Mirror Theory Research Articles

Revisiting Variable Output Length XOR Pseudorandom Function

Let σ be some positive integer and C ⊆ {(i, j) : 1 ≤ i < j ≤ σ}. The theory behind finding a lower bound on the number of distinct blocks P1, . . . , Pσ ∈ {0, 1}n satisfying a set of linear equations {Pi ⊕Pj = ci,j : (i, j) ∈ C} for some ci,j ∈ {0, 1}n, is called mirror theory. Patarin introduced the mirror theory and provided a proof for this. However, the proof, even for a special class of equations, is complex and contains several non-trivial gaps. As an application of mirror theory, XORP[w] (known as XOR construction) returning (w−1) block output, is a pseudorandom function (PRF) for some parameter w, called width. The XOR construction can be seen as a basic structure of some encryption algorithms, e.g., the CENC encryption and the CHM authenticated encryption, proposed by Iwata in 2006. Due to potential application of XORP[w] and the nontrivial gaps in the proof of mirror theory, an alternative simpler analysis of PRF-security of XORP[w] would be much desired. Recently (in Crypto 2017) Dai et al. introduced a tool, called the χ2 method, for analyzing PRF-security. Using this tool, the authors have provided a proof of PRF-security of XORP[2] without relying on the mirror theory. In this paper, we resolve the general case; we apply the χ2 method to obtain a simpler security proof of XORP[w] for any w ≥ 2. For w = 2, we obtain a tighter bound for a wider range of parameters than that of Dai et al.. Moreover, we consider variable width construction XORP[∗] (in which the widths are chosen by adversaries adaptively), and also provide variable output length pseudorandom function (VOLPRF) security analysis for it. As an application of VOLPRF, we propose an authenticated encryption which is a simple variant of CHM or AES-GCM and provides much higher security than those at the cost of one extra blockcipher call for every message.

Mirror theories of 3d mathcal{N} = 2 SQCD

Using a recently proposed duality for U(N ) supersymmetric QCD (SQCD) in three dimensions with monopole superpotential, in this paper we derive the mirror dual description of mathcal{N} = 2 SQCD with unitary gauge group, generalizing the known mirror dual description of abelian gauge theories. We match the chiral ring of the dual theories and their partition functions on the squashed sphere. We also conjecture a generalization for SQCD with orthogonal and symplectic gauge groups.

Design of Compact Bandpass Filters Using Novel Dual-Mode Dielectric Patch Resonator

This paper introduces a new dual-mode dielectric patch resonator (DPR), which consists of a thin square dielectric patch with high permittivity and a low-permittivity substrate with bottom ground plane. A pair of TM11 degenerate modes can act as the dominate mode by fusing the dielectric patch and the substrate with the ground plane, whose resonant frequency is derived by using the combination of mixed magnetic wall method and mirror theory. It can be found that the constructed dual-mode DPR owns both merits of the planar transmission line and the dielectric resonator at the same time, i.e., low-profile configuration and high unloaded quality factor (Q u ). Based on the proposed dual-mode DPR, a single-ended bandpass filter (BPF) and a differential BPF is designed respectively. Good agreement can be observed between their respective simulated and measured results. Both of them showcase several advantages such as low passband loss, low profile, and compact size.

Towards deconstruction of the Type D (2,0) theory

We propose a four-dimensional supersymmetric theory that deconstructs, in a particular limit, the six-dimensional (2, 0) theory of type Dk. This 4d theory is defined by a necklace quiver with alternating gauge nodes O(2k) and Sp(k). We test this proposal by comparing the 6d half-BPS index to the Higgs branch Hilbert series of the 4d theory. In the process, we overcome several technical difficulties, such as Hilbert series calculations for non-complete intersections, and the choice of O versus SO gauge groups. Consistently, the result matches the Coulomb branch formula for the mirror theory upon reduction to 3d.

Four-order temperature protection for high-power 256-step LED current dimming chip

This study presents a high-resolution current-mode approach for LED dimming. We propose the 256-level currents to control LED brightness with 8-bit binary code. Based on current mirror theory, a switchable current is controlled by 8-switch current mirror arrays. To prolong the lifespan of LED driver, four order of the temperature sensor is proposed to control LED driving current. The diode is used as temperature sensor. In order to protect over heating of LED driver, the four sensing levels are used to control LED current. The over voltage protection is also designed to avoid to damage power MOS of this chip. With full-costumed design, the chip area included pads is only 1.87mm2 using TSMC 0.25μm high-voltage technology. The single chip can drive 72W LED devices in maximum when the LED driving current is 1.2A and the supply voltage is 60V. The 256-step current levels are used for LED dimming, where the resolution of current to luminance can achieve 1mA. The maximum driving efficiency can be up to 98%, and our lighting efficiency can be improved by 20% compared with switching modulation.

