concession or a backtrack, but rather boldly moving forward. With the schism between die-hard story players and casual fans who thought the heyday of the series was back in 2007, it would have seemed unlikely 343 could please both camps—and yet, improbably, they've managed to have their cake and eat it too. This is Forward Unto Dawn's Halo Infinite story review.
Caution: Pardon Our Dust
Halo Infinite's campaign is structured radically differently than a traditional Halo game. Its hybrid, hub-world approach is most similar to the side story Halo 3: ODST, albeit with millions more dollars thrown at it. Whereas New Mombasa in ODST mostly coasted by on jazz and neon-soaked atmosphere, Halo Infinite's centerpiece is the woods and plains of Installation 07, Zeta Halo—a ring long cloaked in mystery and fan theories. It's not quite an open world like most examples of the genre, and that more focused nature applies to its story, which alternates the open-ended surface segments with the story-focused, linear "dungeons" in the bowels of the installation. 343 seems quite conscious that one of the narrative pitfalls of open world games is that any sense of urgency is deflated by the pursuit of side quests and hunting collectibles, which is probably why the game's characters exhort you to continue the main storyline when you are off doing a side task, and the back third of the game mostly abandons the open world for shepherding you from one story mission to the next with few breaks.
The result is a campaign that is different mechanically, but that narratively doesn't stray too far from classic Halo campaigns. Awakening six months after a disastrous battle with the Banished that left the UNSC broken and scattered on a damaged Zeta Halo, Master Chief (and, by extension, players) have to pick up the pieces of what happened and lead the resistance against the Banished. Gone are Lasky, Infinity, Palmer, Locke, and the Spartan-IVs (basically 343's sum total of major contributions to the franchise's character roster.) Fortunately, however, 343 doesn't seem interested in simply tossing them into the sun or killing them off in the opening mission (RIP Jul 'Mdama), rather leaving room for them to be alive and active somewhere else on the ring. In fact, 343's true magic with Infinite might be finally pleasing everyone rather than alienating them with their switch in focus: while the campaign at first glance seems like a dismissal of everything they've developed, at a deeper level Infinite successfully embraces old and new together in a way that 343 has always struggled with previously.
This is most clearly seen in the environment of Zeta Halo itself. For Halo 4, 343's art department under Kenneth Scott redesigned most aspects of the universe. The Forerunner's Baroque, angular geometry was simplified, smoothed over, and generally glowed from every corner. The Covenant got a major physiological redesign, to the point that they would later have to explain some of the changes as subspecies. Even the sounds and weapons departed substantially from what players were used to. The end result was often alienating, and felt too much like 343 felt they had to change things to prove they owned Halo. This change occasionally resulted in tangible damage to storytelling, like how Halo Wars 2's return to the Ark didn't actually feel like players were returning to a fan-favorite location.
What we get in Halo Infinite is much more successful. While there are definitely some obvious wholesale reversions here solely for fan service—the Master Chief's armor, or the Halo Reach-lifted Assault Rifle—the feeling one gets walking through the corridors of Zeta Halo is of every bit of previous Forerunner level design being thrown into a blender and reassembled. There is plenty of the classic Forerunner look in the return of rich patterns and beloved doors in Zeta Halo's interiors, but also the large temple-like rooms from Halo 2's "Delta Halo" temples, or the wide, low hexagonal passageways from Halo 4's "Reclaimer". The look of Zeta Halo returns a lot of Bungie-era texture, but retains much of the massing of 343's "Tronrunner" look. The ring is familiar, yet different enough to inspire wonder and exploration, as befits a story that has a similar core of rediscovery. Halo games have struggled to give players a sense of discovery and wonder creeping around Forerunner ruins, but with Halo 4, and again here, 343 Industries have done a great job making you marvel at a Halo ring again.
On Zeta Halo, Master Chief, the Weapon, and the Pilot work together to recapture UNSC bases, rescue marines, and disable Banished operations. Learning that the Banished are looking for something at the Conservatory, Chief and Cortana descend into the bowels of the ring and come face-to-face with the Harbinger, an awakened alien who has allied with the Banished to rebuild the ring. The Harbinger wants to release her people, the Endless. Master Chief ultimately kills the Banished leadership and the Harbinger, stopping the "Reformation" of Zeta Halo and its potential activation, while leaving the larger threat the Banished and Endless may pose very much alive.
Step Inside (Of My Head)
Back in June 2021, our speculation based on the campaign reveals ended with a suggestion that Halo Infinite would invert the character arcs of Halo 4:
[In Halo 4] Cortana asked Chief which of them was really a machine—Chief single-mindedly pursuing his mission, while Cortana grappled with her mortality. But what we see of Infinite has pushed Chief's humanity to the fore—his reassurances to the Pilot, his gentleness with his fallen comrades, and his offer to the Weapon of a new goal, a new mission. Perhaps the arc of this new relationship is Chief helping the Weapon to discover the humanity she was denied by her creators.
This is, broadly speaking, the story of Infinite, which focuses on titles and myths, but also strips characters down to their human cores. For all the mysteries Halo Infinite explores (and they leave a lot of plot threads hanging when credits roll), its biggest successes and the questions it satisfactorily answers are from a character standpoint. The Master Chief is someone who is burdened with regrets, believing that if he'd managed to save Cortana during Halo 4, or successfully talked her out of her plans in Halo 5, millions might have been saved. But he's also someone who knows exactly who he is—a soldier at heart, who will keep fighting until he's dead.
In comparison, the other major characters of Infinite are plagued with doubts or adrift with purpose. The Pilot, Echo-216, just wants to flee, convinced the Banished are unstoppable and the Chief is suicidal. Gradually, it is revealed that he ran from the fight on Infinity and stole the Pelican to get away, and Chief inspires him to keep fighting. The Weapon, with her original purpose of containing Cortana completed, is at first meeting happy to get deleted and fulfill her purpose, but by the end of the story treats Chief's attempt to do just that as a horrible betrayal. The game cuts before she can announce her name (and hopefully, it's not Cortana, because at this point that'd be like naming your kid Adolf in the Halo universe) but she has moved from being a tool to a person, digital though she may be.
The character interplay is a major part of the early part of the story, and it's generally satisfactory. While the Weapon sometimes feels inconsistent in her naïveté, her different role in the story and new relationship with Chief manage to engage, and she demonstrates how she is different from Cortana while slotting into the same gameplay role. The Pilot, meanwhile, is more of a mixed bag. For the first third of the story he mostly pops onto the radio to complain, and while the revelation of his cowardly past and the loss of his family makes his actions more understandable, it's still not any more fun to have someone griping in your ear in between ferrying you places.
And then there's Escharum. While Halo Infinite never goes full Halo 2 and has playable missions from the perspective of the enemy, the cinematics regularly shift to the Banished point of view throughout. I wouldn't say Escharum ever manages to pop into being a compelling character, but I think Infinite does a better job with him as an antagonist than Atriox in Halo Wars 2, who had very little of a personal rapport with the Spirit of Fire characters. Here, however, Escharum at least gets lengthy speechifying sessions to Chief. We get the sense Escharum is someone who expected to die gloriously in battle and instead is still alive after the war is over. Wounded by the loss of his homeworld and clearly dying slowly, Escharum sees in Chief the chance to have either a glorious death or one final triumph that will cement his legend. It's interesting that the classic trope of the villain proclaiming himself not so different from the protagonist is actually inverted, with the Master Chief understanding Escharum's point of view—that, at his core, he was a soldier, just like him.
The other characters are in the game to function as mini-bosses, and don't really transcend those roles. The Spartan Killers Hyperius and Tovarus don't make much of an impression, and neither do the Elites Jega 'Rdomnai or Chak Lok. While Jega seems to have some interesting relationship with Escharum, as the war chief relies on him as the one person he trusts most to kill Chief, they mostly exist as gameplay obstacles to overcome. Likewise, there are a few missed opportunities in terms of the characters—particularly Despondent Pyre, the elusive Monitor of Installation 07. Fans have wondered where she was for years, and it turns out that question is unanswered and she's destroyed literally minutes after we meet her. Her role is replaced by submonitor Adjutant Resolution, who especially with his accent and the different monitor casing he's in, feels like a Wheatley clone from Portal 2. Both pale in comparison to previous AIs like Guilty Spark, or Exuberant Witness in Halo 5.
The most enigmatic character is the Harbinger, but her inscrutability and lack of clearly stating just about anything might make for good fan speculation, but make her less compelling without more clearly-defined goals.
The Play Is The Thing
As was speculated before release, Halo Infinite uses a "one-take" system of cutscenes, where rather than having distinct cuts, the camera moves and appears to be seamless in and out of gameplay. As someone who has felt 343's games have suffered from often jarring choices in how they staged cinematics and approached the continuity in their storytelling mechanics, this choice generally works, though it is severely undercut by inelegant loading screens, even on a top-of-the-line Series X. Nevertheless, the choice keeps the focus on the characters and supports the smaller-scale story being told.
Ever since Halo 3's introduction of Terminals, the Halo franchise has slowly evolved its additional storytelling in-game, and while Halo Infinite doesn't have the "weapons down" plot segments of Halo 5, it continues its legacy of "intel" collectibles with Banished, human, and Forerunner audio logs scattered throughout the game. Unfortunately, the audio logs in particular feel like they're not fully baked. The gold standard for this kind of storytelling mechanic is arguably the BioShock series, which uses audio diaries and the tableau players come across to tell stories that get fleshed out as players find more logs. From the heartbreaking story of a family that commits suicide after the loss of their daughter, to the mundane realities of living in a city underwater, BioShock richly rewards players for exploring nooks and crannies and observing your surroundings, piecing together mysteries and the fates of side characters.
In comparison, Infinite, despite having its more open world, doesn't reward story players much for their trouble. Audio logs feel scattered around and haphazard, and there's rarely characters whose stories you can piece together across the ring. The human element found in side stories like Halo 5′s Meridian colonist Evelyn Collins is just missing. While we learn more about the Spartans who we strip for parts in the campaign, relatively little is spent on them as characters rather than answering basic questions about where people ended up. While the upcoming Rubicon Protocol will probably detail what life was like for the UNSC in the aftermath of the fall of Infinity, it's disappointing this game doesn't elaborate more on that period in a meaningful way and give us more stories to chase after.
This weakness stands in contrast to the main plot, which moves at a satisfactory clip (although there are usually one too many fetch quests you have to do for each objective that feel like padding, perhaps drawing the wrong lessons for Combat Evolved's story) and has both story developments and character changes sprinkled throughout. The environmental storytelling is also more successful in these sections. For example curious players hunting around in the area with the cylixes (themselves the first true canon representation of a concept seen in Cortana's retelling of "Origins" in Halo Legends) are rewarded finding a protected Flood cylix hidden off the beaten path. Hanging back and letting dialogue play often triggers additional lines. Players who want to explore are generally rewarded.
The ending clearly aims squarely at replicating the end of Halo: Combat Evolved—the battle is won, but it is clear a larger war is still looming. The impact of the ending, however, feels a little blunted, both because in some ways it feels like we only get the opening acts of a story, and also because the focus on not alienating new players comes with drawbacks. Chief among them is Cortana's goodbye—maybe this truly is the end of the character (The Weapon assuming her mantle aside) and if so, I can't help but feel a little let down. Cortana's actions are handwaved with an apology to Chief which feels sincere, but also feels like a narrative shortcut. Why did Cortana, so sure of her plan for the greater good one game ago, suddenly decide to change course? Her decision feels robbed of impact when we never see it besides scattered flashbacks and a glorified voicemail.
The ending also feels a bit too mysterious for its own good, throwing out a number of proper nouns and mysterious dialogue at the player, and not explaining next to any of it. While fans will have fun debating the nature of the Endless and how they may have survived the Halo Array's activation, what exactly the Criterion is or who the Grand Edict is, where Atriox has been (no, he probably wasn't sent back in time) it sometimes feels like a dash of the timid 343 of old, concerned about plotting too much without first gauging fan response. The mention of Offensive Bias in the closing Legendary narration, too, feels like a namedrop without context and robbed of its thematic resonance—the Forerunner AI built to fight Mendicant Bias has clear parallels to The Weapon and Cortana, yet is absent in this game, where it would be most appropriate.
Halo Infinite is intended to be the platform for the franchise going forward, which leaves the question of when we will have any answers for these questions up in the air. Hopefully, we will see 343 push forward with future campaign expansions on the Halo Infinite platform, and it won't be another six years to wait for the next major story. The final shot of Chief, the Weapon, and Pilot ends with the Pilot cheerily saying "here we go!" underscored by a restatement of Martin O'Donnell's Halo 2 "The Last Spartan" music cue—implying that there is, once again, a fight to finish, and hopefully it'll be sooner than we think. With the universe irrevocably altered by the events of Infinite, it'll be a treat to see what is in store next.
Possible dates for the beginning of the 343 Era arguably stretch as far back as 2008, when the internal studio was getting up and running, to the official unveiling of 343 Industries alongside Halo Legends in July 2009. More common answers would be 343's release of the Halo: Reach Title Update in September 2011, or the release of Halo: Combat Evolved Anniversary in November 2011. If your definition is solely major games released, then the Bungie era doesn't end until Halo 4's anniversary in 2022. ↩
Tom Phillips (April 26, 2017). "Halo 5's lack of Master Chief was a 'huge disappointment', 343 admits". Eurogamer. ↩
CategoriesArticle Post H5
Tagscampaign continuity Halo Infinite narrative review


