arXiv subjects

Michael Robinson

Publications and source records attributed to Michael Robinson.

At least 37 records · Page 2Linked to original sources

arXiv2022

Statistical detection of format dialects using the weighted Dowker complex

This paper provides an experimentally validated, probabilistic model of file behavior when consumed by a set of pre-existing parsers. File behavior is measured by way of a standardized set of Boolean "messages" produced as the files are read. By thresholding the posterior probability that a file exhibiting a particular set of messages is from a particular dialect, our model yields a practical classification algorithm for two dialects. We demonstrate that this thresholding algorithm for two dialects can be bootstrapped from a training set consisting primarily of one dialect. Both the (parametric) theoretical and the (non-parametric) empirical distributions of file behaviors for one dialect yield good classification performance, and outperform classification based on simply counting messages. Our theoretical framework relies on statistical independence of messages within each dialect. Violations of this assumption are detectable and allow a format analyst to identify "boundaries" between dialects. A format analyst can therefore greatly reduce the number of files they need to consider when crafting new criteria for dialect detection, since they need only consider the files that exhibit ambiguous message patterns.

cs.CE↗

arXiv2021

Constant rank factorizations of smooth maps

Sonar systems are frequently used to classify objects at a distance by using the structure of the echoes of acoustic waves as a proxy for the object's shape and composition. Traditional synthetic aperture processing is highly effective in solving classification problems when the conditions are favorable but relies on accurate knowledge of the sensor's trajectory relative to the object being measured. This article provides several new theoretical tools that decouple object classification performance from trajectory estimation in synthetic aperture sonar processing. The key insight is that decoupling the trajectory from classification-relevant information involves factoring a function into the composition of two functions. The article presents several new general topological invariants for smooth functions based upon their factorizations over function composition. These invariants specialize to the case when a sonar platform trajectory is deformed by a non-small perturbation. The mathematical results exhibited in this article apply well beyond sonar classification problems. This article is written in a way that supports full mathematical generality.

cs.CE↗

arXiv2021

Metric Comparisons of Relations

This paper defines a new pseudometric for binary relations between finite sets that measures consensus among subsets. The main results are (1) a concise restatement of this pseudometric with an intuitively appealing interpretation via a full and faithful functor from the category of relations to a category of relation multisets and (2) that the pseudometric can be bounded without an expensive search of possible mappings, based solely on the dimensions of the relations themselves. Additionally, (3) an algorithm is described to calculate this bound with time and memory complexity at worst proportional to the product of those dimensions: $\mathcal{O}(m \times n).$. The tools developed in this paper should find broad application in exploratory data analysis. We provide one such application by briefly exploring ad hoc consensus specifications for the well-known PDF file format.

math.GT↗

arXiv2021

Aggregation sheaves for greedy modal decompositions

This article develops a new theoretical basis for decomposing signals that are formed by the linear superposition of a finite number of modes. Each mode depends nonlinearly upon several parameters; we seek both these parameters and the weights within the superposition. The particular focus of this article is upon solving the decomposition problem when the number of modes is not known in advance. A sheaf-theoretic formalism is introduced that describes all modal decomposition problems, and it is shown that minimizing the local consistency radius within this sheaf is guaranteed to solve them. Since the modes may or may not be well-separated, a greedy algorithm that identifies the most distinct modes first may not work reliably. This article introduces a novel mathematical formalism, aggregation sheaves, and shows how they characterize the behavior of greedy algorithms that attempt to solve modal decomposition problems.

math.MG↗

arXiv2021

Super-resolving star clusters with sheaves

This article explains an optimization-based approach for counting and localizing stars within a small cluster, based on photon counts in a focal plane array. The array need not be arranged in any particular way, and relatively small numbers of photons are required in order to ensure convergence. The stars can be located close to one another, as the location and brightness errors were found to be low when the separation was larger than $0.2$ Rayleigh radii. To ensure generality of our approach, it was constructed as a special case of a general theory built upon topological signal processing using the mathematics of sheaves.

astro-ph.IM↗

arXiv2020

Looking for non-compliant documents using error messages from multiple parsers

Whether a file is accepted by a single parser is not a reliable indication of whether a file complies with its stated format. Bugs within both the parser and the format specification mean that a compliant file may fail to parse, or that a non-compliant file might be read without any apparent trouble. The latter situation presents a significant security risk, and should be avoided. This article suggests that a better way to assess format specification compliance is to examine the set of error messages produced by a set of parsers rather than a single parser. If both a sample of compliant files and a sample of non-compliant files are available, then we show how a statistical test based on a pseudo-likelihood ratio can be very effective at determining a file's compliance. Our method is format agnostic, and does not directly rely upon a formal specification of the format. Although this article focuses upon the case of the PDF format (ISO 32000-2), we make no attempt to use any specific details of the format. Furthermore, we show how principal components analysis can be useful for a format specification designer to assess the quality and structure of these samples of files and parsers. While these tests are absolutely rudimentary, it appears that their use to measure file format variability and to identify non-compliant files is both novel and surprisingly effective.

