arXiv subjects

Ian Wood

Publications and source records attributed to Ian Wood.

At least 19 recordsLinked to original sources

arXiv2026

Spectrum of the Maxwell Equations for a Flat Interface between Non-Homogeneous Dispersive Media in 2D and 3D

The present work concerns the time-harmonic Maxwell equations in two- and three-dimensional space, divided into two half-spaces by a flat interface. The two half-spaces are filled with media whose electric permittivity is frequency-dependent and varies as a function of the distance from the interface only; this dependence is assumed to satisfy a regularity condition in each half-space but may be discontinuous at the interface. No specific model for the frequency dependence is assumed. For the associated operator pencil, we characterise subsets of the resolvent set and separate subsets of the Weyl spectrum corresponding to radiation away from the interface and along the interface, respectively. The characterisation of the sets is via conditions on the fundamental solutions. If the media are periodic in the direction orthogonal to the interface, a more explicit description of these sets can be given in terms of Floquet theory of related Sturm-Liouville equations. These results generalise earlier work in one and two dimensions where the media were assumed to be homogeneous in each half-space.

math.SP↗

arXiv2024

ConvoCache: Smart Re-Use of Chatbot Responses

We present ConvoCache, a conversational caching system that solves the problem of slow and expensive generative AI models in spoken chatbots. ConvoCache finds a semantically similar prompt in the past and reuses the response. In this paper we evaluate ConvoCache on the DailyDialog dataset. We find that ConvoCache can apply a UniEval coherence threshold of 90% and respond to 89% of prompts using the cache with an average latency of 214ms, replacing LLM and voice synthesis that can take over 1s. To further reduce latency we test prefetching and find limited usefulness. Prefetching with 80% of a request leads to a 63% hit rate, and a drop in overall coherence. ConvoCache can be used with any chatbot to reduce costs by reducing usage of generative AI by up to 89%.

cs.CL↗

arXiv2024

SenTopX: Benchmark for User Sentiment on Various Topics

Toxic sentiment analysis on Twitter (X) often focuses on specific topics and events such as politics and elections. Datasets of toxic users in such research are typically gathered through lexicon-based techniques, providing only a cross-sectional view. his approach has a tight confine for studying toxic user behavior and effective platform moderation. To identify users consistently spreading toxicity, a longitudinal analysis of their tweets is essential. However, such datasets currently do not exist. This study addresses this gap by collecting a longitudinal dataset from 143K Twitter users, covering the period from 2007 to 2021, amounting to a total of 293 million tweets. Using topic modeling, we extract all topics discussed by each user and categorize users into eight groups based on the predominant topic in their timelines. We then analyze the sentiments of each group using 16 toxic scores. Our research demonstrates that examining users longitudinally reveals a distinct perspective on their comprehensive personality traits and their overall impact on the platform. Our comprehensive dataset is accessible to researchers for additional analysis.

cs.SI↗

arXiv2023

Challenges with Passwordless FIDO2 in an Enterprise Setting: A Usability Study

Fast Identity Online 2 (FIDO2), a modern authentication protocol, is gaining popularity as a default strong authentication mechanism. It has been recognized as a leading candidate to overcome limitations (e.g., it is phishing resistant) of existing authentication solutions. However, the task of deprecating weak methods such as password-based authentication is not trivial and requires a comprehensive approach. While security, privacy, and end-user usability of FIDO2 have been addressed in both academic and industry literature, the difficulties associated with its integration with production environments, such as solution completeness or edge-case support, have received little attention. In particular, complex environments such as enterprise identity management pose unique challenges for any authentication system. In this paper, we identify challenging enterprise identity lifecycle use cases (e.g., remote workforce and legacy systems) by conducting a usability study, in which 118 professionals shared their perception of challenges to FIDO2 integration from their hands-on field experience. Our analysis of the user study results revealed serious gaps such as account recovery (selected by over 60% of our respondents), and identify priority development areas for the FIDO2 community.

cs.CR↗

arXiv2023

An analysis of scam baiting calls: Identifying and extracting scam stages and scripts