text:
More Details Released On 2010 Rolls-Royce RR4
New "baby Phantom" will get a 500-plus-hp turbo V-12 and an eight-speed transmission.
STEVE SILER
KGP PHOTOGRAPHY, THE MANUFACTURER
Rolls-Royce has let us in on a few more details about its upcoming RR4, the so-called "baby Phantom" previewed as the fetching 200EX concept at the 2009 Geneva auto show. While showing the car to potential customers in New York, Rolls-Royce CEO Tom Purves announced that the crisply styled RR4 (which won't be its final name) will be powered by an all-new 6.6-liter V-12 with twin turbochargers and an output of more than 500 hp. A ZF eight-speed transmission will transfer the power to the wheels.
The official company line is that the powertrain will be unique to Rolls-Royce, but we suspect brand exclusivity will be limited to just this particular tuning, and that a tweaked version of this engine will appear in the BMW 7-series with different specs.
The 200EX is currently on a world tour to gauge interest (and garner deposits) for the first new Rolls-Royce sedan since BMW took the brand in its fresh new direction with the Phantom line. In contrast to most of the rest of the automobile market, Rolls-Royce actually posted a sales increase in 2008, thanks to the new Phantom coupe and convertible variants. Expect more details about the RR4 to be made known as it marches toward production in Goodwood later this year.

redpajama_set_name: RedPajamaCommonCrawl


text:
Highland Spring is a Scottish supplier of natural source bottled water. It produces still and sparkling water at its factory in Blackford, Perth and Kinross, although despite the name this area is not within the Scottish Highlands. Its water is sourced from protected, organic land in the Ochil Hills.

Highland Spring is the UK's leading natural source water brand. UK sales volumes grew by 6.3% to 348.6 million litres in 2021, securing a healthy market share of 10.0% of the total UK plain packaged water volumes.

The company has expanded through organic growth  and also by acquisition, taking over the Gleneagles Spring Water Company, also based in Blackford, in 2001, the Speyside Glenlivet Water Company, based in Ballindalloch in 2009, and acquiring Campsie Spring (Glasgow) from Greencore in 2010. The company formally ceased production at the Speyside Glenlivet Water Company site in 2020.

Simon Oldham and Mark Steven were appointed Joint Managing Directors in August 2021, following Les Montgomery's retirement from as Chief Executive after 36 years with the business. The company is owned by billionaire UAE businessman Mahdi Al Tajir.

In June 2018, the company became the first UK water brand to introduce and trial a 100% recycled and recyclable plastic bottle in a bid to cut plastic waste. Following the success of the trial, in January 2019, it formally launched a commercial bottle range that was 100% recycled and recycled called "Eco-Bottle". As of 2020, its entire "Eco-Bottle" sub-range is made from 100% recycled PET plastic.

In August 2022 the business launched a landmark rail freight facility adjacent to its headquarters in Blackford, the facility which has been 10 years in development is part of their ambition to reach net zero by 2040.

References

External links
Highland Spring official site
Highland Spring Group official site

Bottled water brands
Companies based in Perth and Kinross
Scottish brands

redpajama_set_name: RedPajamaWikipedia


13 places to buy or diy mid century modern front doors. Pella sliding french doors replacement window contractor, cleveland siding contractor: vinyl siding, shake, scallop. Maricopapro maricopapro added a new photo in anthem. Wicked willys willys knight 66b hemmings motor news, 42 best cabin stairs images on pinterest stairs, small.


text:
Mammal Species of the World. A Taxonomic and Geographic Reference is een Engelstalig mammalogisch naslagwerk over onder andere de taxonomie, nomenclatuur en verspreiding van alle recente zoogdieren tot op soortniveau. Er zijn drie edities verschenen, in 1982, 1993 en 2005.

Het grootste gedeelte van het werk, de Checklist of Mammal Species of the World, bestaat uit de behandeling van de individuele taxa. De nadruk ligt op de lagere rangen; de indeling boven de orde wordt niet behandeld. Dit gedeelte is verdeeld in hoofdstukken, die sinds de tweede editie door aparte auteurs samengesteld worden. Dit gedeelte wordt gecompleteerd door een omvangrijke bibliografie en index.

De indeling is in de derde editie gebaseerd op McKenna en Bells gezaghebbende naslagwerk Classification of Mammals: Above the Species Level. De volgorde van geslachten en soorten is alfabetisch, maar bij hogere taxa is die gebaseerd op vermoedelijke verwantschappen.

De ingangen bevatten de wetenschappelijke naam van het taxon, de naam van de eerste beschrijver, het jaar van eerste beschrijving en de plaats van eerste beschrijving, een Engelse naam (alleen voor soorten, sinds de derde editie), de typelocatie (soorten) of typesoort (geslachten), de synoniemen, de beschermingsstatus volgens de Amerikaanse Endangered Species Act (U.S. ESA), de International Union for Conservation of Nature and Natural Resources (IUCN) en CITES (alleen voor soorten), het verspreidingsgebied (alleen voor soorten) en een commentaarsectie, die bijvoorbeeld afwijkende indelingen kan geven. In sommige hoofdstukken (bijvoorbeeld dat over de Muroidea) is die sectie uitgebreider dan in andere.

De eerste editie, geredigeerd door James H. Honacki, Kenneth E. Kinman en James W. Koeppl, werd in juni 1982 gepubliceerd en omvatte 4170 soorten op 694 pagina's.

De tweede editie werd geredigeerd door Don E. Wilson en DeeAnn M. Reeder en in juni 1993 door de Smithsonian Institution uitgegeven. Deze editie omvatte 4629 soorten, waarvan 171 sinds 1982 beschreven, op 1207 pagina's.

In december 2005 werd de derde editie gepubliceerd bij Johns Hopkins University, eveneens geredigeerd door Wilson en Reeder. Deze editie omvat 5416 soorten, waarvan 260 nieuw beschreven sinds 1993, op 2142 pagina's in twee delen. Deze editie omvatte daarnaast nog 37 378 synoniemen en 9373 literatuurverwijzingen.

Literatuur
Honacki, J.H., Kinman, K.E. & Koeppl, J.W. 1982. Mammal Species of the World: a taxonomic and geographic reference. Lawrence, Kansas: Allen Press/The Association of Systematics Collections, 694 pp. ISBN 978-0-942924-00-8

Wilson, D.E. & Reeder, D.M. (eds.). 1993. Mammal Species of the World: a taxonomic and geographic reference. 2nd ed. Washington, D.C.: Smithsonian Institution Press, 1207 pp. ISBN 978-1-56098-217-3

Externe links
 Wilson & Reeder's Mammal Species of the World, 3rd edition – Internetversie van de derde editie

Mammalogie


9 out of 10 based on 525 ratings. 2,969 user reviews.
HONDA EX800 OWNER'S MANUAL Pdf Download.
wwwalslib››Honda Manuals›Portable Generator›EX800Page 3 Thank you for purchasing a Honda generator. This manual covers operation and maintenance of the EX800 generator. All information in this publication available at the time of approval for printing. Honda Motor Co., Ltd. reserves the right to make changes at any time without notice and without incurring any obligation.
wwwalslib››2005 TRX400EX Sportrax 400EXView and Download Honda 2005 TRX400EX Sportrax 400EX owner's manual online. 2005 TRX400EX Sportrax 400EX Offroad Vehicle pdf manual download.
wwwon›Search›honda 400ex manualATV/Moto-X Honda Clymer Manual Models TRX 400EX 1999-2003 WSM M454-2. $38 $ 38. 95. $9 shipping. Only 3 left in stock - order soon. JONASC Rear Brake Caliper Assembly Fits Honda Sportrax 400 TRX 400EX TRX400 1999-2004. $39 $ 39.


text:
\subsection{Proofs of Section~\ref{sec:infinite_samples}}
\label{apx:proofs_infinite_samples}

\distributionsEquivalence*

\begin{proof}
	First, note that a non-Markovian policy $\pi \in \Pinm$ can always reduce to a Markovian policy $\pi \in \Pim$ by conditioning the decision rules on the history length. Thus, $\distset{\NM}{x} \supseteq \distset{\M}{x}$ is straightforward for any $x \in \{ \infty, \gamma, T \}$.
From the derivations in~\citep[][Theorem 5.5.1]{puterman2014markov}, we have that $\distset{\M}{x} \supseteq \distset{\NM}{x}$ as well. Indeed, for any non-Markovian policy $\pi \in \Pinm$, we can build a (non-stationary) Markovian policy $\pi' \in \Pim$ as
	\begin{equation*}
	\begin{aligned}
        &\pi' = \big( \pi'_1, \pi'_2, \ldots, \pi'_t, \ldots \big),
        &\text{such that } \pi'_t (a | s) = \frac{d_t^\pi (s, a)}{d_t^\pi (s)},\;\; \forall s \in \mathcal{S}, \forall a \in \mathcal{A}.
    \end{aligned}
    \end{equation*}
    For $t = 0$, we have that $d^\pi_0 (\cdot) = d^{\pi'}_0 (\cdot)= \mu (\cdot)$, which is the initial state distribution. We proceed by induction to show that if $d^\pi_{t-1} (\cdot) = d^{\pi'}_{t-1} (\cdot)$, then we have
    \begin{align*}
        d_t^{\pi'}(s)
        &= \sum_{s' \in \mathcal{S}} \sum_{a \in \mathcal{A}} d_{t-1}^{\pi'} (s') \pi'_{t-1} (a | s') P(s | s', a) \\
        &= \sum_{s' \in \mathcal{S}} \sum_{a \in \mathcal{A}}  \frac{d_{t-1}^{\pi'} (s') }{d^\pi_{t-1} (s')} d^\pi_{t-1} (s', a) P(s | s', a) \\
        &= \sum_{s' \in \mathcal{S}} \sum_{a \in \mathcal{A}}  d^\pi_{t-1} (s', a) P(s | s', a) \\
        &= d_t^\pi (s).
    \end{align*}
    Since $d_t^\pi (s) = d_t^{\pi'} (s)$ holds for any $t \geq 0$ and $\forall s \in \mathcal{S}$, we have  $d_{\infty}^{\pi} (\cdot) = d_{\infty}^{\pi'} (\cdot)$, $d_{\gamma}^{\pi} (\cdot) = d_{\gamma}^{\pi'} (\cdot)$, $d_{T}^{\pi} (\cdot) = d_{T}^{\pi'} (\cdot)$, and thus $\distset{\M}{x} \supseteq \distset{\NM}{x}$. Then, $\distset{\NM}{x} \equiv \distset{\M}{x}$ follows.
\end{proof}