Mirror theory and cryptography

“Mirror Theory” is the theory that evaluates the number of solutions of affine systems of equalities $$({=})$$ and non equalities ( $$\ne $$ ) in finite groups. It is deeply related to the security and attacks of many generic cryptographic secret key schemes, for example random Feistel schemes (balanced or unbalanced), Misty schemes, Xor of two pseudo-random bijections to generate a pseudo-random function etc. In this paper we will assume that the groups are abelian. Most of time in cryptography the group is $$((\mathbb {Z}/2\mathbb {Z})^n, \oplus )$$ and we will concentrate this paper on these cases. We will present here general definitions, some theorems, and many examples and computer simulations.

Towards Verified Software: Mirror Theory of Programming

Towards Verified Software: Mirror Theory of Programming

Temporal-Spatial Features of Intention Understanding Based on EEG-fNIRS Bimodal Measurement

Understanding the actions of other people is a key component of social interaction. This paper used an electroencephalography and functional near infrared spectroscopy (EEG-fNIRS) bimodal system to investigate the temporal-spatial features of action intention understanding. We measured brain activation while participants observed three actions: 1) grasping a cup for drinking; 2) grasping a cup for moving; and 3) no meaningful intention. Analysis of EEG maximum standardized current density revealed that brain activation transitioned from the left to the right hemisphere. EEG-fNIRS source analysis results revealed that both the mirror neuron system and theory of mind network are involved in action intention understanding, and the extent to which these two systems are engaged appears to be determined by the clarity of the observed intention. These findings indicate that action intention understanding is a complex and dynamic process.

Research on vector acoustic focusing and shielding technology

Vector acoustic focusing and shielding technology was discussed in this paper. Based on time reversal mirror (TRM) theory, the received sound pressure signals which contained radiation noise from the target and interference sources were weighted in the frequency domain. Combination of the output sound pressure signals and received particle velocity signals can form unilateral directivity, so focusing on the target and shielding interference sources can be achieved simultaneously. Shielding weight vector was also calculated when multiple interference sources existed in detection area. In terms of acoustic shielding, interference signal in a selected area was suppressed, so the detection performance to the targets outside the area could be improved. Better than scalar hydrophone array, vector array can distinguish between left and right, and further more, the output “beam” of the array has a narrower main lobe and larger radio of main lobe to side lobe. The simulation indicated that one or multiple interference sources were all suppressed under vector acoustic shielding technology so that detection performance was improved.

From Self-identification to Self-destruction—A Mirror Image Interpretation of Dorian Gray’s Psychic Transformation

Oscar Wilde, the representative of Aestheticism, is the most controversial figure in English literary history. The Picture of Dorian Gray, as his first and only novel, has been the object of study for a long time. The study of the protagonist from the psychoanalytic angle is still new and has potential research value for its in-depth analysis. According to Lacanian mirror theory, the self-construction of an individual is formed under the influence of the other’s mirror image. In the novel, under the influence of all the elements, Dorian experiences the psychic transformation and gradually ends up in self-destruction after alienating his self-identification. The thesis aims to explore the critical mirrors in the process pf Dorian’s transformation in the light of Lagan’s theory so that the understanding the protagonist can be expanded.

The myth of broken mirror theory of autism: Origins, problems and prospects

自闭症患者在社会沟通和交往障碍上主要涉及社会情感互动缺陷、非语言行为交流缺陷、发展维持和理解人际关系的缺陷。该群体在社会认知过程中潜在自动的直觉成分受损被视为其独特的临床症状。鉴于镜像神经元系统在社会认知的直觉成分上扮演的重要角色,该系统的功能障碍假说（或称“碎镜”理论）被提出并用以解释自闭症的成因及其异常表现。然而,在经历了10年的发展与证据检验后,该理论潜在的问题逐渐暴露。当前的研究显示,迄今为止人类镜像神经元系统的研究存在内在缺陷,镜像神经元系统至多是社会认知的附带原因,该系统功能障碍也并非自闭症患者社会认知障碍的必要条件。碎镜理论面临来自临床行为研究与认知神经科学实验证据的广泛质疑。未来,伴随自闭症研究对象的变化,镜像神经元的社会响应学说的提出,双个体范式、第二人称神经科学范式与计算精神病学的兴起,镜像神经元与自闭症的真正关系将有望得以阐明。

