A universal quantum estimator

Almost all computational tasks in the modem computer can be designed from basic building blocks. These building blocks provide a powerful and efficient language for describing algorithms. In quantum computers, the basic building blocks are the quantum gates. In this tutorial, we will look at quantum gates that act on one and two qubits and briefly discuss how these gates can be used in quantum networks

Certain Invertible Operator-Block Matrices Induced by C*-Algebras and Scaled Hypercomplex Numbers

The main purposes of this paper are (i) to enlarge scaled hypercomplex structures to operator-valued cases, where the operators are taken from a C*-subalgebra of an operator algebra on a separable Hilbert space, (ii) to characterize the invertibility conditions on the operator-valued scaled-hypercomplex structures of (i), (iii) to study relations between the invertibility of scaled hypercomplex numbers, and that of operator-valued cases of (ii), and (iv) to confirm our invertibility of (ii) and (iii) are equivalent to the general invertibility of (2×2)-block operator matrices

Schur Analysis Over the Unit Spectral Ball

We begin a study of Schur analysis when the variable is now a matrix rather than a complex number. We define the corresponding Hardy space, Schur multipliers and their realizations, and interpolation. Possible applications of the present work include matrices of quaternions, matrices of split quaternions, and other algebras of hypercomplex numbers

Probabilities with Values in Scaled Hyperbolic Numbers

In this paper, we introduce a notion of a probabilistic measure which takes values in t-scaled hyperbolic numbers for t ∈ R, with a system of axioms generalizing directly Kolmogorov’s axioms. i.e., we establish a suitable measure theory in the set Dt of all t-scaled hyperbolic numbers for arbitrarily fixed t ∈ R

Dynamical Systems of Operators Induced by Scaled Hypercomplex Rings

In this paper, we consider a family of the hypercomplex rings H = {Ht}t∈R scaled by R, and the dynamical system of R acting on H via a certain action θ of R. i.e., we study an analysis on dynamical system induced by H . In particular, we are interested in free-probabilistic information on the dynamical system dictated by our hypercomplex analysis

Prevalence and predictors of video game addiction: a study based on a national representative sample of gamers

Video gaming has become a popular leisure activity in many parts of the world, and an increasing number of empirical studies examine the small minority that appears to develop problems as a result of excessive gaming. This study investigated prevalence rates and predictors of video game addiction in a sample of gamers, randomly selected from the National Population Registry of Norway (N =3389). Results showed there were 1.4 % addicted gamers, 7.3 % problem gamers, 3.9 % engaged gamers, and 87.4 % normal gamers. Gender (being male) and age group (being young) were positively associated with addicted-, problem-, and engaged gamers. Place of birth (Africa, Asia, South- and Middle America) were positively associated with addicted- and problem gamers. Video game addiction was negatively associated with conscientiousness and positively associated with neuroticism. Poor psychosomatic health was positively associated with problem- and engaged gaming. These factors provide insight into the field of video game addiction, and may help to provide guidance as to how individuals that are at risk of becoming addicted gamers can be identified

Scaled Global Operators and Fueter Variables on Non-zero Scaled Hypercomplex Numbers

In this paper we describe the rise of global operators in the scaled quaternionic case, an important extension from the quaternionic case to the family of scaled hypercomplex numbers Ht, t ∈ R∗ , of which the H−1 = H is the space of quaternions and H1 is the space of split quaternions.We also describe the scaled Fueter-type variables associated to these operators, developing a coherent theory in this field. We use these types of variables to build different types of function spaces on Ht. Counterparts of the Hardy space and of the Arveson space are also introduced and studied in the present setting. The two different adjoints in the scaled hypercomplex numbers lead to two parallel cases in each instance. Finally we introduce and study the notion of rational function

Protecting Privacy Through Approximating Optimal Parameters for Sequence Unlearning in Language Models

Although language models (LMs) demonstrate exceptional capabilities on various tasks, they are potentially vulnerable to extraction attacks, which represent a significant privacy risk. To mitigate the privacy concerns of LMs, machine unlearning has emerged as an important research area, which is utilized to induce the LM to selectively forget about some of its training data. While completely retraining the model will guarantee successful unlearning and privacy assurance, it is impractical for LMs, as it would be time-consuming and resource-intensive. Prior works efficiently unlearn the target token sequences, but upon subsequent iterations, the LM displays significant degradation in performance. In this work, we propose Privacy Protection via Optimal Parameters (POP), a novel unlearning method that effectively forgets the target token sequences from the pretrained LM by applying optimal gradient updates to the parameters. Inspired by the gradient derivation of complete retraining, we approximate the optimal training objective that successfully unlearns the target sequence while retaining the knowledge from the rest of the training data. Experimental results demonstrate that POP exhibits remarkable retention performance post-unlearning across 9 classification and 4 dialogue benchmarks, outperforming the state-of-the-art by a large margin. Furthermore, we introduce Remnant Memorization Accuracy that quantifies privacy risks based on token likelihood and validate its effectiveness through both qualitative and quantitative analyses.Comment: Accepted to ACL2024 finding

Who controls the narrative? The (re)productions of power and coloniality in the higher education in emergencies community

In this article, we critically examine the coloniality of knowledge production processes within the education in emergencies community and explore how and why such actions continue despite mounting critique. We do so by reflecting on our joint involvement in a consultancy for a large donor which sought to map range of threats facing higher education systems under political or ideological coercion. As the work progressed, it became clear that our own academic freedom was being diminished by the funder’s own political and diplomatic interests, limiting the contexts we could include or not in our analysis. Reflecting on this experience, we map out the various drivers that implicate many higher education scholars, ourselves included, in projects that perpetuate epistemic erasure, ignorance and/or violence. We explore how collectively, we become implicated in the very systems of imperialism, capitalism and racism we critique – largely through our continued relationship with and dependence on a small group of funders. This is shaped by enterprises of academic capitalism coupled with the rise of the neoliberal university. Rather than accept these dynamics as a given, however, we argue for the importance of finding small spaces of resistance within our everyday scholarly work to unsettle such forces