Inverse tasks can uncover potential reasoning gaps as Large Language Models (LLMs) scale up. In this work, we explore the redefinition task, in which we assign alternative values to well-known physical constants and units of measure, prompting LLMs to respond accordingly. Our findings show that not only does model performance degrade with scale, but its false confidence also rises. Moreover, while factors such as prompting strategies or response formatting are influential, they do not preclude LLMs from anchoring to memorized values.

The famous example of the double-Watt mechanism given by Connelly and Servatius raises some problems concerning the classical definitions of higher-order flexibility and rigidity, respectively, as they attest the cusp configuration of the mechanism a third-order rigidity, which conflicts with its continuous flexion. Some attempts were done to resolve the dilemma but they could not settle the problem. As cusp mechanisms demonstrate the basic shortcoming of any local mobility analysis using higher-order constraints, we present a global approach inspired by Sabitov's finite algorithm for testing the bendability of a polyhedron, which allows us (a) to compute iteratively configurations with a higher-order flexion and (b) to come up with a proper redefinition of higher-order flexibility and rigidity. We also give algorithms for computing the flexion orders as well as the associated flexes. The presented approach is demonstrated on several examples (double-Watt mechanisms and Tarnai's Leonardo structure). Moreover, we determine all configurations of a given 3-RPR manipulator with a third-order flexion and present a corresponding joint-bar framework of flexion order 23.

The historical evolution of Artificial Intelligence (AI) dates back to the year 1996 when Deep Blue AI defeated the then world chess champion. Garry Kasparov The year 2019 witnessed geopolitical paradigm where there was a race for technological supremacy between superpowers. It is estimated that by 2034-40, 50 per cent of the jobs would be automated in United States i.e.; within the next 15 years (Lee Kai Fu, AI Superpowers). Also majority of researchers predict singularity by 2045 -- a stage where machines become more advanced than human beings. This necessitates one to understand AI, its benefits, its major issues and its implications on government and social order.

Artificial intelligence (AI) is the new terrain of contestation in international relations, wrapped in uncertainty about loss of technological control and human oversight. 'Whoever becomes the leader in this sphere will become the ruler of the world', Russian President Vladimir Putin famously stated in 2017 (RT, 2017). Since then, a plethora of public and private actors have issued statements on how AI would change society for the better or for the worse, highlighting infrastructural developments, military applications and impact on jobs and human relations. Some of these statements revealed concrete plans to address AI-related challenges, but the majority remained principled positions on limiting risks associated with disruptive technologies (Ulnicane et al., 2020, Jobin et al., 2019). As recognition grows that tools based on algorithmic processing and machine learning bring about as many promises as commotions, governments are under increased pressure to react for the wellbeing of their citizens and for their raison d'être (Taeihagh, 2021).

Until recently, allegations of "racism" in the public sphere have operated like first degree murder charges do in courts of law--in order to establish such a charge, mainstream media often demanded proof of the alleged racist's intent. Dictionary definitions have long tracked this blinkered view of'racism.' For decades, Merriam-Webster's entry described racism as a "belief" of racial supremacy, or a program designed to put that belief into action. Because many people--and some judges--treat dictionary definitions as if they were legal prescriptions, accusations of racism have required proof of intent--a purposeful, race-based disparity in conduct or consequence. Thus, the legal framework for considering racial discrimination has largely echoed the dictionary's narrow take on racism.

We work under the threat of being replaced by machines smarter than us. Vinod Khosla, a Silicon Valley venture capitalist, says that the medical profession is approaching extinction and predicts that the majority of our work will eventually be outsourced to algorithms and other artificial tools of clinical reasoning. But I think my profession is headed to evolution, not extinction. Much of what we once did with our eyes, hands, and ears has been replaced by machines. In my corner of the United States, a child who comes to an emergency department with abdominal pain is likely to have a CT scan before ever being examined by a physician.

The interactive computation paradigm is reviewed and a particular example is extended to form the stochastic analog of a computational process via a transcription of a minimal Turing Machine into an equivalent asynchronous Cellular Automaton with an exponential waiting times distribution of effective transitions. Furthermore, a special toolbox for analytic derivation of recursive relations of important statistical and other quantities is introduced in the form of an Inductive Combinatorial Hierarchy.

Scene: It's 2017, and your CEO calls you in. She asks about your market segmentation--you have five personas, based on demographic data. Then she hands you a report from the data scientist. He's identified nine distinct segments, based on purchase intent and customer behavior, for which there is an opportunity to increase margin by better targeting service offerings and marketing messages. "I thought our data scientist was focused on optimizing our media mix," you mention.