\optimalMarkovDistributions*

\begin{proof}
	The result is straightforward from Theorem~\ref{thr:distributions_equivalence} and noting that the set of non-Markovian policies $\Pinm$ with arbitrary history-length is as powerful as the general set of policies $\Pi$. Thus, for every policy $\pi \in \Pi$ there exists a (possibly randomized) policy $\pi' \in \Pim$ inducing the same (stationary, discounted or marginal) state distribution of $\pi$, \ie $d^\pi (\cdot) = d^{\pi'} (\cdot)$, which implies $H \big( d^\pi (\cdot) \big) = H \big( d^{\pi'} (\cdot) \big)$. If it holds for any $\pi \in \Pi$, then it holds for $\pi^* \in \argmax_{\pi \in \Pi} H \big( d^\pi (\cdot) \big)$.
\end{proof}

\subsection{Proofs of Section~\ref{sec:finite_samples}}
\label{apx:proofs_finite_samples}

\regret*
\begin{proof}
	The result $\mathcal{R}_{T - t} (\pi_{\NM}, h_t) = 0$ for a policy $\pi_{\NM} \in \Pic{\D}{\NM}$ is a direct implication of Lemma~\ref{thr:optimal_deterministic}, whereas $\mathcal{R}_{T - t} (\pi_{\M}, h_t) \geq 0$ for any $\pi_{\M} \in \Pim$ is given by Lemma~\ref{thr:regret_bounds}, which states that even an optimal Markovian policy $\pi_{\M}^* \in \argmax_{\pi \in \Pim} \mathcal{E} (\pi)$ suffers expected regret-to-go $\mathcal{R}_{T - t} (\pi_{\M}^*) \geq 0$.
\end{proof}

\sufficientCondition*
\begin{proof}
	This result is a direct consequence of the combination of Lemma~\ref{thr:law_total_variance} and Lemma~\ref{thr:regret_bounds}. Indeed, if the policy $\pi_{\M} \in \argmax_{\pi \in \Pim} \mathcal{E} (\pi)$ is randomized in $s_t$ we have
	\begin{equation*}
		0 < \Var \big[ \mathcal{B} ( \pi_{\M} (a^*|s_t) ) \big] = \Var_{hs_t \sim p^{\pi_{\NM}}_t} \big[ \EV \big[ \mathcal{B} ( \pi_{\NM} (a^* | hs_t) ) \big] \big],
	\end{equation*}
	from Lemma~\ref{thr:law_total_variance}, which gives a lower bound to the expected regret-to-go $\underline{\mathcal{R}}_{T - t} (\pi_{\M}, h_t) > 0$ through Lemma~\ref{thr:regret_bounds}.
\end{proof}

\lawTotalVariance*
\begin{proof}
	Let us consider the random variable $A \sim \mathcal{P}$ denoting the event ``the agent takes action $a^* \in \mathcal{A}$''. Through the law of total variance~\cite{bertsekas2002introduction}, we can write the variance of $A$ given $s \in \mathcal{S}$ and $t \geq 0$ as
	\begin{align}
		\Var \big[ A | s, t \big]
		&= \EV \big[ A^2 | s, t \big] - \EV \big[ A | s, t \big]^2 \nonumber \\
		&= \EV_{h} \Big[ \EV \big[ A^2 | s, t, h \big] \Big] - \EV_{h} \Big[ \EV \big[ A | s, t, h \big] \Big]^2 \nonumber \\
		&= \EV_{h} \Big[ \Var \big[ A | s, t, h \big] + \EV \big[ A | s, t, h \big]^2 \Big]
		- \EV_{h} \Big[ \EV_{\pi} \big[ A | s, t, h \big] \Big]^2 \nonumber \\
		&= \EV_{h} \Big[ \Var \big[ A | s, t, h \big] \Big] +\EV_{h} \Big[  \EV \big[ A | s, t, h \big]^2 \Big] - \EV_{h} \Big[ \EV \big[ A | s, t, h \big] \Big]^2 \nonumber \\
		&= \EV_{h} \Big[ \Var \big[ A | s, t, h \big] \Big] + \Var_{h} \Big[ \EV\big[ A | s, t, h \big] \Big]. \label{eq:lotv1}
	\end{align}
	Now let the conditioning event $h$ be distributed as $h \sim p^{\pi_{\NM}}_{t - 1}$, so that the condition $s, t, h$ becomes $hs$ where $hs = (s_{0}, a_{0}, s_{1}, \ldots, s_{t} = s) \in \mathcal{H}_{t}$, and let the variable $A$ be distributed according to $\mathcal{P}$ that maximizes the objective~\eqref{eq:finite_samples_entropy} given the conditioning. Hence, we have that the variable $A$ on the left hand side of~\eqref{eq:lotv1} is distributed as a Bernoulli $\mathcal{B} (\pi_{\M} (a^* | s, t))$, where $\pi_{\M} \in \argmax_{\pi \in \Pim} \mathcal{E} (\pi)$, and the variable $A$ on the right hand side of~\eqref{eq:lotv2} is distributed as a Bernoulli $\mathcal{B} (\pi_{\NM} (a^* | hs))$, where $\pi_{\NM} \in \argmax_{\pi \in \Pinm} \mathcal{E} (\pi)$. Thus, we obtain
	\begin{equation}
		\Var \big[ \mathcal{B} ( \pi_{\M} (a^*|s, t) ) \big] = \EV_{hs \sim p^{\pi_{\NM}}_t} \big[ \Var \big[ \mathcal{B} ( \pi_{\NM} (a^* | hs) ) \big] \big] + \Var_{hs \sim p^{\pi_{\NM}}_t} \big[ \EV \big[ \mathcal{B} ( \pi_{\NM} (a^* | hs) ) \big] \big].
	\label{eq:lotv2}
	\end{equation}
	Under Assumption~\ref{ass:unique_action}, we know from Lemma~\ref{thr:optimal_deterministic} that the policy $\pi_{\NM}$ is deterministic, \ie $\pi_{\NM} \in \Pic{\D}{\NM}$, so that $\Var \big[ \mathcal{B} ( \pi_{\NM} (a^* | hs) ) \big] = 0$ for every $hs$, which concludes the proof.
\end{proof}

\regretBounds*
\begin{proof}
	From the definition of the expected regret-to-go (Definition~\ref{thr:regret-to-go}), we have that
	\begin{equation*}
		\mathcal{R}_{T - t} (\pi_{\M}, h_t) = H^* - \EV_{h_{T - t} \sim p^{\pi_{\M}}_{T - t}} \big[ H \big( d_{h_t \oplus h_{T - t}} (\cdot) \big) \big],
	\end{equation*}
	in which we will omit $h_t$ in the regret-to-go $\mathcal{R}_{T - t} (\pi_{\M}, h_t) = \mathcal{R}_{T - t} (\pi_{\M})$ as $h_t$ is fixed by the statement. To derive a lower bound and an upper bound to $\mathcal{R}_{T - t} (\pi_{\M})$ we consider the impact that taking a sub-optimal action $a \in \mathcal{A} \setminus \{ a^* \}$ in state $s_t$ would have in a best-case and a worst-case CMP respectively, which is detailed in Lemma~\ref{thr:best_case_cmp} and Lemma~\ref{thr:worst_case_cmp}. Especially, we can write
\begin{align*}
	\mathcal{R}_{T - t} (\pi_{\M})
	&= H^* - \EV_{h_{T - t} \sim p^{\pi_{\M}}_{T - t}} \big[ H \big( d_{h_t \oplus h_{T - t}} (\cdot) \big) \big] \\
	&\geq H^* - \pi_{\M} (a^* | s_t) H^* - \big( 1 - \pi_{\M} (a^* | s_t) \big) H_{2}^* \\
	&= ( H^*- H^*_2 ) \big( 1 - \pi_{\M} (a^* | s_t) \big)
\end{align*}
and
\begin{align*}
	\mathcal{R}_{T - t} (\pi_{\M})
	&= H^* - \EV_{h_{T - t} \sim p^{\pi_{\M}}_{T - t}} \big[ H \big( d_{h_t \oplus h_{T - t}} (\cdot) \big) \big] \\
	&\leq H^* - \pi_{\M} (a^* | s_t) H^* - \big( 1 - \pi_{\M} (a^* | s_t) \big) H_* \\
	&= ( H^* - H_* ) \big( 1 - \pi_{\M} (a^* | s_t) \big).
\end{align*}
	Then, we note that the event of taking a sub-optimal action $a \in \mathcal{A} \setminus \{ a^* \}$ with a policy $\pi_{\M}$ can be modelled by a Bernoulli distribution $\mathcal{B}$ with parameter $\big( 1 - \pi_{\M} (a^* | s_t) \big)$. By combining the equation of the variance of a Bernoulli random variable with Lemma~\ref{thr:law_total_variance} we obtain
	\begin{equation*}
		\Var \big[ \mathcal{B} ( \pi_{\M} (a^*|s_t) ) \big] = \pi_{\M} (a^* | s_t) \big( 1 - \pi_{\M} (a^* | s_t) \big) = \Var_{hs \sim p^{\pi_{\NM}}_t} \big[ \EV \big[ \mathcal{B} ( \pi_{\NM} (a^* | hs_t) ) \big] \big]
	\end{equation*}
	which gives
	\begin{align*}
		\mathcal{R}_{T - t} (\pi_{\M}) &\geq \frac{ H^*- H^*_2 }{\pi_{\M} (a^* | s_t)} \Var_{hs \sim p^{\pi_{\NM}}_t} \big[ \EV \big[ \mathcal{B} ( \pi_{\NM} (a^* | hs_t) ) \big] \big] := \underline{\mathcal{R}}_{T - t} (\pi_{\M}) \\
		\mathcal{R}_{T - t} (\pi_{\M}) &\leq \frac{ H^* - H_* }{\pi_{\M} (a^* | s_t)} \Var_{hs \sim p^{\pi_{\NM}}_t} \big[ \EV \big[ \mathcal{B} ( \pi_{\NM} (a^* | hs_t) ) \big] \big] := \overline{\mathcal{R}}_{T - t} (\pi_{\M})
	\end{align*}
\end{proof}

\begin{lemma}[Worst-Case CMP]
	For any $t$-step trajectory $h_t \in \mathcal{H}_{[T]}$, taking a sub-optimal action $a \in \mathcal{A} \setminus \{a^*\}$ at step $t$ in the worst-case CMP $\underline{\mathcal{M}}$ gives a final entropy
	\begin{equation*}
		H_* = \min_{h \in \mathcal{H}_{T - t}} H(d_{h_t \oplus h} (\cdot)),
	\end{equation*}
	where the minimum is attained by
	\begin{equation*}
		\underline{h}_{T - t} = \big( s_i \in \argmax_{s \in \mathcal{S}} d_{h_t} (s) \big)_{i = t + 1}^{T} \in \argmin_{h \in \mathcal{H}_{T - t}} H(d_{h_t \oplus h} (\cdot)).
	\end{equation*}
	\label{thr:worst_case_cmp}
\end{lemma}
\begin{proof}
	The worst-case CMP $\underline{\mathcal{M}}$ is designed such that the agent cannot recover from taking a sub-optimal action $a_t \in \mathcal{A} \setminus \{ a^* \}$ as it is absorbed by a worst-case state given the trajectory $h_t$. A worst-case state is one that maximizes the visitation frequency in $h_t$, \ie $\underline{s} \in \argmax_{s \in \mathcal{S}} d_{h_t} (s)$, so that the visitation frequency becomes increasingly unbalanced. A sub-optimal action at the first step in $\underline{\mathcal{M}}$ leads to $T - 1$ visits to the initial state $s_0 \sim \mu$, and the final entropy is zero.
\end{proof}

