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In mathematics, conformal geometry is the study of the set of angle-preserving (conformal) transformations on a space. In a real two dimensional space, conformal geometry is precisely the geometry of Riemann surfaces. In space higher than two dimensions, conformal geometry may refer either to the study of conformal transformations of what are called "flat spaces" (such as Euclidean spaces or spheres), or to the study of conformal manifolds which are Riemannian or pseudo-Riemannian manifolds with a class of metrics that are defined up to scale. Study of the flat structures is sometimes termed Möbius geometry, and is a type of Klein geometry.

A conformal field theory (CFT) is a quantum field theory that is invariant under conformal transformations. In two dimensions, there is an infinite-dimensional algebra of local conformal transformations, and conformal field theories can sometimes be exactly solved or classified.

A Majorana fermion (/maɪəˈrɑːnə ˈfɛərmiːɒn/[1]), also referred to as a Majorana particle, is a fermion that is its own antiparticle. They were hypothesised by Ettore Majorana in 1937. The term is sometimes used in opposition to a Dirac fermion, which describes fermions that are not their own antiparticles.

Epiphenomenalism is the view that mental events are caused by physical events in the brain, but have no effects upon any physical events. Behavior is caused by muscles that contract upon receiving neural impulses, and neural impulses are generated by input from other neurons or from sense organs. On the epiphenomenalist view, mental events play no causal role in this process

In vision, filling-in phenomena are those responsible for the completion of missing information across the physiological blind spot, and across natural and artificial scotomata

The quantum harmonic oscillator is the quantum-mechanical analog of the classical harmonic oscillator. Because an arbitrary smooth potential can usually be approximated as a harmonic potential at the vicinity of a stable equilibrium point, it is one of the most important model systems in quantum mechanics. Furthermore, it is one of the few quantum-mechanical systems for which an exact, analytical solution is known

Creation operators and annihilation operators are mathematical operators that have widespread applications in quantum mechanics, notably in the study of quantum harmonic oscillators and many-particle systems

The information paradox appears when one considers a process in which a black hole is formed through a physical process and then evaporates away entirely through Hawking radiation. Hawking's calculation suggests that the final state of radiation would retain information only about the total mass, electric charge and angular momentum of the initial state. Since many different states can have the same mass, charge and angular momentum this suggests that many initial physical states could evolve into the same final state. Therefore, information about the details of the initial state would be permanently lost. However, this violates a core precept of both classical and quantum physics—that, in principle, the state of a system at one point in time should determine its value at any other time.[3][4] Specifically, in quantum mechanics the state of the system is encoded by its wave function. The evolution of the wave function is determined by a unitary operator, and unitarity implies that the wave function at any instant of time can be used to determine the wave function either in the past or the future.

The loss of information can be quantified in terms of the change in the fine-grained von Neumann entropy of the state. A pure state is assigned a von Neumann entropy of 0 whereas a mixed state has a finite entropy. The unitary evolution of a state according to Schrödinger's equation preserves the entropy.

The weak and the strong cosmic censorship hypotheses are two conjectures concerned with the global geometry of spacetimes. The weak cosmic censorship hypothesis asserts there can be no singularity visible from future null infinity. In other words, singularities need to be hidden from an observer at infinity by the event horizon of a black hole

A simple agreement for future equity (SAFE) is an agreement between an investor and a company that provides rights to the investor for future equity in the company similar to a warrant, except without determining a specific price per share at the time of the initial investment. The SAFE investor receives the future shares when a priced round of investment or liquidity event occurs. SAFEs are intended to provide a simpler mechanism for startups to seek initial funding than convertible notes.

A simple agreement for future equity (SAFE) is an agreement between an investor and a company that provides rights to the investor for future equity in the company similar to a warrant, except without determining a specific price per share at the time of the initial investment. The SAFE investor receives the future shares when a priced round of investment or liquidity event occurs. SAFEs are intended to provide a simpler mechanism for startups to seek initial funding other than convertible notes

most methods still operate on low-level image pixels, which hinders the exploitation of high-level semantics for representation models. In this study, we propose to use a semantic-rich visual tokenizer as the reconstruction target for masked prediction, providing a systematic way to promote MIM from pixel-level to semantic-level. Specifically, we introduce vector-quantized knowledge distillation to train the tokenizer, which discretizes a continuous semantic space to compact codes