Phone scams remain a difficult problem to tackle due to the combination of protocol limitations, legal enforcement challenges and advances in technology enabling attackers to hide their identities and reduce costs. Scammers use social engineering techniques to manipulate victims into revealing their personal details, purchasing online vouchers or transferring funds, causing significant financial losses. This paper aims to establish a methodology with which to semi-automatically analyze scam calls and infer information about scammers, their scams and their strategies at scale. Obtaining data for the study of scam calls is challenging, as true scam victims do not in general record their conversations. Instead, we draw from the community of ``scam baiters'' on YouTube: individuals who interact knowingly with phone scammers and publicly publish their conversations. These can not be considered as true scam calls, however they do provide a valuable opportunity to study scammer scripts and techniques, as the scammers are unaware that they are not speaking to a true scam victim for the bulk of the call. We applied topic and time series modeling alongside emotion recognition to scammer utterances and found clear evidence of scripted scam progressions that matched our expectations from close reading. We identified social engineering techniques associated with identified script stages including the apparent use of emotion as a social engineering tool. Our analyses provide new insights into strategies used by scammers and presents an effective methodology to infer such at scale. This work serves as a first step in building a better understanding of phone scam techniques, forming the ground work for more effective detection and prevention mechanisms that draw on a deeper understanding of the phone scam phenomenon.

cs.CR↗

arXiv2023

Those Aren't Your Memories, They're Somebody Else's: Seeding Misinformation in Chat Bot Memories

One of the new developments in chit-chat bots is a long-term memory mechanism that remembers information from past conversations for increasing engagement and consistency of responses. The bot is designed to extract knowledge of personal nature from their conversation partner, e.g., stating preference for a particular color. In this paper, we show that this memory mechanism can result in unintended behavior. In particular, we found that one can combine a personal statement with an informative statement that would lead the bot to remember the informative statement alongside personal knowledge in its long term memory. This means that the bot can be tricked into remembering misinformation which it would regurgitate as statements of fact when recalling information relevant to the topic of conversation. We demonstrate this vulnerability on the BlenderBot 2 framework implemented on the ParlAI platform and provide examples on the more recent and significantly larger BlenderBot 3 model. We generate 150 examples of misinformation, of which 114 (76%) were remembered by BlenderBot 2 when combined with a personal statement. We further assessed the risk of this misinformation being recalled after intervening innocuous conversation and in response to multiple questions relevant to the injected memory. Our evaluation was performed on both the memory-only and the combination of memory and internet search modes of BlenderBot 2. From the combinations of these variables, we generated 12,890 conversations and analyzed recalled misinformation in the responses. We found that when the chat bot is questioned on the misinformation topic, it was 328% more likely to respond with the misinformation as fact when the misinformation was in the long-term memory.

cs.CL↗

arXiv2022

Complete Non-Selfadjointness for Schrödinger Operators on the Semi-Axis

In this note we investigate complete non-selfadjointness for all maximally dissipative extensions of a Schrödinger operator on a half-line with dissipative bounded potential and dissipative boundary condition. We show that all maximally dissipative extensions that preserve the differential expression are completely non-selfadjoint. However, it is possible for maximally dissipative extensions to have a one-dimensional reducing subspace on which the operator is selfadjoint. We give a characterisation of these extensions and the corresponding subspaces and present a specific example.

math.SP↗

arXiv2022

The spectral form of the functional model for maximally dissipative operators: A Lagrange identity approach

The spectral and scattering properties of non-selfadjoint problems pose a mathematical challenge. Apart from exceptional cases, the well-developed methods used to examine the spectrum of selfadjoint problems are not applicable. One of the tools to attack non-selfadjoint problems are functional models. A drawback of many functional models is that their constructions require objects which may be difficult to describe explicitly, such as operator square roots, making it hard to apply the results to specific examples. We develop a functional model for the case when the non-selfadjointness arises both in additive terms and in the boundary conditions which is based on the Lagrange identity. The flexibility of the choice of the $Γ$-operators in the Lagrange identity means that these can be chosen so that expressions arising in the model are given explicitly in terms of physical parameters (coefficients, boundary conditions and Titchmarsh-Weyl $M$-function) of the maximally dissipative operator. The presentation of such explicit expressions for the spectral form of the functional model is arguably the main contribution of the present paper. In the spectral form of the functional model, the selfadjoint dilation is very simple, being the operator of multiplication by an independent variable in some auxiliary vector-valued function space. We also obtain an explicit expression for the completely non-selfadjoint part of the operator and an operator-analytic proof of the famous result by Sz.-Nagy-Foias on the pure absolute continuity of the spectrum of the minimal selfadjoint dilation. Finally, we consider an example of a limit circle Sturm-Liouville operator.

math.SP↗

arXiv2022

Spectrum of the Maxwell Equations for a Flat Interface between Homogeneous Dispersive Media