\begin{lemma}[Best-Case CMP]
	For any $t$-step trajectory $h_t \in \mathcal{H}_{[T]}$, taking a sub-optimal action $a \in \mathcal{A} \setminus \{ a^* \}$ at step $t$ in the best-case CMP $\overline{\mathcal{M}}$ gives a final entropy
	\begin{equation*}
		H^*_2 = \max_{h \in \mathcal{H}_{T - t} \setminus \mathcal{H}_{T - t}^*} H(d_{h_t \oplus h} (\cdot))
		\quad s. t. \; \mathcal{H}_{T - t}^* = \argmax_{h \in \mathcal{H}_{T - t}} H(d_{h_t \oplus h} (\cdot))
	\end{equation*}
	where the maximum is attained by
	\begin{equation*}
		\overline{h}_{T - t} = s_{2}^* \oplus \big(  \ h_{T - t - 1}^* \in \mathcal{H}_{T - t - 1}^* \big) \in \argmax_{h \in \mathcal{H}_{T - t} \setminus \mathcal{H}^*_{T - t}} H \big( d_{h_t \oplus h} (\cdot) \big),
	\end{equation*}
	in which $s_{2}^*$ is any state that is the second-closest to a uniform entry in $d_{h_t \oplus \overline{h}_{T - t}}$.
	\label{thr:best_case_cmp}
\end{lemma}
\begin{proof}
	The best-case CMP $\overline{\mathcal{M}}$ is designed such that taking a sub-optimal action $a \in \mathcal{A} \setminus \{ a^* \}$ at step $t$ minimally decreases the final entropy. Especially, instead of reaching at step $t + 1$ an optimal state $s^*$, \ie a state that maximally balances the state visits of the final trajectory, the agent is drawn to the second-to-optimal state $s_{2}^*$, from which it gets back on track on the optimal trajectory for the remaining steps. Note that visiting $s_{2}^*$ cannot lead to the optimal final entropy, achieved when $s^*$ is visited at step $t + 1$, due to the sub-optimality of action $a$ at step $t$ and Assumption~\ref{ass:unique_action}.
\end{proof}

\paragraph{Instantaneous Regret}
Although the objective~\eqref{eq:finite_samples_entropy} is non-additive across time steps, we can still define a notion of \emph{pseudo-instantaneous regret} by comparing the regret-to-go of two subsequent time steps. In the following, we provide the definition of this expected pseudo-instantaneous regret along with lower and upper bounds to the regret suffered by an optimal Markovian policy.
\begin{definition}[Expected Pseudo-Instantaneous Regret]
	Consider a policy $\pi \in \Pi$ interacting with a CMP over $T - t$ steps starting from the trajectory $h_t$. We define the expected pseudo-instantaneous regret of $\pi$ at step $t$ as $r_t (\pi) := \max \big( 0, \mathcal{R}_{T - t} (\pi, h_t) - \mathcal{R}_{T - t - 1} (\pi, h_{t + 1}) \big)$.
	\label{thr:regret}
\end{definition}
\begin{restatable}[]{corollary}{instantaneousRegretBounds}
    \label{thr:instantaneous_regret_bounds}
	Let $\pi_{\M} \in \Pim$ be a Markovian policy such that $\pi_{\M} \in \argmax_{\pi \in \Pim} \mathcal{E} (\pi)$ on a CMP $\mathcal{M}$. Then, for any $h_t \in \mathcal{H}_{[T]}$, it holds $\underline{r}_t (\pi_{\M}) \leq r_t (\pi_{\M}) \leq \overline{r}_t (\pi_{\M})$ such that
	\begin{align*}
		\underline{r}_t (\pi_{\M}) &= \max \Big( 0, \ H^* \big( \mathcal{V}_t (\pi_{\M}) - \mathcal{V}_{t + 1} (\pi_{\M}) \big) - H^*_2 \mathcal{V}_t (\pi_{\M}) + H_{*} \mathcal{V}_{t + 1} (\pi_{\M}) \Big), \\
		\overline{r}_t (\pi_{\M}) &= \max \Big( 0, \ H^* \big( \mathcal{V}_t (\pi_{\M}) - \mathcal{V}_{t + 1} (\pi_{\M}) \big) - H_* \mathcal{V}_t (\pi_{\M}) + H^*_2 \mathcal{V}_{t + 1} (\pi_{\M}) \Big),
	\end{align*}
	where
	\begin{equation*}
		\mathcal{V}_t (\pi_{\M}) := \frac{1}{ \pi_{\M} (a^*| s_t)} \Var_{hs_t \sim p^{\pi_{\NM}}_t} \big[ \EV \big[ \mathcal{B} ( \pi_{\NM} (a^* | hs_t) ) \big] \big].
	\end{equation*}
\end{restatable}
\begin{proof}
	From the Definition~\ref{thr:regret}, we have that $r_t (\pi_{\M}) = \mathcal{R}_{T - t} (\pi_{\M}) - \mathcal{R}_{T - t - 1} (\pi_{\M})$. Recall that
	\begin{align*}
		&\underline{\mathcal{R}}_{T - t} (\pi) = \mathcal{V}_{t} (\pi) \big( H^* - H^*_2 \big),
		&\overline{\mathcal{R}}_{T - t} (\pi) = \mathcal{V}_{t} (\pi) \big( H^* - H_* \big),
	\end{align*}
	from Lemma~\ref{thr:regret_bounds}. Then, we can write
	\begin{align*}
		\underline{r}_t (\pi_{\M}) &\geq \underline{\mathcal{R}}_{T - t} (\pi_{\M}) - \overline{\mathcal{R}}_{T - t - 1} (\pi_{\M}) = H^* \big( \mathcal{V}_t (\pi_{\M}) - \mathcal{V}_{t + 1} (\pi_{\M}) \big) - E^*_2 \mathcal{V}_t (\pi_{\M}) + H_* \mathcal{V}_{t + 1} (\pi_{\M}),
	\end{align*}
	and
	\begin{align*}
		\overline{r}_t (\pi_{\M}) &\leq \overline{\mathcal{R}}_{T - t} (\pi_{\M}) - \underline{\mathcal{R}}_{T - t - 1} (\pi_{\M}) = H^* \big( \mathcal{V}_t (\pi_{\M}) - \mathcal{V}_{t + 1} (\pi_{\M}) \big) - H_* \mathcal{V}_t (\pi_{\M}) + H^*_2 \mathcal{V}_{t + 1} (\pi_{\M}).
	\end{align*}
\end{proof}

\subsection{Proofs of Section~\ref{sec:complexity_analysis}}
\label{apx:proofs_complexity_analysis}

\npHardness*

\begin{proof}
To prove the theorem, it is sufficient to show that there exists a problem $\Psi_c \in$ NP-hard so that $\Psi_c \leq_p \Psi_0$. We show this by reducing 3SAT, a well-known NP-complete problem, to $\Psi_0$. To derive the reduction we consider two intermediate problems, namely $\Psi_1$ and $\Psi_2$. Especially, we aim to show that the following chain of reductions hold:
    \begin{equation*}
        \Psi_0 \geq_m \Psi_1 \geq_p \Psi_2 \geq_p \text{3SAT}
    \end{equation*}
First, we define $\Psi_1 $ and we prove that $\Psi_0 \geq_m \Psi_1$. Informally, $\Psi_1$ is the problem of finding a reward-maximizing Markovian policy $\pi_{\M} \in \Pi_{\M}$ w.r.t. the entropy objective~\eqref{eq:finite_samples_entropy} encoded through a reward function in a convenient POMDP $\widetilde{\mathcal{M}}^R_\Omega$. We can build $\widetilde{\mathcal{M}}^R_\Omega$ from the CMP $\mathcal{M}$ similarly as the extended MDP $\widetilde{\mathcal{M}}^R_T$ (see Section~\ref{sec:preliminaries} and the proof of Lemma~\ref{thr:optimal_deterministic} for details), except that the agent only access the observation space $\widetilde{\Omega}$ instead of the extended state space $\widetilde{\mathcal{S}}$. In particular, we define $\widetilde{\Omega} = \mathcal{S}$ (note that $\mathcal{S}$ is the state space of the original CMP $\mathcal{M}$),  $\widetilde{O} (\widetilde{o} | \widetilde{s}) = \widetilde{s}_{-1}$,
and the reward function $\widetilde{R}$ assigns value 0 to all states $\widetilde{s} \in \widetilde{S}$ such that $|\widetilde{s}| \neq T$, otherwise (if $|\widetilde{s}| = T$) the reward corresponds to the entropy value of the state visitation frequences induced by the trajectory codified through $\widetilde{s}$.

Then, the reduction $\Psi_0 \geq_m \Psi_1$ works as follows. We denote as $\mathcal{I}_{\Psi_i}$ the set of possible instances of problem $\Psi_i$. We show that $\Psi_0$ is harder than $\Psi_1$ by defining the polynomial-time functions $\psi$ and $\phi$ such that any instance of $\Psi_1$ can be rewritten through $\psi$ as an instance of $\Psi_0$, and a solution $\pi_{\NM}^* \in \Pinm$ for $\Psi_0$ can be converted through $\phi$ into a solution $\pi_{\M}^* \in \Pim$ for the original instance of $\Psi_1$.
    \[ \begin{tikzcd}
    \mathcal{I}_{\Psi_1} \arrow{r}{\psi} & \mathcal{I}_{\Psi_0} \arrow{d} \\%
    \pi_{\M}^* & \arrow{l}{\phi} \pi_{\NM}^*
    \end{tikzcd}
    \]
The function $\psi$ sets $\mathcal{S} = \widetilde{\Omega}$ and derives the transition model of $\mathcal{M}$ from the one of $\widetilde{\mathcal{M}}^R_\Omega$, while $\phi$ converts the optimal solution of $\Psi_0$ by computing
\begin{equation}
    \pi_{\M}^* (a | o, t) = \sum_{ho \in \mathcal{H}_o} p^{\pi_{\NM}^{*}}_t (ho) \pi_{\NM}^* (a|ho)
\end{equation}
where $\mathcal{H}_o$ stands for the set of histories $h \in \mathcal{H}_{t}$ ending in the observation $o \in \Omega$.
Thus, we have that $\Psi_0 \geq_m \Psi_1$ holds. We now define $\Psi_2$ as the policy existence problem w.r.t. the problem statement of $\Psi_1$. Hence, $\Psi_2$ is the problem of determining whether the value of a reward-maximizing Markovian policy $\pi_{\M}^* \in \argmax_{\pi \in \Pim} \mathcal{J}_{\widetilde{\mathcal{M}}^R_\Omega} (\pi)$ is greater than 0. Since computing an optimal policy in POMDPs is in general harder than the relative policy existence problem ~\citep[][Section 3]{lusena2001complexity}, we have that $\Psi_1 \geq_p \Psi_2$.

For the last reduction, \ie $\Psi_2 \geq_p \text{3SAT}$, we extend the proof of Theorem 4.13 in \cite{mundhenk2000complexity}, which states that the policy existence problem for POMDPs is $\NP$-complete. In particular, we show that this holds within the restricted class of POMDPs defined in $\Psi_1$.

