It is essential to approach the interpretation of our algorithm's results with caution and subject them to critical evaluation. In this section, we provide the definition of partial ancestral graphs (P AGs). A P AG shares the same adjacencies as any MAG in the observational equivalence class of MAGs. Section 2. For any v W, let G In this section, we derive the causal effect for the SMCM in Figure 3(top), i.e., (6), as well as prove D.1 Proof of (6) First, using the law of total probability, we have P(y |do (t = t)) = null Rule 3a, (c) follows from Rule 1, and (g) follows from Rule 2. D.2 Proof of Theorem 3.1 Lemma 1. Suppose Assumptions 1 to 3 hold. Given this claim, Theorem 3.1 follows from Tian and Pearl [2002, Theorem 4].

Science Biology Evolution Humans really don't need chins Homo sapiens are the only primates that have them, but they don't make us special. Breakthroughs, discoveries, and DIY tips sent six days a week. Auguste Rodin's is one of the art world's most recognizable images. The monumental depiction of a man hunched forward, right hand resting against his chin, is synonymous with humanity's capacity for deep contemplation, abstract thinking, and self-reflection. But while Rodin crafted his work of art in hopes of highlighting our unique cognitive abilities, the sculpture inadvertently highlights another facet that sets us apart from all other species: are the only primates to boast chins.

'Unlike any other species, most humans will burn themselves repeatedly over their lifetime.' Breakthroughs, discoveries, and DIY tips sent six days a week. Humanity's relationship with fire is unique across all of evolutionary history . Learning to harness the power of flame is arguably our most monumental technological breakthrough as a species--one that allowed to flourish across the planet. But fire is not without its inherent dangers .

Small jaws mean big problems for modern humans. Modern diets gave us smaller jaws--and a lifetime of orthodontic problems. Breakthroughs, discoveries, and DIY tips sent six days a week. Every year, millions of children and teens undergo a common ritual of growing up: getting braces. And it's not just young folks who turn to metal brackets to handle some common dental issues--the Cleveland Clinic estimates that some 20% of new orthodontic patients are over the age of 18 .

With great biological havoc comes great opportunity. Breakthroughs, discoveries, and DIY tips sent every weekday. About 445 million years ago, our planet completely changed. Massive glaciers formed over the supercontinent Gondwana, sucking up sea water like an icy sponge. Now called the Late Ordovician mass extinction (LOME), Earth's first major mass extinction wiped out about 85 percent of all marine species as the ocean chemistry radically changed and Earth's climate turned bitter cold. However, with great biological havoc also comes opportunity.

Why do we have five fingers and toes? It all goes back to our fishy ancestors. The answer to why we have five fingers and toes is surprisingly difficult to suss out. Breakthroughs, discoveries, and DIY tips sent every weekday. The popular nursery rhyme is an early childhood memory for many of us.

We resolve a 30-year-old open problem concerning the power of unlabeled data in online learning by tightly quantifying the gap between transductive and standard online learning. In the standard setting, the optimal mistake bound is characterized by the Littlestone dimension $d$ of the concept class $H$ (Littlestone 1987). We prove that in the transductive setting, the mistake bound is at least $Ω(\sqrt{d})$. This constitutes an exponential improvement over previous lower bounds of $Ω(\log\log d)$, $Ω(\sqrt{\log d})$, and $Ω(\log d)$, due respectively to Ben-David, Kushilevitz, and Mansour (1995, 1997) and Hanneke, Moran, and Shafer (2023). We also show that this lower bound is tight: for every $d$, there exists a class of Littlestone dimension $d$ with transductive mistake bound $O(\sqrt{d})$. Our upper bound also improves upon the best known upper bound of $(2/3)d$ from Ben-David, Kushilevitz, and Mansour (1997). These results establish a quadratic gap between transductive and standard online learning, thereby highlighting the benefit of advance access to the unlabeled instance sequence. This contrasts with the PAC setting, where transductive and standard learning exhibit similar sample complexities.