The paper determines and classifies the spectrum of a non-self-adjoint operator pencil generated by the time-harmonic Maxwell problem with a nonlinear dependence on the frequency for the case of two homogeneous materials joined at a planar interface. We study spatially one-dimensional and two-dimensional reductions in the whole space $\mathbb{R}$ and $\mathbb{R}^2$. The dependence on the spectral parameter, i.e. the frequency, is in the dielectric function and we make no assumptions on its form. These function values determine the spectral sets. In order to allow also for non-conservative media, the dielectric function is allowed to be complex, yielding a non-self-adjoint problem. The whole spectrum consists of eigenvalues and the essential spectrum, but the various standard types of essential spectra do not coincide in all cases. The main tool for determining the essential spectra are Weyl sequences.

math.SP↗

arXiv2022

How Not to Handle Keys: Timing Attacks on FIDO Authenticator Privacy

This paper presents a timing attack on the FIDO2 (Fast IDentity Online) authentication protocol that allows attackers to link user accounts stored in vulnerable authenticators, a serious privacy concern. FIDO2 is a new standard specified by the FIDO industry alliance for secure token online authentication. It complements the W3C WebAuthn specification by providing means to use a USB token or other authenticator as a second factor during the authentication process. From a cryptographic perspective, the protocol is a simple challenge-response where the elliptic curve digital signature algorithm is used to sign challenges. To protect the privacy of the user the token uses unique key pairs per service. To accommodate for small memory, tokens use various techniques that make use of a special parameter called a key handle sent by the service to the token. We identify and analyse a vulnerability in the way the processing of key handles is implemented that allows attackers to remotely link user accounts on multiple services. We show that for vulnerable authenticators there is a difference between the time it takes to process a key handle for a different service but correct authenticator, and for a different authenticator but correct service. This difference can be used to perform a timing attack allowing an adversary to link user's accounts across services. We present several real world examples of adversaries that are in a position to execute our attack and can benefit from linking accounts. We found that two of the eight hardware authenticators we tested were vulnerable despite FIDO level 1 certification. This vulnerability cannot be easily mitigated on authenticators because, for security reasons, they usually do not allow firmware updates. In addition, we show that due to the way existing browsers implement the WebAuthn standard, the attack can be executed remotely.

cs.CR↗

arXiv2020

The inverse problem for a spectral asymmetry function of the Schrödinger operator on a finite interval

For the Schrödinger equation $-d^2 u/dx^2 + q(x)u = λu$ on a finite $x$-interval, there is defined an "asymmetry function" $a(λ;q)$, which is entire of order $1/2$ and type $1$ in $λ$. Our main result identifies the classes of square-integrable potentials $q(x)$ that possess a common asymmetry function. For any given $a(λ)$, there is one potential for each Dirichlet spectral sequence.

math.SP↗

arXiv2019

Global labor flow network reveals the hierarchical organization and dynamics of geo-industrial clusters in the world economy

Groups of firms often achieve a competitive advantage through the formation of geo-industrial clusters. Although many exemplary clusters, such as Hollywood or Silicon Valley, have been frequently studied, systematic approaches to identify and analyze the hierarchical structure of the geo-industrial clusters at the global scale are rare. In this work, we use LinkedIn's employment histories of more than 500 million users over 25 years to construct a labor flow network of over 4 million firms across the world and apply a recursive network community detection algorithm to reveal the hierarchical structure of geo-industrial clusters. We show that the resulting geo-industrial clusters exhibit a stronger association between the influx of educated-workers and financial performance, compared to existing aggregation units. Furthermore, our additional analysis of the skill sets of educated-workers supplements the relationship between the labor flow of educated-workers and productivity growth. We argue that geo-industrial clusters defined by labor flow provide better insights into the growth and the decline of the economy than other common economic units.

cs.SI↗

arXiv2018

Embedded eigenvalues for perturbed periodic Jacobi operators using a geometric approach

We consider the problem of embedding eigenvalues into the essential spectrum of periodic Jacobi operators, using an oscillating, decreasing potential. To do this we employ a geometric method, previously used to embed eigenvalues into the essential spectrum of the discrete Schrödinger operator. For periodic Jacobi operators we relax the rational dependence conditions on the values of the quasi-momenta from this previous work. We then explore conditions that permit not just the existence of infinitely many subordinate solutions to the formal spectral equation but also the embedding of infinitely many eigenvalues.

math.SP↗

arXiv2018

Essential spectrum for Maxwell's equations

We study the essential spectrum of operator pencils associated with anisotropic Maxwell equations, with permittivity $\varepsilon$, permeability $μ$ and conductivity $σ$, on finitely connected unbounded domains. The main result is that the essential spectrum of the Maxwell pencil is the union of two sets: namely, the spectrum of the pencil $\mathrm{div}((ω\varepsilon + i σ) \nabla\,\cdot\,)$, and the essential spectrum of the Maxwell pencil with constant coefficients. We expect the analysis to be of more general interest and to open avenues to investigation of other questions concerning Maxwell's and related systems.