The restrictions on the POMDPs class are the following:
\begin{enumerate}
    \item The reward function $R(s)\geq 0$ only in the subset of states reachable in T steps, otherwise $R(s)=0$;
    \item $|\widetilde{\mathcal{S}}|=\widetilde{S}=|\widetilde{\Omega}|^T$.
\end{enumerate}
Both limitations can be overcome in the following ways:
\begin{enumerate}
    \item It suffices to add states with deterministic transitions so that $T=m\cdot n$ can be defined a priori, where T is the number of steps needed to reach the state with positive reward through every possible path. Here $m$ is the number of clauses, and $n$ is the number of variables in the 3SAT instance, as defined in \citep{mundhenk2000complexity};
    \item The POMDPs class defined by $\Psi_1$ is such that $\widetilde{S}=|\widetilde{\Omega}|^T$. Noticing that the set of observations corresponds with the set of variables and that from the previous point $T=m\cdot n$, we have that $|\widetilde{\Omega}|^T = n^{m\cdot n}$, while the POMDPs class used by the proof hereinabove has $\widetilde{S}=m\cdot n^2$. Notice that $n \geq 2$ and $m \geq 1$ implies that $n^{m\cdot n} \geq m\cdot n^2$. Moreover, notice that every instance of 3SAT has $m\geq 1$ and $n\geq 3$. Hence, to extend the proof to the POMDPs class defined by $\Psi_1$ it suffices to add a set of states $\widetilde{S}_p$ s.t. $R(s)=0 \; \forall s\in \widetilde{S}_p$.
\end{enumerate}
Since the chain $\Psi_0 \geq_m \Psi_1 \geq_p \Psi_2 \geq_p \text{3SAT}$ holds, we have that $\Psi_0 \geq_p \text{3SAT}$. Moreover, since $ \text{3SAT} \in \NP$-complete, we can conclude that $\Psi_0$ is $\NP$-hard.
\end{proof}

\subsection{Online Learning of Global Concave Rewards}

Another interesting pair of related works~\cite{cheung2019exploration, cheung2019regret} addresses a reinforcement learning problem for the maximization of concave functions of vectorial rewards, which in a special case~\citep[][Section 6.2]{cheung2019exploration} is akin to our objective function~\eqref{eq:finite_samples_entropy}.
Beyond this similarity in the objective definition, those works and our paper differ for some crucial aspects, and the contributions are essentially non-overlapping. On the one hand, \cite{cheung2019exploration, cheung2019regret} deal with an online learning problem, in which they care for the performance of the policies deployed during the learning process, whereas we only consider the performance of the optimal policy. On the other hand, we aim to compare the classes of non-Markovian and Markovian policies respectively, whereas they consider non-stationary or adaptive strategies to maximize the online objective. Finally, their definition of regret is based on an infinite-samples relaxation of the problem, whereas we account for the performance of the optimal general policy \wrt the finite-sample objective~\eqref{eq:finite_samples_entropy} to define our regret-to-go (Definition~\ref{thr:regret-to-go}).

\subsection{Regret Analysis}

To the purpose of the regret analysis, we will consider the following assumption to ease the notation.\footnote{Note that this assumption could be easily removed by partitioning the action space in $h_t$ as $\mathcal{A} (h_t) = \mathcal{A}_{opt} (h_t) \cup \mathcal{A}_{sub-opt} (h_t)$, such that $\mathcal{A}_{opt} (h_t)$ are optimal actions and $\mathcal{A}_{sub-opt} (h_t)$ are sub-optimal, and substituting any term $\pi (a^* | h_t)$ with $\sum_{a \in \mathcal{A}_{opt} (h_t)} \pi (a | h_t)$ in the results.}
\begin{assumption}[Unique Optimal Action]
	For every CMP $\mathcal{M}$ and trajectory $h_{t} \in \mathcal{H}_{[T]}$, there exists a unique optimal action $a^*\in \mathcal{A}$ \wrt the objective~\eqref{eq:finite_samples_entropy}.
	\label{ass:unique_action}
\end{assumption}
First, we show that the class of deterministic non-Markovian policies is sufficient for the minimization of the regret-to-go, and thus for the maximization of~\eqref{eq:finite_samples_entropy}.
\begin{restatable}[]{lemma}{optimalDeterministic}
	For every CMP $\mathcal{M}$ and trajectory $h_t \in \mathcal{H}_{[T]}$, there exists a deterministic non-Markovian policy $\pi_{\NM} \in \Pic{\NM}{\D}$ such that $\pi_{\NM} \in \argmax_{\pi \in \Pinm} \mathcal{E} (\pi)$, which suffers zero regret-to-go $\mathcal{R}_{T - t} (\pi_{\NM}, h_t) = 0$.
    \label{thr:optimal_deterministic}
\end{restatable}
\begin{proof}
	The result $\mathcal{R}_{T - t} (\pi_{\NM}, h_t) = 0$ is straightforward by noting that the set of non-Markovian policies $\Pinm$ with arbitrary history-length is as powerful as the general set of policies $\Pi$. To show that there exists a deterministic $\pi_{\NM}$, we consider the extended MDP $\widetilde{\mathcal{M}}^R_T$ obtained from the CMP $\mathcal{M}$ as in Section~\ref{sec:preliminaries}, in which the extended reward function is $\widetilde{R} (\widetilde{s}, \widetilde{a}) = H( d_{\widetilde{s}} (\cdot) )$ for every $\widetilde{a} \in \widetilde{\mathcal{A}}$, and every $\widetilde{s} \in \widetilde{\mathcal{S}}$ such that $|\widetilde{s}| = T$, and $\widetilde{R} (\widetilde{s}, \widetilde{a}) = 0 $ otherwise. Since a Markovian policy $\widetilde{\pi}_{\M} \in \Pic{\M}{\D}$ on $\widetilde{\mathcal{M}}^R_T$ can be mapped to a non-Markovian policy $\pi_{\NM} \in \Pic{\NM}{\D}$ on $\mathcal{M}$, and it is well-known~\cite{puterman2014markov} that for any MDP there exists an optimal deterministic Markovian policy, we have that $\widetilde{\pi}_{\M} \in \argmax_{\pi \in \Pim} \mathcal{J}_{\widetilde{\mathcal{M}}^R_T} (\pi) $ implies $\pi_{\NM} \in \argmax_{\pi \in \Pinm} \mathcal{E} (\pi)$.
\end{proof}
Then, in order to prove that the class of non-Markovian policies is also necessary for regret minimization, it is worth showing that Markovian policies can instead rely on randomization to optimize objective~\eqref{eq:finite_samples_entropy}.
\begin{restatable}[]{lemma}{lawTotalVariance}
	Let $\pi_{\NM} \in \Pic{\NM}{\D}$ a non-Markovian policy such that $\pi_{\NM} \in \argmax_{\pi \in \Pi} \mathcal{E} (\pi)$ on a CMP $\mathcal{M}$. For a fixed history $h_t \in \mathcal{H}_t$ ending in state $s$, the variance of the event of an optimal Markovian policy $\pi_{\M} \in \argmax_{\pi \in \Pim} \mathcal{E} (\pi)$ taking $a^* = \pi_{\NM} (h_t)$ in $s$ is given by
	\begin{equation*}
		\Var \big[ \mathcal{B} ( \pi_{\M} (a^*|s, t) ) \big] = \Var_{hs \sim p^{\pi_{\NM}}_t} \big[ \EV \big[ \mathcal{B} ( \pi_{\NM} (a^* | hs) ) \big] \big],
	\end{equation*}
	where $hs \in \mathcal{H}_{t}$ is any history of length $t$ such that the final state is $s$, \ie $hs := (h_{t - 1} \in \mathcal{H}_{t - 1}) \oplus s$, and $\mathcal{B} (x)$ is a Bernoulli with parameter $x$.
    \label{thr:law_total_variance}
\end{restatable}
\begin{proof}[Proof Sketch]
	We can prove the result through the Law of Total Variance (LoTV)~\citep[see][]{bertsekas2002introduction}, which gives
	\begin{align*}
		\Var \big[ \mathcal{B} ( \pi_{\M} (a^*|s, t) ) \big] = \EV_{hs \sim p^{\pi_{\NM}}_t} \big[ \Var \big[ \mathcal{B} ( \pi_{\NM} (a^* | hs) ) \big] \big] \\ + \Var_{hs \sim p^{\pi_{\NM}}_t} \big[ \EV \big[ \mathcal{B} ( \pi_{\NM} (a^* | hs) ) \big] \big], \qquad \forall s \in \mathcal{S}.
	\end{align*}
	Then, exploiting the determinism of $\pi_{\NM}$ (through Lemma~\ref{thr:optimal_deterministic}), it is straightforward to see that $\EV_{hs \sim p^{\pi_{\NM}}_t} \big[ \Var \big[ \mathcal{B} ( \pi_{\NM} (a^* | hs) ) \big] \big] = 0$, which concludes the proof.\footnote{Note that the determinism of $\pi_{\NM}$ does not also imply $\Var_{hs \sim p^{\pi_{\NM}}_t} \big[ \EV \big[ \mathcal{B} ( \pi_{\NM} (a^* | hs) ) \big] \big] = 0$, as the optimal action $\overline{a} = \pi_{\NM} (hs)$ may vary for different histories, which results in the inner expectations $\EV \big[ \mathcal{B} ( \pi_{\NM} (a^* | hs) ) \big]$ being either $1$ or $0$. }
\end{proof}
Unsurprisingly, Lemma~\ref{thr:law_total_variance} shows that, whenever the optimal strategy for~\eqref{eq:finite_samples_entropy} (\ie the non-Markovian $\pi_{\NM}$) requires to adapt its decision in a state $s$ according to the history that led to it ($hs$), an optimal Markovian policy for the same objective (\ie $\pi_{\M}$) must necessarily be randomized.
This is crucial to prove the following result, which establishes lower and upper bounds $\underline{\mathcal{R}}_{T - t}, \overline{\mathcal{R}}_{T - t}$ to the expected regret-to-go of any Markovian policy that optimizes~\eqref{eq:finite_samples_entropy}.
\begin{restatable}[]{lemma}{regretBounds}
    \label{thr:regret_bounds}
	Let $\pi_{\M}$ be an optimal Markovian policy $\pi_{\M} \in \argmax_{\pi \in \Pim} \mathcal{E} (\pi)$ on a CMP $\mathcal{M}$. For any $h_t \in \mathcal{H}_{[T]}$, it holds $\underline{\mathcal{R}}_{T - t} (\pi_{\M}) \leq \mathcal{R}_{T - t} (\pi_{\M}) \leq \overline{\mathcal{R}}_{T - t} (\pi_{\M})$ such that
	\begin{align*}
		\underline{\mathcal{R}}_{T - t} (\pi_{\M}) &= \frac{ H^* - H^*_2  }{ \pi_{\M} (a^* | s_t)} \Var_{hs_t \sim p^{\pi_{\NM}}_t} \big[ \EV \big[ \mathcal{B} ( \pi_{\NM} (a^* | hs_t) ) \big]  \big], \\
		\overline{\mathcal{R}}_{T - t} (\pi_{\M}) &= \frac{ H^* - H_*  }{ \pi_{\M} (a^* | s_t)} \Var_{hs_t \sim p^{\pi_{\NM}}_t} \big[ \EV \big[ \mathcal{B} ( \pi_{\NM} (a^* | hs_t) ) \big]  \big],
	\end{align*}
	where $\pi_{\NM} \in \argmax_{\pi \in \Pic{\NM}{\D}} \mathcal{E} (\pi)$, and $H_*, H^*_2$ are given by
	\begin{align*}
		&H_* = \min_{h \in \mathcal{H}_{T - t}} H(d_{h_t \oplus h} (\cdot)), \\
		&H^*_2 = \max_{h \in \mathcal{H}_{T - t} \setminus \mathcal{H}_{T - t}^*} H(d_{h_t \oplus h} (\cdot)) \\
		&s. t. \; \mathcal{H}_{T - t}^* = \argmax_{h \in \mathcal{H}_{T - t}} H(d_{h_t \oplus h} (\cdot)).
	\end{align*}
\end{restatable}
\begin{proof}[Proof Sketch]
	The crucial idea to derive lower and upper bounds to the regret-to-go is to consider the impact of a sub-optimal action in the best-case and the worst-case CMP respectively (see Lemma~\ref{thr:best_case_cmp},~\ref{thr:worst_case_cmp}). This gives $\mathcal{R}_{T - t} (\pi_{\M}) \geq H^* - \pi_{\M} (a^* | s_t) H^* - \big( 1 - \pi_{\M} (a^* | s_t) \big) H_2^*$ and $\mathcal{R}_{T - t} (\pi_{\M}) \leq H^* - \pi_{\M} (a^* | s_t) H^* - \big( 1 - \pi_{\M} (a^* | s_t) \big) H_*$. Then, with Lemma~\ref{thr:law_total_variance} we get $\Var \big[ \mathcal{B} ( \pi_{\M} (a^*|s_t) ) \big] = \pi_{\M} (a^* | s_t) \big( 1 - \pi_{\M} (a^* | s_t) \big) = \Var_{hs \sim p^{\pi_{\NM}}_t} \big[ \EV \big[ \mathcal{B} ( \pi_{\NM} (a^* | hs_t) ) \big] \big]$, which concludes the proof.
\end{proof}
Finally, the result in Theorem~\ref{thr:regret_theorem} is a direct consequence of Lemma~\ref{thr:regret_bounds}. Note that the upper and lower bounds on the regret-to-go are strictly positive whenever $\pi_{\M} (a^* | s_t) < 1$, as it is stated in Corollary~\ref{thr:sufficient_condition}.

