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Raul Rojas

Publications and source records attributed to Raul Rojas.

At least 19 recordsLinked to original sources
arXiv2026

The Reconstructions of Konrad Zuse's Z3 Computer

This paper reviews the various reconstructions of Konrad Zuse's Z3 computer, built in 1941. The first is the reconstruction made by Zuse himself in the 1960s, which is now housed at the Deutsches Museum in Munich. Second is the 2001 reconstruction, made in Berlin, and which has a didactic purpose. Third is the Z3r, a Z3 reconstruction built by Horst Zuse in honor of his father's 100th birthday. Fourth is the reconstruction by Christoph Traber in Switzerland. All of these machines strive to preserve the cultural heritage that the Z3 represents.

cs.GL↗
arXiv2025

Virtual work, thermodynamic structure of the spacetime, and black hole criticality

We propose a new way to relate the black hole thermodynamics and geometry by generalizing the Euclidean formalism to include "virtual geometries", which do not necessarily satisfy Einstein equations. This provides a physically well motivated route to study black hole criticality and obtain the Landau Ginzburg potential. We compute the "virtual thermodynamic potential" and show that it satisfies a modified quantum statistical relation that is compatible with the first law of black hole thermodynamics supplemented with an extra term, interpreted as virtual work in previous literature. The novelty is that, within our formalism, we can explicitly compute this term as the first derivative of the virtual thermodynamic potential with respect to the horizon radius that is considered as the order parameter. Imposing the physical condition that the first derivative vanishes is at the basis of the matching between the first law of black hole thermodynamics and (one of the) Einstein equations evaluated at the horizon. Interestingly, imposing the physical conditions that the second and third derivatives vanish, we can concretely study the criticality and existence of swallow tails. As a specific example, we apply this formalism to an exact four dimensional asymptotically flat hairy black hole, namely the generalized Kaluza Klein (KK) black hole when the dilaton potential is included, and show that it is thermodynamically stable and has a non-trivial critical behaviour corresponding to an inverted swallowtail.

hep-th↗
arXiv2024

Unconventional Universal Computation in Babbage's Analytical Engine

This paper shows that the programming model of Babbage's Analytical Engine, although unconventional, can be harnessed in order to simulate indirect addressing, a capability that was not included in the original instruction set. That is, in a theoretical sense, the Analytical Engine was as universal as computers we have today. We show how to implement indirect addressing for a working memory of fixed size; this makes it possible to simulate a Turing machine with a finite tape. The result is, of course, only of theoretical and historical interest, without any practical implications.

cs.LO↗
arXiv2024

Higher-curvature gravity in AdS$_3$, holographic $c$-theorems and black hole microstates

We construct higher-derivative gravity theories in three dimensions that admit holographic $c$-theorems and exhibit a unique maximally symmetric vacuum, at arbitrary order $n$ in the curvature. We show that these theories exhibit special properties, the most salient ones being the decoupling of ghost modes around Anti-de Sitter (AdS) space, the enhancement of symmetries at linearized level, and the existence of a one-parameter generalization of the Bañados-Teitelboim-Zanelli (BTZ) black hole that, while being asymptotically AdS, is not of constant curvature but rather exhibits a curvature singularity. For such black holes, we provide a holographic derivation of their thermodynamics. This gives a microscopic picture of black hole thermodynamics for non-supersymmetric solutions, of non-constant curvature in higher-derivative theories of arbitrary order in the curvature.

hep-th↗
arXiv2024

Quantum backreactions in (A)dS3 massive gravity and logarithmic asymptotic behavior

We study the interplay between higher curvature terms and the backreaction of quantum fluctuations in 3-dimensional massive gravity in asymptotically (Anti-)de Sitter space. We focus on the theory at the special point of the parameter space where the two maximally symmetric vacua coincide. In the case of positive cosmological constant, this corresponds to the partially massless point, at which the classical theory admits de Sitter black holes and exhibits an extra conformal symmetry at linear level. We explicitly find the quantum corrected black hole geometry in the semiclassical approximation and show that it induces a relaxation of the standard asymptotic conditions. Nonetheless, the new asymptotic behavior is still preserved by an infinite-dimensional algebra, which, in addition to Virasoro, contains logarithmic supertranslations. Finally, we show that all the results we obtain for the quadratic massive gravity theory can be extended to theories including cubic and quartic terms in the curvature.

hep-th↗
arXiv2023

How Charles Babbage invented the Computer

This paper provides an overview of the successive stages in the development of Charles Babbage's Analytical Engine, based on the blueprints held in the Babbage Papers Archive, accessible online through the Science Museum in London. The first person to decipher these schematics was Allan Bromley, whose contributions in the 1980s and 1990s significantly advanced our understanding of Babbage's pioneering work. The Science Museum's digitization of the Babbage Papers enables a chronological exploration of the evolution of Babbage's machines. The focus is on the Analytical Engine, shedding light on its lesser known but crucial transitional phases.

cs.AR↗
arXiv2023

Algorithms for Proportional Representation in Parliament in Divisor and Multiplicative Form

