Computational universes

Suspicions that the world might be some sort of a machine or algorithm existing ``in the mind'' of some symbolic number cruncher have lingered from antiquity. Although popular at times, the most radical forms of this idea never reached mainstream. Modern developments in physics and computer science have lent support to the thesis, but empirical evidence is needed before it can begin to replace our contemporary world view.Comment: Several corrections of typos and smaller revisions, final versio

Making Room for Emergence

We try to provide in outline an understanding of emergent properties, which should possibly make the idea of emergence not just plausible but compelling. It is our conviction that the core truth of emergentism is neither especially exotic nor counterintuitive, while its apparent eccentricity is essentially due to some prejudicial ontological assumptions. In the first half of the paper our argument develops through Jaegwon Kim\u2019s rejection of emergentism. We argue that Kim\u2019s use of both the \u201ccausal inheritance principle\u201d and the \u201ccausal closure principle\u201d in his criticism of emergence is unwarranted. In the second half of the paper we develop a positive account of emergence through a restoration of the ontological notion of quality. We contend that any monistic ontology, in order to account for experience, must make room for irreducible qualities and that efficaciousness cannot be denied to them. The novelty of emergent properties amounts to a priori unpredictability, due to the very nature of combination. Their efficaciousness is interpreted in terms of qualifying thresholds modulating the mode of efficaciousness

VOAs labelled by complex reflection groups and 4d SCFTs

We define and study a class of $\mathcal{N}=2$ vertex operator algebras $\mathcal{W}_{\mathcal{\mathsf{G}}}$ labelled by complex reflection groups. They are extensions of the $\mathcal{N}=2$ super Virasoro algebra obtained by introducing additional generators, in correspondence with the invariants of the complex reflection group $\mathcal{\mathsf{G}}$. If $\mathcal{\mathsf{G}}$ is a Coxeter group, the $\mathcal{N}=2$ super Virasoro algebra enhances to the (small) $\mathcal{N}=4$ superconformal algebra. With the exception of $\mathcal{\mathsf{G}} = \mathbb{Z}_2$, which corresponds to just the $\mathcal{N}=4$ algebra, these are non-deformable VOAs that exist only for a specific negative value of the central charge. We describe a free-field realization of $\mathcal{W}_{\mathcal{\mathsf{G}}}$ in terms of rank$(\mathcal{\mathsf{G}})$ $\beta \gamma bc$ ghost systems, generalizing a construction of Adamovic for the $\mathcal{N}=4$ algebra at $c = -9$. If $\mathcal{\mathsf{G}}$ is a Weyl group, $\mathcal{W}_{\mathcal{\mathsf{G}}}$ is believed to coincide with the $\mathcal{N}=4$ VOA that arises from the four-dimensional super Yang-Mills theory whose gauge algebra has Weyl group $\mathcal{\mathsf{G}}$. More generally, if $\mathcal{\mathsf{G}}$ is a crystallographic complex reflection group, $\mathcal{W}_{\mathcal{\mathsf{G}}}$ is conjecturally associated to an $\mathcal{N}=3$ $4d$ superconformal field theory. The free-field realization allows to determine the elusive `$R$-filtration' of $\mathcal{W}_{\mathcal{\mathsf{G}}}$, and thus to recover the full Macdonald index of the parent $4d$ theoryComment: 70 page