\section{Introduction}
\input{contents/sections/introduction.tex}

\section{Preliminaries}
\label{sec:preliminaries}
\input{contents/sections/preliminaries.tex}

\section{Infinite Samples: Non-Markovianity Does Not Matter}
\label{sec:infinite_samples}
\input{contents/sections/infinite_samples.tex}

\section{Finite Samples: Non-Markovianity Matters}
\label{sec:finite_samples}
\input{contents/sections/finite_samples.tex}

\section{Complexity Analysis}
\label{sec:complexity_analysis}
\input{contents/sections/complexity_analysis.tex}

\section{Numerical Validation}
\label{sec:numerical_validation}
\input{contents/sections/numerical_validation.tex}

\section{Discussion and Conclusion}
\label{sec:conclusions}
\input{contents/sections/conclusions.tex}

\section*{Acknowledgements}
We would like to thank the reviewers of this paper for their feedbacks and useful advices. We also thank Romain Laroche and Remi Tachet des Combes for having signalled a technical error in a previous draft of the manuscript.

redpajama_set_name: RedPajamaArXiv


Easy Chicken Fried Rice is the perfect quick, delicious weeknight meal!
Today I am back after a few weeks off, moving with small kids is no joke you guys! School starts this week so I am sharing one of our favorite quick and easy meals, Easy Chicken Fried Rice. It is perfect for the hectic weeks that lie ahead with the hustle and bustle of the back to school season.
My favorite thing about this meal is that it can be made even faster with leftovers. Maybe you made a bunch of rice the night before to serve with your tacos, now just turn the leftovers into fried rice. Got leftover chicken, even easier, just chop some up and toss it in! I like to use a frozen veggie mix, you can steam it in the microwave while you prep the other parts of the meal and it is a snap.
My family prefers this dish with white rice, but it is so easy to switch it up and use your favorite type of rice instead. Chicken, carrots, peas, onions and fried egg make this Easy Chicken Fried Rice a great all in one meal. I'm sending all of you mamas and papas out there some good vibes for a safe and happy back to school, I hope you'll enjoy this meal as much as we do!
In a large skillet or wok heat the oil and cook the onion until tender.
Add the cooled rice and cook for about 3 minutes, then stir to cook the other side.
Add the soy sauce and honey, stir to coat the rice.
Stir in the chicken, veggies and fried egg.
Cook for another 3-5 minutes until all ingredients are warm.
Me too too Blair, thanks for sharing!
Yum! We love making fried rice- and a big bowl of this looks so good right now!
It is definitely one of our favorite easy meals!
One of my favorite leftover meals to make !
This does look easy! So perfect as a quick side dish or light dinner!
I am always on the lookout for new leftover recipes!! This is going on my to-make list!
We just moved into our new house back in May and I can't imagine would it would be like with kid! And I am thinking this dinner is genius!
Oh Meg, in our experience moving with kids has never been easy, but I am always more motivated to get their things unpacked and set up. As for dinner, this meal is so easy its a definite win!


Garden Fencing Edinburgh- this fence was installed at the Hermitage, Edinburgh. The syle of fencing is slatted boards 100mm wide fixed onto rails secured to 100mm posts which are concreted into the ground 600mm deep.
The slats are fitted to both sides of the rail and are offset to allow wind to pass through the fence. This serves two purposes – reducing wind turbulance to lea side of fence and reducing wind strain on the fence. It also looks good!
All the timbers are fsc sourced and treated.
Call David on 0800 3286458 or info@garden-co.com for a free no obigation quote.
This entry was posted in Garden Fencing Edinburgh, Fencing Edinburgh, Fencing Services Edinburgn,, Guides, News and tagged Fencing Edinburgh, Fencing Services Edinburgh, Garden fencing Edinburgh by Garden Co. Bookmark the permalink.


text:
Porgs Are Just Chickens Sped Up, According To New ABC 'The Last Jedi' Documentary
By Jade Budowski Twitter @jadebudowski Feb 20, 2018 at 12:49pm
Remember when we found out that funnymen Ben Schwartz and Bill Hader voiced BB-8 in Star Wars: The Force Awakens? It was a delightful surprise, one that made watching the little round droid roll around even more fun. With the recent release of Star Wars: The Last Jedi and many a new creature and stunt to be found, there are some more secrets behind the scenes to be uncovered. Thanks to The Force of Sound, a new documentary from ABC News Features, we now know that the adorable wails of porgs are actually… the cries of chickens, sped up.
That's right. From the feathered truth behind the calls of the adorable porgs and the "vacuum" conversations between Kylo Ren and Rey to creatures at Canto Bight how they pulled of the breathtaking Holdo Manuever, this 30-minute special is a treat for Star Wars fans and tech junkies alike.
As director Rian Johnson points out, this frequently overlooked facet of film is absolutely essential. "Sound is not just a layer we put on top of the storytelling, it is the storytelling," says Johnson. That's exactly what we see in these scenes at Skywalker Ranch, and the chance to watch these professionals do what they do best (for one of the biggest film franchises of all time) is absolutely fascinating.
If you're itching for new Star Wars content and can't wait until it's released on VOD, Blu-Ray, and DVD March 27, The Force of Sound is the perfect way to keep the Force alive.


text:
Rabbis: Don't take charity from criminals
Religious leaders say one must not accept donations from people involved in organized crime so as not to 'purify their conscience.' Publishing criminal's contribution to synagogue can be seen as legitimizing his actions, Hotam rabbinical forum writes in position paper
Kobi Nachshoni|Published: 12.10.13 , 14:12
Rabbis and religious judges specializing in Jewish Law have ruled that one must not accept donations for religious purposes from well-known criminals from the underworld.
On the backdrop of a recent affair which revealed an alleged link between criminal organizations and rabbis' associates, the Hotam rabbinical forum released a position paper stating that "they must be kept away from anything holy, as long as they don't repent and abandon their ways."
Organized crime equals terror
Adv. Ilan Bombach
Op-ed: Shin Bet's investigation methods should be used by police against criminal organizations
According to forum members who are researchers at the Mishpetei Eretz Institute, in principle synagogues and Torah and charity institutions may raise funds from criminals under certain conditions, but "in a case that the donors belong to what is known as 'organized crime' whose goal is to impose force and intimidation – in this case it is forbidden to accept any charity from them."
'Din rodef' on criminals
The rabbis explained that the donation could "purify the conscience" of the criminals and make their bad ways appear legitimate. In addition, they ruled that due to the risk the criminals pose to the entire public, these people are subject to "din rodef" ("law of the pursuer") – a serious halachic definition, which in its original meaning permits killing them.
Another reason mentioned by the Hotam forum members is "defamation of God," which may be caused as a result of the donation: "If it is publicized that Torah institutions are receiving donations from a famous criminal… this will lead to Torah becoming less valuable in the eyes of the public."
They further noted that "publicizing the criminal's donation to the synagogue can be seen as legitimizing his actions, and also includes the prohibition of flattering the evil."
The rabbis ruled, however, that in case of concerns that the money rejected by religious institutions would be used for crime or that the refusal to accept it would lead to harassment by the criminals – one must accept the donation but avoid using it for mitzvah purposes. "If possible, one must work to return the money to the people it was robbed from."
Charity doesn't atone for all sins
As part of the discussion on the donation of criminals whose crimes are not organized, the institute researchers wrote that the Halacha indeed forbids enjoying stolen goods and accepting charity from people who engage in theft, but that "if they also have legal businesses it is permitted to accept charity from them if one can assume that it comes from the legitimate business" (and not when the amount of the donation is higher than the reasonable income of the legitimate source).
Another condition for accepting the donation is that it does not include any flattery or defamation of God, and that it is done without any publicity. However, they said, meeting that condition is "very difficult" and therefore "it would be better to stay away from it." The recommendation to a private person is to be even more strict and "avoid taking charity from an impure source.
"One must be careful that accepting the charity will not create the impression among the criminal that as long as he gives away some of his money to charity, all his sins are forgiven and he can continue with his bad ways," the rabbis stressed. "So if he continues with his aberrant way and only covers for himself by giving charity – that must not be allowed."
See all talkbacks "Rabbis: Don't take charity from criminals"


Activist and lecturer in law at Southern Cross University, Aiden Ricketts says the protest, now in its seventh week, will not bow to police pressure. He says the police raid was an expensive "festival of force" by the O'Farrell Government.
"What we're seeing today is this kind of symbolic show of force by the state, to come in, allocate a whole lot of tax payers' money, bring a whole lot of police for one day, bust out a blockade, and the truth is there's another 364 days in every year in which the communities will be resisting coal seam gas and we know that the full riot squad aren't going to be there every day," he says.
"It's quite clear that not just in the Lismore local government area, but throughout the northern rivers, 85 to 90 per cent of people are against coal seam gas.


text:
> Destinations
Related topics: Hotels & Lodging, Safety & Security
Hurricane Closes North Carolina Landmark for Renovation
Blockade Runner Beach Resort, a North Carolina landmark and icon of Wrightsville Beach for 55 years, has closed for renovations due to damages sustained from Hurricane Florence.
"We made the decision following several weeks of analysis and assessments with engineers and experts," said Mary Baggett, co-owner and operator of the resort with her brother William Baggett. "The target date for re-opening is early Spring 2019."
Hurricane Florence made landfall at Wrightsville Beach on Sept. 14, delivering destructive winds in excess of 100 mph. Over a five-day period, slow-moving Florence poured totals of 20 to 35 inches of rain into Eastern North Carolina creating record breaking floods, widespread property damage, and a death toll of 40 people in the state.
"We extend our deepest sympathies to the families who lost loved ones, the people rebuilding their lives and homes, and the hard-hit communities and businesses overwhelmed by Hurricane Florence," said William Baggett. "The people of North Carolina are strong and resilient. We will recover from the storm."
Illustrating the enormity of the downpour, the National Weather Service in Raleigh estimated that Hurricane Florence dropped over 8-trillion gallons of rain in the state, the equivalent of about 780,000 gallons of water for every person in North Carolina.
"The major cause of damage was the loss of the roof on the Balcony building and more limited roof damage on the Tower," said Nicolas Montoya, Blockade Runner General Manager. "In the areas penetrated by heavy rain, operations shift from cleanup to restoration."
CoreLogic, a leading provider of data to business and government, estimates $19 billion to $28.5 billion in residential and commercial property damage in the Carolinas and Virginia.
"Our family has owned and operated the Blockade Runner for a half-century," said Mary Baggett. "Over the years, we were honored to host thousands of weddings, vacations, getaways, meetings, conventions, fundraisers, and major events. We look forward to renovating and improving the Blockade Runner and resuming operations in the early Spring."