We consider three algorithms for allocating parliamentary seats by proportional representation. The usual approach to describing such algorithms is to compute a quota of votes that each party uses to "acquire'' representatives. This kind of description follows a divisor method, since the number of representatives for a party is equal to the number of votes for that party, divided by the quota. We show that a simple multiplicative form with different rounding methods produces algorithms equivalent to the divisor methods. The multiplicative form is intuitive and easier to understand for a wider audience.

cs.DS↗
arXiv2020

Exploring Maximum Entropy Distributions with Evolutionary Algorithms

This paper shows how to evolve numerically the maximum entropy probability distributions for a given set of constraints, which is a variational calculus problem. An evolutionary algorithm can obtain approximations to some well-known analytical results, but is even more flexible and can find distributions for which a closed formula cannot be readily stated. The numerical approach handles distributions over finite intervals. We show that there are two ways of conducting the procedure: by direct optimization of the Lagrangian of the constrained problem, or by optimizing the entropy among the subset of distributions which fulfill the constraints. An incremental evolutionary strategy easily obtains the uniform, the exponential, the Gaussian, the log-normal, the Laplace, among other distributions, once the constrained problem is solved with any of the two methods. Solutions for mixed ("chimera") distributions can be also found. We explain why many of the distributions are symmetrical and continuous, but some are not.

stat.ME↗
arXiv2019

Hairy Black Hole Chemistry

We study the thermodynamics of an exact hairy black hole solution in Anti-deSitter (AdS) spacetime. We use the counterterm method supplemented with boundary terms for the scalar field to obtain the thermodynamic quantities and stress tensor of the dual field theory. We then extend our analysis by considering a dynamical cosmological constant and verify the isoperimetric inequality. Unlike the thermodynamics of Reissner-Nördstrom (RN) black hole in this `extended' framework, the presence of the scalar field and its self-interaction make also the criticality possible in the grand canonical ensemble. In the canonical ensemble, we prove that, in fact, there exist two critical points. Finally we comment on a different possible interpretation that is more natural in the context of string theory.

hep-th↗
arXiv2019

Thermodynamically stable asymptotically flat hairy black holes with a dilaton potential

We present a detailed analysis of the thermodynamics of exact asymptotically flat hairy black holes in Einstein-Maxwell-dilaton theory. We compute the regularized action, quasilocal stress tensor, and conserved charges by using a `counterterm method' similar to the one extensively used in the AdS-CFT duality. In the presence of a non-trivial dilaton potential that vanishes at the boundary we prove that, for some range of parameters, there exist thermodynamically stable black holes in the grand canonical and canonical ensembles. To the best of our knowledge, this is the first example of a thermodynamically stable asymptotically flat black hole, without imposing artificial conditions corresponding to embedding in a finite box.

hep-th↗
arXiv2018

Scalar charges and the first law of black hole thermodynamics

We present a variational formulation of Einstein-Maxwell-dilaton theory in flat spacetime, when the asymptotic value of the scalar field is not fixed. We obtain the boundary terms that make the variational principle well posed and then compute the finite gravitational action and corresponding Brown-York stress tensor. We show that the total energy has a new contribution that depends of the asymptotic value of the scalar field and discuss the role of scalar charges for the first law of thermodynamics. We also extend our analysis to hairy black holes in Anti-de Sitter spacetime and investigate the thermodynamics of an exact solution that breaks the conformal symmetry of the boundary.

hep-th↗
arXiv2017

The Keynesian Model in the General Theory: A Tutorial

This small overview of the General Theory is the kind of summary I would have liked to have read, before embarking in a comprehensive study of the General Theory at the time I was a student. As shown here, the main ideas are quite simple and easy to visualize. Unfortunately, numerous introductions to Keynesian theory are not actually based on Keynes opus magnum, but in obscure neoclassical reinterpretations. This is completely pointless since Keynes' book is so readable.

econ.GN↗
arXiv2017

Logistic Regression as Soft Perceptron Learning

We comment on the fact that gradient ascent for logistic regression has a connection with the perceptron learning algorithm. Logistic learning is the "soft" variant of perceptron learning.

stat.ML↗
arXiv2017

Deepest Neural Networks

This paper shows that a long chain of perceptrons (that is, a multilayer perceptron, or MLP, with many hidden layers of width one) can be a universal classifier. The classification procedure is not necessarily computationally efficient, but the technique throws some light on the kind of computations possible with narrow and deep MLPs.

cs.NE↗
arXiv2016

The Design Principles of Konrad Zuse's Mechanical Computers

Konrad Zuse built the Z1, a mechanical programmable computing machine, between 1935/36 and 1937/38. The Z1 was a binary floating-point computing device. The individual logical gates were constructed using metallic plates and interconnection rods. This paper describes the design principles Zuse followed in order to complete a complex calculating machine, as the Z1 was. Zuse called his basic switching elements "mechanical relays" in analogy to the electrical relays used in telephony.

cs.OH↗
arXiv2015

A Tutorial Introduction to the Lambda Calculus

This paper is a concise and painless introduction to the $λ$-calculus. This formalism was developed by Alonzo Church as a tool for studying the mathematical properties of effectively computable functions. The formalism became popular and has provided a strong theoretical foundation for the family of functional programming languages. This tutorial shows how to perform arithmetical and logical computations using the $λ$-calculus and how to define recursive functions, even though $λ$-calculus functions are unnamed and thus cannot refer explicitly to themselves.

cs.LO↗