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Lambda calculus has a concise binary encoding thanks to a clever form of bracket abstraction, inspiration from combinatory logic, and a set of refactoring rules. With self-delineated and non-self-delineated variations, it is an ideal choice for a concrete universal computer for algorithmic information theory. Outside of abstract interpretation, this is the first work I encountered with a wide enough definition of program to include those that don't terminate and that produce a stream of output.

Presents an overview of quantum computing using real numbers instead of complex numbers, and spin as a weird "clock". Qubits memorize their last measurement, but forget it when measured again in a different basis. Quantum gates are orthogonal matrices that rotate qubits. Entanglement correlates qubits so that measuring one affects the other, even at a distance. Quantum algorithms cause interference patterns that amplify correct answers and cancel wrong answers. They can also pair with classical algorithms.

RAPPOR preserves client ε-differential privacy even despite engaging in longitudinal data collection. If necessary, the client encodes its response in a Bloom filter, adds noise, and memoizes it as the Permanent randomized response. It then creates an Instantaneous randomized response from the Permanent one, and sends it to the server. Complex statistical processing on the server noisily determine which bit vectors are present, and their frequencies. Privacy lessens if the client's response to a query changes over time.

In addition to training data memorization, privacy issues in LLM chatbots arise from indirect attribute inference and the security of retained data. Giving feedback to mainstream LLM chatbots with thumb ratings may cause the associated transcript to be retained. Courts recently ordered some LLM chatbot providers to retain user transcripts indefinitely. Retrieval augmented generation is vulnerable to data poisoning attacks. Another privacy risk is that some chatbots can uncannily good at geo-guessing.

Rather than completely reconstruct an abstract syntax tree from a source code every time an edit occurs, an integrated development environment may employ an algorithm that takes as input the existing tree and the edit itself. Parsing expression grammars are similar to context free grammars (but possibly less expressive) except they resolve ambiguity using rule precedence. Using an improved memoization table, the GPeg parsing algorithm applies edits in logarithmic time, versus linear time for other incremental parsers.

The Census Bureau adopted a differential privacy based disclosure avoidance system for the 2020 Census. Its previous strategy was based on randomly swapping individual records in one region with those in another. They also release noisy measurement files. In a clever comparison against the unreleased non-private baseline data, it appears that the new system introduces less bias and noise than the old system, especially for small populations.

Statistics had a rocky relationship with causality historically. Data alone cannot enable causal or counterfactual reasoning. Causal networks are directed Bayesian networks where arrows represent causation. They help clarify which variables to control for and which variables to not control for. Instrumental variables are deliberately randomized variables without causes that can "bypass" confounders. Deduction forms conclusions from hypotheses. Induction forms hypotheses from data.

Luddite today means someone who avoids technology, but the term originated during the Industrial Revolution, when cropping machines threatened the livelihood of certain textile workers. The workers formed gangs, broke into mills, and destroyed the machines intended to replace them. Some mill owners fought back. Violence, death, and resentment ensued. Some inventions create jobs, and some inventions destroy jobs.

Researchers discovered how to create green and red LEDs fairly quickly, but blue LEDs eluded them. Industry understood the potential for digital displays with LEDs of all three primary colors, and funded blue LED efforts well. Shuji Nakamura worked for a small struggling company called Nichia. He convinced his company to let him try to develop a blue LED, and continued long after leadership demanded he stop. His company rewarded him little, but he changed the world.

Network analyses involving randomness tend to scale poorly because the probability distributions the analyses produce grow quickly. McNetKAT derives from ProbNetKAT and trades some capability for better scalability. It models programs as Markov chains. The probabilistic choice operator is a like a conditional, but the guard is a random variable. A space of equivalence classes of states substitutes for the actual state space to keep it smaller.

Signaling channels are low-bandwidth, covert, publicly addressable, multi-hop channels. Applications at the endpoints are privy and modified; intermediate nodes are not. Raceboat is a modular framework for routing application traffic through signaling channels. It can mix-and-match unidirectional signaling channels, and supports sockets. It has composable abstractions for message encoding / decoding, interaction with external services that facilitate data transfer, message bundling, and scheduling strategies.