text:
Print Subscription Services
Subscribe to Home Delivery
Manage Your Print Subscription
Best Preps
Defensive Player Of the Week
Offensive Player of the Week
Summer Camps and Schools
ETX View Magazine
TexasAllOutdoors.com
M. Roberts Digital
Tyler, TX (75702)
Cloudy. Slight chance of a rain shower. Low 46F. Winds NE at 5 to 10 mph..
Cloudy. Slight chance of a rain shower. Low 46F. Winds NE at 5 to 10 mph.
West Brook edges Lufkin
By By BRANDON OGDEN, The Lufkin News
LUFKIN - In a game that featured 19 touchdowns, it all came down to one final play for the Lufkin Panthers.
With 0.2 seconds on the clock, Kordell Rodgers heaved the ball to the end zone, and it appeared it was going to be caught by Dhailon Phillips to give the Panthers a chance to tie the score. However, the ball came free and hit the ground as Beaumont West Brook took a 70-63 decision Friday night at Abe Martin Stadium.
"The effort was good, but we have to make plays," Lufkin head coach Todd Quick said. "We're not making plays when we need to."
After Tre' Grant gave Lufkin a 63-62 lead with 2:25 left, West Brook took the ball and regained the lead with 29 seconds left on a 35-yard run by L'Ravien Elia.
The Panthers took the ball at their own 34 after the kickoff. Completions to Jamel Richemond and Phillips, and an 8-yard run by Rodgers put Lufkin at the West Brook 43 with 7.4 seconds left. Rodgers' first attempt at a Hail Mary was incomplete a few yards in front of the end zone with 0.2 seconds on the clock to set up one final play.
Rodgers finished 24 of 42 for 383 yards with three touchdowns. He also rushed for 130 yards and two scores on 13 carries.
The game was back-and-forth all night. In the first two minutes of the game, West Brook scored on a 60-yard pass from wide receiver Damon Ward to Kandin Robertson, and Lufkin scored on a 49-yard strike from Rodgers to Malik Jackson.
The score was 14-14 heading into the second quarter until West Brook went ahead with a 3-yard run by James Jones. The Panthers responded 35 seconds later with a 64-yard touchdown pass to Phillips.
After a 26-yard touchdown pass from Elia to Bralin Simon that gave West Brook a 28-21 lead, Lufkin used a 50-yard pass from Rodgers to Jackson to set up a 1-yard scoring run by Kahlil Brown, who left the game early with an injury and finished with 65 yards and two touchdowns on 13 carries.
The Panthers took a 35-28 halftime lead thanks to a 4-yard touchdown run by Rodgers with 1:01 remaining in the second quarter.
There wasn't any scoring in the first five minutes of the third quarter until Elia's 19-yard pass to Joel Denley tied the score at 35. Lufkin came back quickly as Rodgers connected for a 23-yard touchdown pass to Richemond, who made a highlight-reel catch in the end zone. West Brook's Robertson answered with his own highlight-worthy catch - a 17-yarder from Elia - to tie the score at 42.
Early in the fourth quarter, Grant gave the Panthers a 49-42 edge with a 2-yard run. Less than a minute later, Elia threw a short pass to Denby, who made a spin move and broke a tackle on the way to an 80-yard touchdown.
After a Lufkin punt, Elia scored on a 56-yard run to put the Bruins ahead 56-49. The Panthers then tied things up with a 5-yard touchdown run by Rodgers.
With 3:32 left, West Brook captured the lead once again on a 22-yard pass from Elia to Robertson, but the extra point went wide left to make the score 62-56. Grant's 39-yard touchdown run and Rodrigo Molina's extra point helped the Panthers grab a 63-62 advantage with 2:25 on the clock.
Elia, who normally splits quarterback duties with Marcus Johnson and had only attempted 26 passes this season, finished 16 of 23 through the air for 308 yards and four touchdowns - all in the second half. He also carried the ball 27 times for 256 yards and two scores. Denley had 19 carries for 178 yards, and he caught seven passes for 145 yards and two touchdowns. Robertson had seven catches for 152 yards and two scores.
The Panthers (4-3, 1-2) have allowed 133 points in their last two games. They dropped a 63-42 contest to The Woodlands on Sept. 30. West Brook (7-1, 3-1) was coming off a 72-7 setback to The Woodlands.
Lufkin sophomore receiver Breylon Garcia left the game in the second half with an injury and was carted out of the stadium on a stretcher.
Jackson made four catches for 125 yards and a touchdown, and Phillips had 11 grabs for 149 yards and a touchdown.
Lufkin will travel to Conroe next Friday to take on Oak Ridge.
Get news sent to you!
Sign up to get our newsletters emailed to you.
Headline News Updates
This email is scheduled for delivery on Monday-Friday at around 6am. It will include the most significant recent articles from all sections of TylerPaper.com.
This email is scheduled for delivery Wednesdays, Fridays and Saturdays at around 9:00 am. It will include the most significant recent articles from the sports section of TylerPaper.com.
This email will only be sent as needed. It will include one or more promotions (special deals/offers/sales, events, contests, etc.).
This email will only be sent as needed. It will include a significant breaking news article from TylerPaper.com.
Global CNC Vertical Machining Centers Market Size to Grow by Almost 443 Million During 2020-2024 | Technavio
Tyler man charged with murder, $800,000 bond
Tyler woman, 25, dies after one-vehicle accident in the city
LaBreya Dejuan Johnson- Mack
tylerpaper.com
100 E. Ferguson, Suite 501
Email: webmaster@tylerpaper.com
© Copyright 2021 TylerPaper.com, 100 E. Ferguson, Suite 501 Tyler, TX | Terms of Use | Privacy Policy


text:
I'd like to introduce you to Sophie – a mother of two young children; Ella, who is eight years old, and Sam, who is five.
Having found herself getting run down by all the demands of raising a young family, Sophie decided to look for more constructive ways of managing her children's more challenging behaviour. She came across Clean questions at a parent workshop and found that they had an almost immediate impact for her:
Clean questions help me to know how to help my children.
For example, Ella has always found it really hard walking into a busy playground and getting to school two minutes before the doors open. There are lots things that could have been making her distressed — noise, space, anticipation, saying goodbye to me — and I'd never really got to the bottom of it. If you don't know what's hard about a situation then it's difficult to know how to fix it.
So I sat down on my bed with her and asked her if it was OK to try and find out what was going on. I asked a few Clean questions about going into the playground and she came up with this brilliant metaphor:
'It's like walking into a room where a bomb of children has just gone off.'
I suddenly understood that there was a really big impact and disorder for her that was to do with the noisiness and the movement. She kept doing this gesture exploding up and out with her hands, which seemed really significant for her. I discovered that her distress wasn't so much about saying goodbye to me or about being nervous at school, it was about dealing with the sensory overload — that bomb of children. So now we make sure we get to school when it's quieter. She's fine if she's already there and things build up as people come in — she can absorb that. But walking into a space that's already full is hard for her.
Everyone had always said, 'She's just clingy, she just needs to get used to it.' But you can't get used to bombs going off. If that's how it feels then it's not something that you should have to get used to. Clean questions gave meaningful depth to her experience — it let me separate the issues out rather than just assuming that it was because she was clingy.
Clean has helped me realise how much the way my thinking colours the way I see things. I'm much more aware now that I am not other people and they are not me — which sounds very obvious, but it's easy to forget that not everybody is thinking or feeling what I'm thinking or feeling. You only have to realise that once and then it has a profound effect forever.


text:
Mudslide odds one in 500
Fairmont "debris flow" created by a perfect storm of events not likely to happen again within the next 500 years.
Sally Macdonald
The aftermath from last July's mudslide on Mountainside Golf Course in Fairmont.
The mudslide that hit Fairmont Hot Springs last July was a once in 500 years event.
The finding was made in a technical report set to be accepted by the Regional District of East Kootenay (RDEK) board of directors on Friday, February 1.
The Fairmont Creek risk assessment found that the July 15, 2012 mudslide was not caused by a temporary dam near the creek's headwaters, as emergency responders believed at the time.
In fact, the mudslide's cause was cumulative, attributed to heavy rain falling on a higher than normal snowpack.
"Rather than any single trigger factor, the 2012 debris flow is judged to have initiated by progressive destabilization of abundant bedload in the mainstem channel by a locally-intensive convective rainstorm at a time when soils were already saturated from an unusually wet spring," reads the report.
"I was surprised that the report noted the event was a 500 year event, while at the same time it mentioned other minor slide events that have occurred within the past 50 years. That was news to me," said Area F board director Wendy Booth.
Fairmont Creek flows for seven kilometres from the peak of Fairmont Mountain, at an elevation of 2,600 metres, to the Columbia River, at an elevation of 820 metres. At its headwaters, the creek runs through steep, bedrock-controlled channels. Downstream, it transitions to a lower gradient channel before flowing through Marble Canyon.
Leading up to the July mudslide, snow pillow stations nearby reported a winter snow pack up to 170 per cent above normal. Then, starting in mid-May, there was a rapid snow melt. Finally, in the days before July 15, a localized storm cell brought between 20 and 26.4 millimetres of rain.
All of these factors led to the dangerous mudslide that tour through Fairmont at 4:15 p.m. on Sunday, July 15, 2012. An estimated 65,000 cubic metres of debris came down the creek at speeds up to 22 kilometres an hour.
It buried the hot springs source wells under seven metres of debris, washed out the RV park access road, severely damaged a foot bridge to the RV park, filled Marble Canyon with several metres of rock and debris, washed away a walking trail, and inundated several homes with mud, rock and debris. More than 350 people were temporarily evacuated.
The water source for Fairmont Hot Springs Resort and Mountainside Golf Course was lost, forcing the resort to close for three weeks during peak season, leading to a $1.5 million loss of revenue. Seven holes of the golf course were affected.
However, geologists predict such an event is only likely to happen once every 500 years, with only a 10 per cent chance it will happen again in the next 50 years.
Still, smaller, hazardous debris flows are likely to happen every 25 years, the report finds.
"With predicted climate change effects on precipitation, the increased frequency of storm events, and the potential for increased runoff due to wildfire, there is a corresponding increase in the potential for debris flow," reads the report.
At risk from future debris flows are: 16 multi-family dwellings and 88 single-family dwelling; approximately 350 people; Mountainside Golf Course; a Community Recreation Centre; Fairmont Fire Hall; the only access to the RV Park; and Highway 93/95.
The report makes 12 recommendations in five phases to protect those assets from future slides. Phase 1 includes: restoring the channel and riprap dyke through Marble Canyon (work already underway); reconstructing the channel through the golf course; maintaining the golf course pond as a flood control structure; and inspecting drainage structures between the golf course and the creek's outflow into the Columbia River. Phase 2 focuses on work upstream of Marble Canyon, including: widening the creek's channel upstream of the resort; building a bridge over the access road to the RV Park; increasing the channel capacity through Marble Canyon and installing a refuge area on the walking trail; and constructing a debris flow barrier system in the canyon. Phase 3 is to complete a watershed management plan; phase 4 is to conduct five-year inspections along the length of the creek; and phase five is to install a rainfall gauge at the resort. In total, the recommended mitigation measures would cost $2.5 million.
Prepared by Clarke Geoscience and Golder Associates, both of Kelowna, the Fairmont Creek Debris Flow Hazard and Risk Assessment was commissioned by the RDEK in September and completed this month. It was funded by the Provincial Emergency Program with technical review by the Water Stewardship Division of the Ministry of Forests, Lands and Natural Resource Operations.
The board will discuss the report at its January 31 and February 1 meetings. Staff is recommending the board present the results of the assessment to the Fairmont community and consider it for future funding opportunities.
"The report mentions various things that can and should be done," said Wendy Booth. "In order to complete all the recommendations in the report, it is about a $2 million price tag. I currently don't know where that funding is going to come from, however I intend to do my best to secure the funding. Fingers crossed."
Nelson proposed to join Kootenay–Columbia riding
No money for Jumbo reps


Sofas in the style of the classic living room London, completely made by hand in Italy are suitable for the most elegant classic ambience. The sofas in the style of the living room London, are the artisan production, and, with their majestic forms, but at the same time simple, are very suitable to the combination with pieces of elaborate furniture, such as the wooden coffee tables, hand-carved and finished in gold leaf. The ancient technique consists in applying hand-thin gold foils on the surface of the wood, and the result is exclusive and luxurious furniture. Every particular of these sofas in style is nice and finished in details, so that they can be placed even in the center of the room with their backs machining pleated. The fabrics with which they are made are all of the highest quality, and can be chosen from a sample-rich, able to satisfy every taste and give the perfect tone to any environment. The shape of the collection London is softly rounded and it gives these sofas not only an elegant and sophisticated look, but also all the comfort that befits a sitting room in which to receive guests in comfort.