Cyphers: On the Historiography of Digital Architecture

This dissertation reflects on the methods and concepts employed in constructing a history of digital architecture. By focusing on the methodological issues, it complements and expands the research developed for the monographic study Digital Architecture Beyond Computers (DABC) and the book chapter “Crypto Architecture”. In both pieces digital architecture is understood to cover a period of time that stretches well beyond the appearance of the modern digital computer (after World War Two). The notion of computing numbers and symbols to apprehend and intervene in our reality is in fact a much older idea than the invention of the modern digital computer. This dissertation reflects on the approach suggested by both writings by analysing the conceptual basis of computation in order to devise an appropriate historiographic approach to digital architecture. The aim of the investigation is to move beyond a technologically‐driven, utilitarian view of computation in favour of a more conceptual position that foregrounds computation’s fundamental logic and the role of the disciplines that informed and continue to inform it. This broader perspective aims at establishing a relation between the artifacts and the processes of digital architecture; that is, between what digital architecture is (which DABC explores through case studies in which computation and design affected one another), and how it is generated (the techniques and methods deployed to design architecture). This dissertation introduces a specific conceptual figure to articulate the historiography of digital architecture: the cypher. Cyphers address the fundamental challenges emerging from constructing a history of digital architecture, they organise the vast collections of case studies forming the history of digital architecture, foreground the conceptual motivations behind computation, and acknowledge the role that different disciplines (philosophy, logic, semiotic) have played in shaping what we call digital architecture

Fiber Bundles, Yang-Mills Theory, and General Relativity

I articulate and discuss a geometrical interpretation of Yang-Mills theory. Analogies and disanalogies between Yang-Mills theory and general relativity are also considered.Comment: 54 page

Advancement Auto-Assessment of Students Knowledge States from Natural Language Input

Knowledge Assessment is a key element in adaptive instructional systems and in particular in Intelligent Tutoring Systems because fully adaptive tutoring presupposes accurate assessment. However, this is a challenging research problem as numerous factors affect students’ knowledge state estimation such as the difficulty level of the problem, time spent in solving the problem, etc. In this research work, we tackle this research problem from three perspectives: assessing the prior knowledge of students, assessing the natural language short and long students’ responses, and knowledge tracing.Prior knowledge assessment is an important component of knowledge assessment as it facilitates the adaptation of the instruction from the very beginning, i.e., when the student starts interacting with the (computer) tutor. Grouping students into groups with similar mental models and patterns of prior level of knowledge allows the system to select the right level of scaffolding for each group of students. While not adapting instruction to each individual learner, the advantage of adapting to groups of students based on a limited number of prior knowledge levels has the advantage of decreasing the authoring costs of the tutoring system. To achieve this goal of identifying or clustering students based on their prior knowledge, we have employed effective clustering algorithms. Automatically assessing open-ended student responses is another challenging aspect of knowledge assessment in ITSs. In dialogue-based ITSs, the main interaction between the learner and the system is natural language dialogue in which students freely respond to various system prompts or initiate dialogue moves in mixed-initiative dialogue systems. Assessing freely generated student responses in such contexts is challenging as students can express the same idea in different ways owing to different individual style preferences and varied individual cognitive abilities. To address this challenging task, we have proposed several novel deep learning models as they are capable to capture rich high-level semantic features of text. Knowledge tracing (KT) is an important type of knowledge assessment which consists of tracking students’ mastery of knowledge over time and predicting their future performances. Despite the state-of-the-art results of deep learning in this task, it has many limitations. For instance, most of the proposed methods ignore pertinent information (e.g., Prior knowledge) that can enhance the knowledge tracing capability and performance. Working toward this objective, we have proposed a generic deep learning framework that accounts for the engagement level of students, the difficulty of questions and the semantics of the questions and uses a novel times series model called Temporal Convolutional Network for future performance prediction. The advanced auto-assessment methods presented in this dissertation should enable better ways to estimate learner’s knowledge states and in turn the adaptive scaffolding those systems can provide which in turn should lead to more effective tutoring and better learning gains for students. Furthermore, the proposed method should enable more scalable development and deployment of ITSs across topics and domains for the benefit of all learners of all ages and backgrounds

Machine Learning Techniques as Applied to Discrete and Combinatorial Structures

Machine Learning Techniques have been used on a wide array of input types: images, sound waves, text, and so forth. In articulating these input types to the almighty machine, there have been all sorts of amazing problems that have been solved for many practical purposes. Nevertheless, there are some input types which don’t lend themselves nicely to the standard set of machine learning tools we have. Moreover, there are some provably difficult problems which are abysmally hard to solve within a reasonable time frame. This thesis addresses several of these difficult problems. It frames these problems such that we can then attempt to marry the allegedly powerful utility of existing machine learning techniques to the practical solvability of said problems