cs.OH↗

arXiv2020

Sheaf-theoretic framework for optimal network control

In this paper, we use tools from sheaf theory to model and analyze optimal network control problems and their associated discrete relaxations. We consider a general problem setting in which pieces of equipment and their causal relations are represented as a directed network, and the state of this equipment evolves over time according to known dynamics and the presence or absence of control actions. First, we provide a brief introduction to key concepts in the theory of sheaves on partial orders. This foundation is used to construct a series of sheaves that build upon each other to model the problem of optimal control, culminating in a result that proves that solving our optimal control problem is equivalent to finding an assignment to a sheaf that has minimum consistency radius and restricts to a global section on a particular subsheaf. The framework thus built is applied to the specific case where a model is discretized to one in which the state and control variables are Boolean in nature, and we provide a general bound for the error incurred by such a discretization process. We conclude by presenting an application of these theoretical tools that demonstrates that this bound is improved when the system dynamics are affine.

math.AT↗

arXiv2020

Topology in cyber research

We give an idiosyncratic overview of applications of topology to cyber research, spanning the analysis of variables/assignments and control flow in computer programs, a brief sketch of topological data analysis in one dimension, and the use of sheaves to analyze wireless networks. The text is from a chapter in the forthcoming book Mathematics in Cyber Research, to be published by Taylor and Francis.

math.AT↗

arXiv2020

Assignments to sheaves of pseudometric spaces

An assignment to a sheaf is the choice of a local section from each open set in the sheaf's base space, without regard to how these local sections are related to one another. This article explains that the consistency radius -- which quantifies the agreement between overlapping local sections in the assignment -- is a continuous map. When thresholded, the consistency radius produces the consistency filtration, which is a filtration of open covers. This article shows that the consistency filtration is a functor that transforms the structure of the sheaf and assignment into a nested set of covers in a structure-preserving way. Furthermore, this article shows that consistency filtration is robust to perturbations, establishing its validity for arbitrarily thresholded, noisy data.

math.AT↗

arXiv2020

Cosheaf Representations of Relations and Dowker Complexes

The Dowker complex is an abstract simplicial complex that is constructed from a binary relation in a straightforward way. Although there are two ways to perform this construction -- vertices for the complex are either the rows or the columns of the matrix representing the relation -- the two constructions are homotopy equivalent. This article shows that the construction of a Dowker complex from a relation is a non-faithful covariant functor. Furthermore, we show that this functor can be made faithful by enriching the construction into a cosheaf on the Dowker complex. The cosheaf can be summarized by an integer weight function on the Dowker complex that is a complete isomorphism invariant for the relation. The cosheaf representation of a relation actually embodies both Dowker complexes, and we construct a duality functor that exchanges the two complexes. Finally, we explore a different cosheaf that detects the failure of the Dowker complex itself to be a faithful functor.

math.AT↗

arXiv2020

Topological Differential Testing

We introduce topological differential testing (TDT), an approach to extracting the consensus behavior of a set of programs on a corpus of inputs. TDT uses the topological notion of a simplicial complex (and implicitly draws on richer topological notions such as sheaves and persistence) to determine inputs that cause inconsistent behavior and in turn reveal \emph{de facto} input specifications. We gently introduce TDT with a toy example before detailing its application to understanding the PDF file format from the behavior of various parsers. Finally, we discuss theoretical details and other possible applications.

cs.SE↗

arXiv2020

The geometry of syntax and semantics for directed file transformations

We introduce a conceptual framework that associates syntax and semantics with vertical and horizontal directions in principal bundles and related constructions. This notion of geometry corresponds to a mechanism for performing goal-directed file transformations such as "eliminate unsafe syntax" and suggests various engineering practices.

cs.LO↗

arXiv2019

A Sheaf Theoretical Approach to Uncertainty Quantification of Heterogeneous Geolocation Information