These inventions can be new products or new methods and processes. Our firm focuses primarily on patents in the area of chemistry, pharmaceuticals, and biotechnology. We have handled patent protection for everything: from new drugs for cancer and schizophrenia, to new toothpaste formulations, to new kinds of chocolate, and much more. We regularly represent start-up biotech companies, as well as multinational pharmaceutical and consumer product companies.
Most of our firm's business involves drafting, filing, and prosecuting patent applications. We handle patent filings directly with the patent office in the U.S., and we work with our network of foreign patent agents to obtain patent protection in countries around the world.
All of our attorneys and patent agents have degrees in chemistry, biology, or biochemistry. Some have doctoral degrees and/or have worked at major pharmaceutical companies. All have taken and passed the examination to practice before the United States Patent and Trademark Office (USPTO). The attorneys have law degrees and have also passed a state bar examination.
We have many years of experience in prosecuting patent applications before the USPTO, and where necessary, appealing cases to the Patent Trial and Appeal Board, to federal district court, and to the U.S. Court of Appeals for the Federal Circuit. We have recently handled several appeals from the USPTO to district court, and to the Federal Circuit, involving calculation of patent term adjustment, which is particularly important to pharmaceutical companies. We have also represented clients in complex proceedings before the patent office, such as interferences, reissues, re-examinations, and inter partes review (IPR).
Many of our attorneys, including Mike Straher, Brian Stegman, and Tom Hoxie, have worked at senior positions in corporate patent departments or research departments. Tom Hoxie, for example, has experience as an expert witness in a number of cases, where he has testified not only about pharmaceutical patent matters, but about ordinary and customary licensing practices in the pharmaceutical industry. We are familiar with drug development and approval processes, and we can make sure that your patent strategy is coordinated with your regulatory strategy.
We can help large and small companies to develop cost-effective strategies to protect their chemical, pharmaceutical and biotechnology inventions, while avoiding infringing on other parties' patent rights. We can help investors in determining whether a target company has strong intellectual property protection for its products or has exposure to third party claims of infringement. In addition, we can negotiate and implement agreements with employees, consultants, and third parties to protect your intellectual property and to acquire, assign, or license intellectual property rights as needed. We have the expertise to protect your intellectual property and enforce your rights, even if it means going to court.


text:
← "Patio Tomatoes" by Krista Lukas
"For Those Who Never Know What to Say to Widows" by M →
TEN THOUSAND VOICES by Rick KempaPosted by Rattle
Review by John Yohe
TEN THOUSAND VOICES
by Rick Kempa
Littoral Press
2013, 80 pp., $16.00
www.littoralpress.com
I continue to think of Rick Kempa as the Poet Laureate of the American Southwest: Based in Rock Springs, Wyoming, Kempa is an avid backpacker/explorer, especially of the Grand Canyon. He's also busy: In addition to this latest book of poetry, Ten Thousand Voices, he has an upcoming book of his own essays on hiking in the Colorado Plateau, as well as two anthologies he's edited, one of poetry, one of essays, about the Canyon (through Vishnu Temple Press). And though Ten Thousand Voices does have poems about the Southwest and the Grand Canyon, including the great, "What the Canyon Teaches," it also contains poems about Kempa's travels elsewhere in America, including Vermont, and my old stomping grounds, Michigan. In fact, this book is about America, and Kempa reveals himself, not as just a regional poet, but as an American poet.
Although the general theme of the book is travel, the real subject is the people that Kempa meets and talks to along the way, their voices become the poetry, showing that voices are poetry. The best example of this, and one of my favorites of the collection, is "Invitation," which begins:
If you come here tonight, I'll show you everything
that shaped my day: How Megan put the tail from the pig-
roast in my hand, and Jack shouted, "Stop! Two lady-
bugs are fucking on your head!" Found a marble. Larry
said, "Work is prayer." Women in Tibet use cow dung
for mascara. Climbed a sycamore. Sartre wrote, "Being
is doing." Heard the first cicada drone: No thing
too big we can't join hands around, and you will show me
what you found, if you come here. …
"Invitation" is also a good example of Kempa's use of the prose poem, which, I feel, allows for a more casual-sounding (although that description is deceptive) language, maybe because it invites in a more story-telling/narrative style. Meaning more approachable. Meaning closer to a "spoken" voice. The human voice as poetry.
I also love the juxtaposition of the quote from Sartre with the quotes from Larry, and even Jack, all three equally meaningful bits of philosophy (should not we all pause to observe the small miracles in life, like ladybugs fucking on our heads?). At first I took this poem to be an example of how poets find the truly interesting people in life, but then I realized that Kempa is saying everyone is interesting, all ten thousand voices of us, and it just takes noticing them. That's what a poet does best maybe, is notice, which serves as a reminder that we could too.
That said, another function of the poet is as "wiseperson" and teacher of, and for, the tribe, and Kempa's voice has a compelling power, especially when used in a musical, chant-like way, using lists and repetition to build energy, like in another favorite of mine, "History of My Water Bottle, June 20th 1986," in which each line is a description (one more voices!) of all the people who filled a younger hitchhiking Kempa's water bottle on one given day. Or in the aforementioned "What the Canyon Teaches":
… How few are your needs. Sip, nibble, nap, lack nothing.
How strong is your body, forgiving of abuses and neglect.
How simple is your task, a sequence of sure steps.
How safe you are on this earth, if you attend to it.
How intricate, how lush, life is. Sit still, know its wealth.
How precious is each moment you are privileged to draw breath.
Born in Puerto Rico, John Yohe grew up in Michigan, and currently lives in Portland, Oregon. He has worked as a wildland firefighter, deckhand/oiler, runner/busboy, bike messenger, wilderness ranger, as well as a teacher of writing. He has lived in Mexico, Spain, France, and traveled to six continents. His first full-length collection of poetry, What Nothing Reveals, is out now. His work has appeared previously in such journals as Fence, Rattapallax, Rattle, and The Hat. A complete list of his publications, and poetry, fiction and non-fiction writing samples, can be found at his website. (www.johnyohe.com)


Home → Shipping Container → Steel Or Aluminum? Which Type Of Shipping Container Will Address Your Needs?
Steel Or Aluminum? Which Type Of Shipping Container Will Address Your Needs?
While steel is commonly used to manufacture standard ISO containers, aluminum also happens to be another metal that is used to make ISO shipping containers. However, shipping containers that are made out of two different metals will be different not only in terms of structural integrity, but also in terms of functionality. Generally, dry and refrigerated shipping containers are used to transport international cargo. Steel shipping containers are commonly used to carry dry cargo and they come as open top and flat rack containers. The evolution of today's sturdier steel containers can be attributed to the thorough process of sandblasting and heavy duty coating that not only adds to the metal's strength, but also makes it corrosion-resistant. Earlier, some cargo manufacturers used aluminum to make dry boxes, but ultimately, the industry replaced aluminum with steel after it realized that steel had more strength to endure the weight of heavy cargo.
Refrigerated containers, also called reefer containers, are required to carry lighter objects and they are often made out of aluminum. Such containers come with thick insulated walls and they are lighter in weight compared to their steel counterparts which makes them an ideal option for the transportation of frozen or temperature-sensitive items. Besides, aluminum shipping containers are also noted for their thermal efficiency. Notably, once the refrigerated containers lose their cooling functionality after their service-life, they can be used to carry frozen as well as dry cargo or anything that needs to be insulated from the external elements. To sum up, steel containers are ideal for transporting dry goods whereas aluminum containers can be used efficiently to carry frozen items.
However, if you need to address your general portable storage needs, you may need to consider a number of factors including maintenance, lifespan, and function while choosing between steel containers and aluminum containers. It is a pricy job to repair aluminum containers as you will need to invest considerably in welding processes. Additionally, aluminum containers have shorter life-spans compared to steel containers. You may consider using aluminum containers if you need to protect temperature-sensitive products from extreme external environment. On the other hand, it is quite easy to implement general modifications in steel containers and they can be repaired in a cost-effective manner as well. Steel containers are stronger and diverse and they can be used for various purposes. Steel containers are noted for their architecture, creative structures, and adaptability to modifications and this explains why they have emerged as the most popular ocean freight options.


text:
/*****************************************************************************
 OSSLDES.cpp

 OpenSSL (3)DES implementation
 *****************************************************************************/

#include "config.h"
#include "OSSLDES.h"
#include <algorithm>
#include "odd.h"

bool OSSLDES::wrapKey(const SymmetricKey* /*key*/, const SymWrap::Type /*mode*/, const ByteString& /*in*/, ByteString& /*out*/)
{
	ERROR_MSG("DES does not support key wrapping");

	return false;
}

bool OSSLDES::unwrapKey(const SymmetricKey* /*key*/, const SymWrap::Type /*mode*/, const ByteString& /*in*/, ByteString& /*out*/)
{
	ERROR_MSG("DES does not support key unwrapping");

	return false;
}

const EVP_CIPHER* OSSLDES::getCipher() const
{
	if (currentKey == NULL) return NULL;

	// Check currentKey bit length; 3DES only supports 56-bit, 112-bit or 168-bit keys
	if (
#ifndef WITH_FIPS
	    (currentKey->getBitLen() != 56) &&
#endif
	    (currentKey->getBitLen() != 112) &&
            (currentKey->getBitLen() != 168))
	{
		ERROR_MSG("Invalid DES currentKey length (%d bits)", currentKey->getBitLen());

		return NULL;
	}

	// People shouldn't really be using 56-bit DES keys, generate a warning
	if (currentKey->getBitLen() == 56)
	{
		DEBUG_MSG("CAUTION: use of 56-bit DES keys is not recommended!");
	}

	// Determine the cipher mode
	if (currentCipherMode == SymMode::CBC)
	{
		switch(currentKey->getBitLen())
		{
			case 56:
				return EVP_des_cbc();
			case 112:
				return EVP_des_ede_cbc();
			case 168:
				return EVP_des_ede3_cbc();
		};
	}
	else if (currentCipherMode == SymMode::ECB)
	{
		switch(currentKey->getBitLen())
		{
			case 56:
				return EVP_des_ecb();
			case 112:
				return EVP_des_ede_ecb();
			case 168:
				return EVP_des_ede3_ecb();
		};
	}
	else if (currentCipherMode == SymMode::OFB)
	{
		switch(currentKey->getBitLen())
		{
			case 56:
				return EVP_des_ofb();
			case 112:
				return EVP_des_ede_ofb();
			case 168:
				return EVP_des_ede3_ofb();
		};
	}
	else if (currentCipherMode == SymMode::CFB)
	{
		switch(currentKey->getBitLen())
		{
			case 56:
				return EVP_des_cfb();
			case 112:
				return EVP_des_ede_cfb();
			case 168:
				return EVP_des_ede3_cfb();
		};
	}

	ERROR_MSG("Invalid DES cipher mode %i", currentCipherMode);

	return NULL;
}

bool OSSLDES::generateKey(SymmetricKey& key, RNG* rng /* = NULL */)
{
	if (rng == NULL)
	{
		return false;
	}

	if (key.getBitLen() == 0)
	{
		return false;
	}

	ByteString keyBits;

	// don't count parity bit
	if (!rng->generateRandom(keyBits, key.getBitLen()/7))
	{
		return false;
	}

	// fix the odd parity
	size_t i;
	for (i = 0; i < keyBits.size(); i++)
	{
		keyBits[i] = odd_parity[keyBits[i]];
	}

	return key.setKeyBits(keyBits);
}

size_t OSSLDES::getBlockSize() const
{
	// The block size is 64 bits
	return 64 >> 3;
}

redpajama_set_name: RedPajamaGithub