*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!
*

**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

Massless Scattering by Equating Extrapolated Dictionaries:

**Preview**: Let \(Z^{I}\) with index \(I=-1,0,...,4\) be coordinates on embedding space \(R^{2,4}\) where
the light cone
of origin \(\mathbb{R}^{2,4}\) is cut out by:
\(\left(Z^{-1}\right)^2+\left(Z^0\right)^2\)
where the origin \(Z^{I}=0\) is removed. The remaining light code is positively rescaled, where the quotient
is \(Z^I \sim t Z^I, t \in \mathbb{R}_{+}\), arriving at....
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more

**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

**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

**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

**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

**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

**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...
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**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
that...read more

**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.
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**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 \(X\)....
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**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...
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**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...
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**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...
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**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 \(S \subseteq \mathbb{R}^{n}\)...
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**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...
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**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 \(U \subset M\)...
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**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...
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**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. \(E \subseteq \left\{\left\{x, y\right\}\;|\;x, y \in V\;and\;x \neq y\right\}\)...
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**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...
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**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...
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