Argyres–Douglas theories, S1 reductions, and topological symmetries

In a recent paper, we proposed closed-form expressions for the superconformal indices of the and Argyres–Douglas (AD) superconformal field theories (SCFTs) in the Schur limit. Following up on our results, we turn our attention to the small S1 regime of these indices. As expected on general grounds, our study reproduces the S3 partition functions of the resulting dimensionally reduced theories. However, we show that in all cases—with the exception of the reduction of the SCFT—certain imaginary partners of real mass terms are turned on in the corresponding mirror theories. We interpret these deformations as R symmetry mixing with the topological symmetries of the direct S1 reductions. Moreover, we argue that these shifts occur in any of our theories whose four-dimensional superconformal symmetry does not obey an SU(2) quantization condition. We then use our R symmetry map to find the four-dimensional ancestors of certain three-dimensional operators. Somewhat surprisingly, this picture turns out to imply that the scaling dimensions of many of the chiral operators of the four-dimensional theory are encoded in accidental symmetries of the three-dimensional theory. We also comment on the implications of our work on the space of general SCFTs.

Floer cohomology of -equivariant Lagrangian branes

Building on Seidel and Solomon’s fundamental work [Symplectic cohomology and$q$-intersection numbers, Geom. Funct. Anal.22(2012), 443–477], we define the notion of a$\mathfrak{g}$-equivariant Lagrangian brane in an exact symplectic manifold$M$, where$\mathfrak{g}\subset SH^{1}(M)$is a sub-Lie algebra of the symplectic cohomology of$M$. When$M$is a (symplectic) mirror to an (algebraic) homogeneous space$G/P$, homological mirror symmetry predicts that there is an embedding of$\mathfrak{g}$in$SH^{1}(M)$. This allows us to study a mirror theory to classical constructions of Borel, Weil and Bott. We give explicit computations recovering all finite-dimensional irreducible representations of$\mathfrak{sl}_{2}$as representations on the Floer cohomology of an$\mathfrak{sl}_{2}$-equivariant Lagrangian brane and discuss generalizations to arbitrary finite-dimensional semisimple Lie algebras.

Mirror symmetry and loop operators

Wilson loops in gauge theories pose a fundamental challenge for dualities. Wilson loops are labeled by a representation of the gauge group and should map under duality to loop operators labeled by the same data, yet generically, dual theories have completely different gauge groups. In this paper we resolve this conundrum for three dimensional mirror symmetry. We show that Wilson loops are exchanged under mirror symmetry with Vortex loop operators, whose microscopic definition in terms of a supersymmetric quantum mechanics coupled to the theory encode in a non-trivial way a representation of the original gauge group, despite that the gauge groups of mirror theories can be radically different. Our predictions for the mirror map, which we derive guided by branes in string theory, are confirmed by the computation of the exact expectation value of Wilson and Vortex loop operators on the three-sphere.

Intact Automatic Imitation and Typical Spatial Compatibility in Autism Spectrum Disorder: Challenging the Broken Mirror Theory.

A lack of imitative behavior is frequently described as a core feature of Autism Spectrum Disorder (ASD), and is consistent with claims of mirror neuron system dysfunction in these individuals. Previous research has questioned this characterization of ASD however, arguing that when tests of automatic imitation are used--which do not require higher-level cognitive processing--imitative behavior is intact or even enhanced in individuals with ASD. In Experiment 1, 60 adult individuals with ASD and a matched Control group completed an automatic imitation task in which they were required to perform an index or a middle finger lift while observing a hand making either the same, or the alternate, finger movement. Both groups demonstrated a significant imitation effect whereby actions were executed faster when preceded by observation of the same action, than when preceded by the alternate action. The magnitude of this "imitation effect" was statistically indistinguishable in the ASD and Control groups. Experiment 2 utilized an improved automatic imitation paradigm to demonstrate that, when automatic imitation effects are isolated from those due to spatial compatibility, increasing autism symptom severity is associated with an increased tendency to imitate. Notably, there was no association between autism symptom severity and spatial compatibility, demonstrating the specificity of the link between ASD symptoms and increased imitation. These results provide evidence against claims of a lack of imitative behavior in ASD, and challenge the "Broken Mirror Theory of Autism."

모듈형 행동선택네트워크를 이용한 거울뉴런과 마음이론 기반의 의도대응 모델

Although service robots in various fields are being commercialized, most of them have problems that depend on explicit commands by users and have difficulty to generate robust reactions of the robot in the unstable condition using insufficient sensor data. To solve these problems, we modeled mirror neuron and theory of mind systems, and applied them to a robot agent to show the usefulness. In order to implement quick and intuitive response of the mirror neuron, the proposed intention-response model utilized behavior selection networks considering external stimuli and a goal, and in order to perform reactions based on the long-term action plan of theory of mind system, we planned behaviors of the sub-goal unit using a hierarchical task network planning, and controled behavior selection network modules. Experiments with various scenarios revealed that appropriate reactions were generated according to external stimuli.