Integration of heterogeneous sensors is a challenging problem across a range of applications. Prominent among these are multi-target tracking, where one must combine observations from different sensor types in a meaningful way to track multiple targets. Because sensors have differing error models, we seek a theoretically-justified quantification of the agreement among ensembles of sensors, both overall for a sensor collection, and also at a fine-grained level specifying pairwise and multi-way interactions among sensors. We demonstrate that the theory of mathematical sheaves provides a unified answer to this need, supporting both quantitative and qualitative data. The theory provides algorithms to globalize data across the network of deployed sensors, and to diagnose issues when the data do not globalize cleanly. We demonstrate the utility of sheaf-based tracking models based on experimental data of a wild population of black bears in Asheville, North Carolina. A measurement model involving four sensors deployed among the bears and the team of scientists charged with tracking their location is deployed. This provides a sheaf-based integration model which is small enough to fully interpret, but of sufficient complexity to demonstrate the sheaf's ability to recover a holistic picture of the locations and behaviors of both individual bears and the bear-human tracking system. A statistical approach was developed for comparison, a dynamic linear model which was estimated using a Kalman filter. This approach also recovered bear and human locations and sensor accuracies. When the observations are normalized into a common coordinate system, the structure of the dynamic linear observation model recapitulates the structure of the sheaf model, demonstrating the canonicity of the sheaf-based approach. But when the observations are not so normalized, the sheaf model still remains valid.

physics.data-an↗

arXiv2018

Developing Cyber Buffer Zones

The United Nations conducts peace operations around the world, aiming tomaintain peace and security in conflict torn areas. Whilst early operations werelargely successful, the changing nature of warfare and conflict has often left peaceoperations strugglingto adapt. In this article, we make a contribution towardsefforts to plan for the next evolution in both intra and inter-state conflict: cyberwarfare. It is now widely accepted that cyber warfare will be a component offuture conflicts, and much researchhas been devoted to how governments andmilitaries can prepare for and fight in this new domain [1]. Despite the vastamount of research relating to cyber warfare, there has been less discussion onits impact towards successful peace operations. This is agap in knowledge thatis important to address, since the restoration of peace following conflict of anykind is of global importance. It is however a complex topic requiring discussionacross multiple domains. Input from the technical, political, governmental andsocietal domains are critical in forming the concept of cyber peacekeeping.Previous work on this topic has sought to define the concept of cyber peacekeeping[2, 3, 4]. We build upon this work by exploring the practicalities ofstarting up a cyber peacekeeping component and setting up a Cyber Buffer Zone (CBZ).

cs.CY↗

arXiv2018

Developing Cyber Peacekeeping: Observation, Monitoring and Reporting

Cyber peacekeeping is an emerging and multi-disciplinary field of research, touching upon technical, political and societal domains of thought. In this article we build upon previous works by developing the cyber peacekeeping activity of observation, monitoring and reporting. We take a practical approach: describing a scenario in which two countries request UN support in drawing up and overseeing a ceasefire which includes cyber terms. We explore how a cyber peacekeeping operation could start up and discuss the challenges it will face. The article makes a number of proposals, including the use of a virtual collaborative environment to bring multiple benefits. We conclude by summarising our findings, and describing where further work lies.

cs.CY↗

arXiv2018

Local homology of abstract simplicial complexes

This survey describes some useful properties of the local homology of abstract simplicial complexes. Although the existing literature on local homology is somewhat dispersed, it is largely dedicated to the study of manifolds, submanifolds, or samplings thereof. While this is a vital perspective, the focus of this survey is squarely on the local homology of abstract simplicial complexes. Our motivation comes from the needs of the analysis of hypergraphs and graphs. In addition to presenting many classical facts in a unified way, this survey presents a few new results about how local homology generalizes useful tools from graph theory. The survey ends with a statistical comparison of graph invariants with local homology.

math.AT↗

arXiv2018

An Introduction to Cyber Peacekeeping

Peacekeeping is a noble and essential activity, helping to bring peace to conflict torn areas and providing security to millions of people around the world. Peacekeepers operate in all domains of war: buffer zones on land, no fly zones in the air and ensuring free passage at sea. With the emergence of cyberspace as a domain of war, questions on the role of peacekeeping in this domain naturally arise. There is extensive research around the topic of cyber warfare, but surprisingly little on how to restore and maintain peace in its aftermath. This is a significant gap which needs addressing. We begin by providing an overview of peacekeeping, describing its overarching goals and principles, using the United Nations model as a reference. We then review existing literature on cyber peacekeeping. The paper progresses to discuss the question of whether cyber peacekeeping is needed, and if so, if it is a plausible concept. We explore some ideas on how cyber peacekeeping could be performed and the challenges cyber peacekeepers will face, before making suggestions on where future work should be focused.

cs.CY↗

arXiv2017

Internet of Cloud: Security and Privacy issues

The synergy between the cloud and the IoT has emerged largely due to the cloud having attributes which directly benefit the IoT and enable its continued growth. IoT adopting Cloud services has brought new security challenges. In this book chapter, we pursue two main goals: 1) to analyse the different components of Cloud computing and the IoT and 2) to present security and privacy problems that these systems face. We thoroughly investigate current security and privacy preservation solutions that exist in this area, with an eye on the Industrial Internet of Things, discuss open issues and propose future directions

cs.CR↗