math.FA↗

arXiv2018

Weyl Solutions and J-selfadjointness for Dirac operators

We consider a non-selfadjoint Dirac-type differential expression \begin{equation} D(Q)y:= J_n \frac{dy}{dx} + Q(x)y, \quad\quad\quad (1) \end{equation} with a non-selfadjoint potential matrix $Q \in L^1_{loc}({\mathcal I},\mathbb{C}^{n\times n})$ and a signature matrix $J_n =-J_n^{-1} = -J_n^*\in \mathbb{C}^{n\times n}$. Here ${\mathcal I}$ denotes either the line $\mathbb{R}$ or the half-line $\mathbb{R}_+$. With this differential expression one associates in $L^2(\mathcal I,\mathbb{C}^{n})$ the (closed) maximal and minimal operators $D_{\max}(Q)$ and $D_{\min}(Q)$, respectively. One of our main results states that $D_{\max}(Q) = D_{\min}(Q)$ in $L^2(\mathbb{R},\mathbb{C}^{n})$. Moreover, we show that if the minimal operator $D_{\min}(Q)$ in $L^2(\mathbb{R},\mathbb{C}^{n})$ is $j$-symmetric with respect to an appropriate involution $j$, then it is $j$-selfadjoint. Similar results are valid in the case of the semiaxis $\mathbb{R}_+$. In particular, we show that if $n=2p$ and the minimal operator $D_{\min}(Q)$ in $L^2(\mathbb{R}_+,\mathbb{C}^{2p})$ is $j$-symmetric, then there exists a $2p\times p$-Weyl-type matrix solution $Ψ(z, \cdot)\in L^2(\mathbb{R}_+,\mathbb{C}^{2p\times p})$ of the equation $D^+_{\max}(Q)Ψ(z, \cdot)= zΨ(z, \cdot)$. A similar result is valid for the expression (1) with a potential matrix having a bounded imaginary part. This leads to the existence of a unique Weyl function for the expression (1). The differential expression (1) is of significance as it appears in the Lax formulation of the vector-valued nonlinear Schr{ö}dinger equation.

math.SP↗

arXiv2018

Spectral results for perturbed periodic Jacobi matrices using the discrete Levinson technique

For an arbitrary Hermitian period-$T$ Jacobi operator, we assume a perturbation by a Wigner-von Neumann type potential to devise subordinate solutions to the formal spectral equation for a (possibly infinite) real set, $S$, of the spectral parameter. We employ discrete Levinson type techniques to achieve this, which allow the analysis of the asymptotic behaviour of the solution. This enables us to construct infinitely many spectral singularities on the absolutely continuous spectrum of the periodic Jacobi operator, which are stable with respect to an $l^1$-perturbation. An analogue of the quantisation conditions from the continuous case appears, relating the frequency of the oscillation of the potential to the quasi-momentum associated with the purely periodic operator.

math.SP↗

arXiv2016

Eigenvalues for perturbed periodic Jacobi matrices by the Wigner-von Neumann approach

The Wigner-von Neumann method, which was previously used for perturbing continuous Schrödinger operators, is here applied to their discrete counterparts. In particular, we consider perturbations of arbitrary $T$-periodic Jacobi matrices. The asymptotic behaviour of the subordinate solutions is investigated, as too are their initial components, together giving a general technique for embedding eigenvalues, $λ$, into the operator's absolutely continuous spectrum. Introducing a new rational function, $C(λ;T)$, related to the periodic Jacobi matrices, we describe the elements of the a.c. spectrum for which this construction does not work (zeros of $C(λ;T)$); in particular showing that there are only finitely many of them.

math.FA↗

arXiv2016

The Proper Dissipative Extensions of a Dual Pair

Let $A$ and $(-\widetilde{A})$ be dissipative operators on a Hilbert space $\mathcal{H}$ and let $(A,\widetilde{A})$ form a dual pair, i.e. $A\subset\widetilde{A}^*$, resp.\ $\widetilde{A}\subset A^*$. We present a method of determining the proper dissipative extensions $\widehat{A}$ of this dual pair, i.e. $A\subset \widehat{A}\subset\widetilde{A}^*$ provided that $\mathcal{D}(A)\cap\mathcal{D}(\widetilde{A})$ is dense in $\mathcal{H}$. Applications to symmetric operators, symmetric operators perturbed by a relatively bounded dissipative operator and more singular differential operators are discussed. Finally, we investigate the stability of the numerical range of the different dissipative extensions.

math.FA↗