Flow characteristics of ultra-high pressure micro-impinging streams

This work studies miniature impingement flow fields using Powell's macro-tube impinging mirror model by simulating five faces, x=0.04 mm, 0.08 mm, 0.10 mm, 0.12 mm, 0.16 mm, in the impact zone. Analysis of the simulation provides a detailed picture of the axial direction speed, speed in the radial direction, and dynamic pressure. The distribution curves of the axial velocity, radial velocity, and dynamic pressure obtained by theoretical derivation show that the two impinging stream strands are symmetrical about the ζ=0 impact surface. These distributions are consistent between simulation and theoretical results, showing that there is a mirrored distribution within ultra-micro impingement flow fields and further supporting Powell's proposed mirror theory.

Bridge over troubled discourse: the influence of the Golden Gate Bridge on community discourse and suicide

Purpose – The purpose of this paper is to examine the Golden Gate Bridge (GGB) as a work of art and the role of the bridge in shaping community identity and discourse. Particular attention is focussed on the discourse surrounding mental illness and suicide, which perpetuate the problem of suicides involving the bridge as a means and mechanism of death. An analysis of the person who attempts or completes suicide is also performed. Design/methodology/approach – Multiple research articles, writings, and a cinematic production are drawn on to frame the argument in terms of Michel Foucault's adaption of Pantopticism Theory and Jacques Lacan's Mirror Theory, which includes the concepts of the Real, the Imaginary, and the Symbolic. Findings – The GGB is a major factor in shaping the discourse on mental illness and suicide in the San Francisco community. The influences the GGB exerts combines with and exacerbates a culture of stigma, which perpetuates negative discourse and increases the risk of suicides in those already vulnerable. Research limitations/implications – The research for this paper was performed at a distance and was conducted, with the exception of one personal communication, by literature search and application to theory. Ethnographic research would be a logical next step to study the phenomenon further. Practical implications – Theory developed from this paper could be used in determining a relevant course of action for adding to existing suicide prevention efforts in the San Francisco Area and any other community with a prominent icon, such as the GGB, that may be exerting a negative influence on the suicide rates of that area. Social implications – An awareness of how art, culture, and psychology interact would increase awareness of the creation of a stigmatized environment and perhaps precipitate a change in the underlying negative discourse. Originality/value – This paper takes a fresh look at the phenomenon of violent death by suicide where a physical object/icon (the GGB) is used as a means to die. The particular theories and approach used to explain the interactions that intensify the suicide death rate have never been combined and interwoven in such an interdisciplinary way to seek an explanation.

Absent yet popular? Explaining news visibility of Members of the European Parliament

AbstractMembers of the European Parliament (MEPs) represent their citizens in European Union policy making, having the power to approve, amend or reject the near majority of legislation. The media inform EU citizens about their representatives and are able to hold them publicly accountable. However, we know little about whether, and to what extent, MEPs are visible in the news. This study investigates the visibility of MEPs in national broadsheets in Britain, France, the Netherlands, Germany and Italy. It seeks to explain individual‐level variation by employing an original dataset of news visibility of 302 MEPs over a period of 25 months (September 2009–September 2011) and tests the applicability of the news values and mirror theories in the context of supranational politics. The results show that political office, length of tenure and domestic party leadership have a positive effect. Legislative activities have a mixed effect on MEP news visibility. Attendance negatively affects news visibility, while non‐attached MEPs receive more news coverage. In short, despite the core supranational nature of EP legislative politics, MEP news visibility primarily depends on journalists’ domestic considerations. This informs both our understanding of MEP parliamentary behaviour and journalism studies in the context of the EU.

Monopole operators and Hilbert series of Coulomb branches of 3d $ \mathcal{N} $ = 4 gauge theories

This paper addresses a long standing problem - to identify the chiral ring and moduli space (i.e. as an algebraic variety) on the Coulomb branch of an N = 4 superconformal field theory in 2+1 dimensions. Previous techniques involved a computation of the metric on the moduli space and/or mirror symmetry. These methods are limited to sufficiently small moduli spaces, with enough symmetry, or to Higgs branches of sufficiently small gauge theories. We introduce a simple formula for the Hilbert series of the Coulomb branch, which applies to any good or ugly three-dimensional N = 4 gauge theory. The formula counts monopole operators which are dressed by classical operators, the Casimir invariants of the residual gauge group that is left unbroken by the magnetic flux. We apply our formula to several classes of gauge theories. Along the way we make various tests of mirror symmetry, successfully comparing the Hilbert series of the Coulomb branch with the Hilbert series of the Higgs branch of the mirror theory.