Alejandro Rosales

Aside from the website owner, Alejandro:

Hello, World! This website is dedicated in memory to my best boy and best girl: PK and Lucy. Here, I share what I am having fun learning about. Lastly, remember to try to be the person your dog thinks you are!

Quantum Enhanced Machine Learning

Preview: Using quantum computing, the authors suggest obtaining a quantum advantage for Support Vector Machine SVM processing. In order to do this, the authors suggest mapping the SVM feature space provided in the purely classical data to quantum state space. For the problem, we have data from a training set \(T\)... read more

Multi-Store Memory Model

Preview: The central executive is responsible for controlled processing and allocation of data to subsystems in working memory. Such subsystems include the visuospatial sketchpad and phonological loop, where the phonological loop can further be subdivided into the phonological store and the articulatory process. The primary functions of the central executive is... read more

Massless Scattering by Equating Extrapolated Dictionaries

Preview: The authors' goal is to understand better how the holographic principle extends from asymptotically AdS spacetimes to asymptotically flat spacetimes. The authors mention this would provide a powerful toolkit to examine gravitational scattering. Various attempts at a holographic description include reconstructing bulk geometries from data at null infinity. The protocols... read more

Quantum Enhanced Machine Learning

Preview: Using quantum computing, the authors suggest obtaining a quantum advantage for Support Vector Machine SVM processing. In order to do this, the authors suggest mapping the SVM feature space provided in the purely classical data to quantum state space. For the problem, we have data from a training set \(T\)... read more

Multilevel Development of Cognitive Abilities for Artificial Intelligence

Preview: In biological intelliegent systems there are multiple mechanisms working in congruence on multiple levels, both at the structural and neurobiological level to develop complex cognitive abilities. What remains unknown is which mechanisms are necessary and sufficent to synthetically replicate these cognitive abilities for artificial intelligence. A neurocomputational model is offered... read more

Deontology, Consequentialism, Virtue Ethics

Preview: Virtue Ethics is a branch of one of three major approaches to normative ethics, where normative ethics, at the risk of over simplification, is concerened with criterias for what is right and wrong. Virtue ethics can be indentified from the other approaches to normative ethics, as that which emphasizes virutes... read more

Quantum Algorithms

Preview: Suppose we want to evaluate a function \(f(x)\), where the function \(f\) expresses some computation or algorithm. A use case for quantum parallelism is to evaluate \(f(x)\) with many different values for the output of the computation or algorithm on the input \(x\) simultaneously. In essence, we can evaluate many... read more

Anatomy and Histology of the Hippocampus

Preview: The hippocampus contains two parts, the Cornu ammonia (Hippocampus Proper) and the dentate gyrus, where the hippocampal sulcus separates both parts. Both parts curve into each other and below the sulcus lies the subiculum. Since the hippocampus is a part of the allocortex or archicortex, there exists a zone more

Connections in the Human Structural Connectome

Preview: From the human structural connectome, the authors attempt to extract architectural feautres using diffusion spectrum imaging (DSI) and encode the data required into triplcate as undirected, weighted network. They do so to capute as much information about possible paths which transmit as human process and preform complex behaviors. read more

Chern Class

Preview: Chern classes are a part of algebraic topology, as well as other math groups, and are characteristic classes related to complex vector bundles. Let \(X\) be a topological space of closure-finite weak CW complex and let \(V\) be a line bundle. The first chern class is the only nontrivial Chern class and is an element of the second cohomology group of \(X\).... read more

Topological Neuroscience

Preview: One main theoretical framework that is used to model, estimate, and simulate brain networks from complex network science is graph theory. A graph being a composition of a set of intereconnected elements know as vertices and edges. The vertices in a network can represent brain areas, while edges can represent... read more

Information Theory

Preview: Three properties were required by Shannon: \(I(p) \geq 0\), i.e. information is a real non-negative measure. \(I(p_{1},p_{2})=I(p_{1})+I(p_{2})\) for independent events. \(I(p)\) is a continous function of \(p\). The mathematical function that satisfies these requirements is: \(I(p)=k\;log(p)\) In the equation, the value of \(k\) is arbitrary... read more

Abstract Algebra

Preview: Abstract Algebra or modern algebra can be defined as the theory of algebraic structures. For the most part, modern abstract algebra deals with four algebraic structures: groups, rings, fields, and vector spaces. We will look at and examine these four algebraic strucutres in this page. The three most commonly studied... read more

Hidden Markov Processes

Preview: Let us first start with a formal definition of a 2 vector convex combination. Then we will break down the definition into parts and analyze the definition. Then we will formally define and analyze a convex combination with a finite number of vectors in the same manner. A subset \(S \subseteq \mathbb{R}^{n}\)... read more

Quantum Mechanics

Preview: First we will introduce the idea of Hilbert Space, which was named after D. Hilbert. Hilbert Space is a nondenumerable infinite complex vector space. Complex space, being a collection of complex numbers with an added structure. The infinite dimensions of Hilbert Space represents a continious spectra of alternative physical states... read more

Differential Manifolds

Preview: An \(n\)-dimensional manifold, or \(n\)-manifold, is a topological space where each point has a neighborhood that is homeomorphic to an open subset on \(n\)-dimensional Euclidean space. This definition can be formally defined as: Let \(M\) be a topological space. A chart in \(M\) consists of an open subset \(U \subset M\)... read more

Neurobiological Bases of Memory Formation

Preview: In long-term memory consolidation stress hormones, such as glucocorticoids, affect glucocorticoid receptors (GR) in pre- and post-synaptic neurons. These neurons mediates the brains ability to form long-term memories. So, when an individual is under stress the brains ability to form long-term memories can be affected. GRs mediate several intracellular signaling... read more

Graph Theory

Preview: \(G = (V, E)\) \(V\) is a set of vertices \(E \subseteq \left\{\left\{x, y\right\}\;|\;x, y \in V\;and\;x \neq y\right\}\) A simple undirected graph \(G\) is an ordered pair or tuple \((V, E)\) where \(V\) and \(E\) are finite sets. \(E \subseteq \left\{\left\{x, y\right\}\;|\;x, y \in V\;and\;x \neq y\right\}\)... read more

Theory of Computation

Preview: A deterministic finite automaton (DFA) is a 5-tuple: \((Q, \Sigma, \delta, q_{0}, F)\) where: \(Q\) is a finite set of states \(\Sigma\) is an alphabet \(\delta\) is a transition function described as \(\delta : Q \times \Sigma \rightarrow Q\) \(q_{0} \in Q\) is the initial state \(F \subseteq Q\) is a... read more

Algorithmic Anaylsis

Preview: Algorithmic analysis is used to help computer scientists understand the resources required by an algorithm for time, storage, and other uses. Algorithmic anlysis must analyze algorithms in a methodical, universal, and fair way. To do this computer scientist implement mathematical models that describe the resources used by algorithms. This work... read more

... And More Soon!