Metal ions are essential cofactors for many proteins. In fact, currently, about half of the structurally characterized proteins contain a metal ion. Metal ions play a crucial role for many applications such as enzyme design or design of protein-protein interactions because they are biologically abundant, tether to the protein using strong interactions, and have favorable catalytic properties e.g. as Lewis acid

Metalloproteins are ubiquitous in nature and are present in all major enzyme families.1,2The metals predominantly found in biological systems are the first and second row alkali and earth alkali metals and the first row transition metals such as zinc and copper. Zinc is the most common transition metal (present in ~10% of deposited structures) and can fulfill both a structural (e.g. in zinc finger proteins) or a catalytic role in up to trinuclear active sites. Zn2+ is an excellent Lewis acid and is most often found in tetrahedral, pentavalent, or octahedral coordination. About 10 % of all reactions catalyzed by enzymes use zinc as cofactor3

Neutrinos are abundant subatomic particles that are famous for passing through anything and everything, only very rarely interacting with matter. About 100 trillion neutrinos pass through your body every second.

Your body is a small-scale mine of radioactive particles. You receive an annual 40-millirem dose from the natural radioactivity originating inside of you. That’s the same amount of radiation you’d be exposed to from having four chest X-rays. Your radiation dose level can go up by one or two millirem for every eight hours you spend sleeping next to your similarly radioactive loved one.

When Potassium-40 decays, it releases a positron, the electron’s antimatter twin, so you also contain a small amount of antimatter. The average human produces more than 4000 positrons per day, about 180 per hour. But it’s not long before these positrons bump into your electrons and annihilate into radiation in the form of gamma rays.

Heart rate variability is where the amount of time between your heartbeats fluctuates slightly. Even though these fluctuations are undetectable except with specialized devices, they can still indicate current or future health problems, including heart conditions and mental health issues like anxiety and depression.

Kernel Flow is a wearable time-domain functional near-infrared spectroscopy (TD-fNIRS) system which Kernel started demoing in spring 2021.[8][9] fNIRs uses infrared light to measure changes in the oxygenation of blood, which is a proxy for neural activity

first Transformer-based frameworks for hyperparameter tuning, learned from large-scale optimization data using flexible text-based representations. While numerous works have previously demonstrated the Transformer’s strong abilities across various domains, few have touched on its optimization-based capabilities, especially over text space. Our core findings demonstrate for the first time some intriguing algorithmic abilities of Transformers: 1) a single Transformer network is capable of imitating highly complex behaviors from multiple algorithms over long horizons; 2) the network is further capable of predicting objective values very accurately, in many cases surpassing Gaussian Processes, which are commonly used in algorithms such as Bayesian Optimization.

The appearance of infinity together with collapsing quantum state due to an observation or interaction which are two challenging features of quantum field theory, become very serious problems in quantum gravity as well as in quantum geometry of space-time

In the technical part the biggest problem comes from the point definition where the classical geometry is constructed on it. By changing the point definition, the technical problem may be approximately bypassed and a mathematical formulation of quantum geometry may be found. On the other hand, the conceptual problem comes from the quantum state collapse due to the observation since in presence of gravity the entanglement between the observer and gravity cannot be eliminated.

Most people travel as an observer, and as a result, “see” a lot. When you travel as an active participant, the experience can transform the way you think, and how you see the world

In finance, a convertible bond or convertible note or convertible debt (or a convertible debenture if it has a maturity of greater than 10 years) is a type of bond that the holder can convert into a specified number of shares of common stock in the issuing company or cash of equal value. It is a hybrid security with debt- and equity-like features.[1] It originated in the mid-19th century, and was used by early speculators such as Jacob Little and Daniel Drew to counter market cornering.

Adaptive gradient algorithms borrow the moving average idea of heavy ball acceleration to estimate accurate first- and second-order moments of gradient for accelerating convergence. However, Nesterov acceleration which converges faster than heavy ball acceleration in theory and also in many empirical cases is much less investigated under the adaptive gradient setting. In this work, we propose the ADAptive Nesterov momentum algorithm, Adan for short, to effectively speedup the training of deep neural networks. Adan first reformulates the vanilla Nesterov acceleration to develop a new Nesterov momentum estimation (NME) method, which avoids the extra computation and memory overhead of computing gradient at the extrapolation point. Then Adan adopts NME to estimate the first- and second-order moments of the gradient in adaptive gradient algorithms for convergence acceleration