Choreographic languages can support out-of-order execution without risking communication integrity violations when the processes do not depend on each other. Ozone attaches integrity keys to messages to denote what code the message originated from. Integrity keys replace selection, the sharing of a conditional guard. They allow out-of-order message receipt. They contain dynamic tokens to disambiguate message origin when procedure calls or concurrent processes are involved.

Bitcoin is a protocol for the exchange of virtual currency without centralized control. Peer nodes have copies of a public ledger called the blockchain. Cryptographic hash pointers make it tamper-proof. Market participants authorize transactions with Digital signatures. Miners extend the blockchain with pending transactions, and Bitcoin rewards them. A requirement to include computationally expensive solutions to puzzles in new blocks sets the cadence of growth.

AlphaEvolve integrates large language models and evolutionary computation to improve or create algorithms. The prompt sampler provides context about past trials and ideas to the LLM ensemble. The LLM ensemble provides proposed improved algorithms to the evaluator pool. The evaluator pool provides algorithms with quality scores to the program database. The program database provides algorithms to the prompt sampler for improvement or inspiration.

Players with private data use secret shares and mathematical sorcery to perform arbitrary computations on their data without revealing anything about it beyond what the output of the computation itself reveals: not to each other, and not to any third party. Techniques differ in properties including which finite fields they work in, how many players they support, their efficiency, and against what kinds of adversaries they are secure.

Algorithm analysis models running time with mathematical expressions. It compares performance ignoring coefficients and constant terms. Greedy algorithms, divide and conquer, and dynamic programming sometimes outperform brute force searches. Does an algorithm exist to solve a problem in polynomial time? If not, can one verify a solution in polynomial time? Reduction techniques compare problems by relative difficulty, even without knowing the performance of the best algorithms.

Human intelligence relies heavily on memorization, interpolation, and reasoning. Large language models can memorize and interpolate, but the ARC benchmark persuasively demonstrates with its easily solvable tasks that they cannot reason in a meaningful way. Program synthesis and discrete program search may complement large language models to cover the deficit. There is a sense in which carefully guarded industry secrets do not count as progress in AI research.

Aliens have always come to people in dreams, secretly bestowing upon them humanity's greatest ideas. But when Chloe does nothing, the aliens decide to communicate with her more directly. Despite doubt, ambivalence, and life struggles, Chloe agrees to make it happen at the last possible moment. She hopes to find purpose, self respect, and approval from the people in her life. But sometimes ideas turn out to be just okay.

Performal models systems as networks with nodes augmented by timestamps. It requires empirical latency measurements within nodes, and uses symbolic latency abstraction to model latency across nodes to produce a "formal" upper bound. How do you empirically measure latency? Do you artificially truncate the latency probability distribution domains to achieve an upper bound? Can you also model bandwidth to calculate total operation time?

Program control structure, termination, timing, observable data distribution, resource exhaustion, and power consumption can all leak information. Security label types enforce information flow policies. Confidentiality prevents flow to inappropriate destinations; dually, integrity prevents flow from inappropriate sources. Label creep occurs when the security labels of data monotonically increase during execution.

Three blue extraterrestrials teleport human artifacts into their spaceship from a debris field. They engage in inscrutable animated banter, squabble, and amuse themselves by playing with the artifacts. Fragments of the demolished planet Earth drift past the spaceship window. A lighthearted fifteen minutes of fun and indifference at the end of all human conflict, hope, despair, love, and life.

Choreographies describe interactions between processes in distributed systems. Inference rules can translate a choreography into the many possible traces (message passing sequences) that arise from concurrency. Choreographic programming language constructs avoid starvation and promote compliance and conformance. Through endpoint projection they produce independent executable build artifacts per process.

Differential privacy usually balances the utility of a dataset with the privacy of the individuals in it. In the secure messaging system Vuvuzela, differential privacy balances the privacy of the users with the efficiency of the system in terms of compute, latency, and network traffic. The percent confidence a powerful adversary can gain over many rounds that Alice and Bob ever communicated translates nicely into the privacy parameter ε.