Approximating Cumulative Pebbling Cost Is Unique Games Hard

The cumulative pebbling complexity of a directed acyclic graph $G$ is defined as $\mathsf{cc}(G) = \min_P \sum_i |P_i|$, where the minimum is taken over all legal (parallel) black pebblings of $G$ and $|P_i|$ denotes the number of pebbles on the graph during round $i$. Intuitively, $\mathsf{cc}(G)$ captures the amortized Space-Time complexity of pebbling $m$ copies of $G$ in parallel. The cumulative pebbling complexity of a graph $G$ is of particular interest in the field of cryptography as $\mathsf{cc}(G)$ is tightly related to the amortized Area-Time complexity of the Data-Independent Memory-Hard Function (iMHF) $f_{G,H}$ [AS15] defined using a constant indegree directed acyclic graph (DAG) $G$ and a random oracle $H(\cdot)$. A secure iMHF should have amortized Space-Time complexity as high as possible, e.g., to deter brute-force password attacker who wants to find $x$ such that $f_{G,H}(x) = h$. Thus, to analyze the (in)security of a candidate iMHF $f_{G,H}$, it is crucial to estimate the value $\mathsf{cc}(G)$ but currently, upper and lower bounds for leading iMHF candidates differ by several orders of magnitude. Blocki and Zhou recently showed that it is $\mathsf{NP}$-Hard to compute $\mathsf{cc}(G)$, but their techniques do not even rule out an efficient $(1+\varepsilon)$-approximation algorithm for any constant $\varepsilon>0$. We show that for any constant $c > 0$, it is Unique Games hard to approximate $\mathsf{cc}(G)$ to within a factor of $c$. (See the paper for the full abstract.)Comment: 28 pages, updated figures and corrected typo

Excited ionic and neutral fragments produced by dissociation of the N2(+)* H band

N I and N II fluorescent radiation was observed when N2 was irradiated by undispersed synchrotron radiation with an upper energy limit of approximately 200 eV. The excited fragments originate from dissociation of a band of excited ionic states of N2 lying between 34.7 and 44 eV

Talent Development for Integration Web 3.0/NFT/SDG into UNSDGs

Sustainable Development mindset with servant leadership has been mentioned in past studies for transformations. Under covid-19, there is a need for new way of committed organizations to provide professional services, for example, business related training services with United Nations sustainable development goals (UNSDGs) and ESG (Environmental, Social and Governance). Moreover, digital art related business services may be a future area for the education sector too. It is time to explore attitudes, skills and values needed for a professional business servant leader to re-design workflow with transformations and services with innovations for driving economic growth

On the Security of Proofs of Sequential Work in a Post-Quantum World

A Proof of Sequential Work (PoSW) allows a prover to convince a resource-bounded verifier that the prover invested a substantial amount of sequential time to perform some underlying computation. PoSWs have many applications including time-stamping, blockchain design, and universally verifiable CPU benchmarks. Mahmoody, Moran, and Vadhan (ITCS 2013) gave the first construction of a PoSW in the random oracle model though the construction relied on expensive depth-robust graphs. In a recent breakthrough, Cohen and Pietrzak (EUROCRYPT 2018) gave an efficient PoSW construction that does not require expensive depth-robust graphs. In the classical parallel random oracle model, it is straightforward to argue that any successful PoSW attacker must produce a long $\mathcal{H}$-sequence and that any malicious party running in sequential time $T-1$ will fail to produce an $\mathcal{H}$-sequence of length $T$ except with negligible probability. In this paper, we prove that any quantum attacker running in sequential time $T-1$ will fail to produce an $\mathcal{H}$-sequence except with negligible probability -- even if the attacker submits a large batch of quantum queries in each round. The proof is substantially more challenging and highlights the power of Zhandry's recent compressed oracle technique (CRYPTO 2019). We further extend this result to establish post-quantum security of a non-interactive PoSW obtained by applying the Fiat-Shamir transform to Cohen and Pietrzak's efficient construction (EUROCRYPT 2018).Comment: 44 pages, 4 figure

A two-dimensional model of low-Reynolds number swimming beneath a free surface

Biological organisms swimming at low Reynolds number are often influenced by the presence of rigid boundaries and soft interfaces. In this paper we present an analysis of locomotion near a free surface with surface tension. Using a simplified two-dimensional singularity model, and combining a complex variable approach with conformal mapping techniques, we demonstrate that the deformation of a free surface can be harnessed to produce steady locomotion parallel to the interface. The crucial physical ingredient lies in the nonlinear hydrodynamic coupling between the disturbance flow created by the swimmer and the free boundary problem at the fluid surface

On the origin of high m magnetospheric waves

A survey of Advanced Rio-Imaging Experiment in Scandinavia data reveals evidence for a previously overlooked generation mechanism of high azimuthal wave number magnetospheric waves. Here we present observations of pulsating cosmic noise absorption with azimuthal wave numbers as high as 380, suggestive of precipitation modulation by magnetospheric waves. Dispersion relations of the small-scale precipitation pulsations are indicative of the proposed origin. Previous studies of magnetospheric waves, together with data from the Charge And Mass Magnetospheric Ion Composition Experiment (Magnetospheric Ion Composition Sensor) instrument aboard the Polar spacecraft, provide support for the theory

Four Dimensional MR Image Analysis of Dynamic Renography

A novel four dimensional image analysis approach including registration and segmentation of dynamic contrast enhanced renal MR images is presented. This integrated method is motivated by the observation of the reciprocity between registration and segmentation in 4D time-series images. Fully automated Fourier-based registration with sub-voxel accuracy and semi-automated time-series segmentation were intertwined to improve the accuracy in a multi-step fashion. We have tested our algorithm on several real patient data sets. Clinical validation showed remarkable and consistent agreement between the proposed method and manual segmentation by experts

Integrated Four Dimensional Registration and Segmentation of Dynamic Renal MR Images

In this paper a novel approach for the registration and segmentation of dynamic contrast enhanced renal MR images is presented. This integrated method is motivated by the observation of the reciprocity between registration and segmentation in 4D time-series images. Fully automated Fourier-based registration with sub-voxel accuracy and semi-automated time-series segmentation were intertwined to improve the accuracy in a multi-step fashion. We have tested our algorithm on several real patient data sets. Clinical validation showed remarkable and consistent agreement between the proposed method and manual segmentation by experts

Managing the Enriched Experience Network - Learning-Outcome Approach to the Experimental Design Life-Cycle

Experimental design methods have long been used in scientific areas such as agriculture, biology and physics to minimise error and assure validity. Although most network researchers performing experiments with testbeds and simulations implicitly follow scientific method, until recently there has been little emphasis on improving experimental design methods. Traditional experimental design focuses on experiments where the scope and objectives are relatively constrained, however network research in innovative areas where there is little or no precedence often has changing objectives that evolve over time. We describe the learning-outcome approach to the experimental design life-cycle that applies the concepts of systems development life-cycle models used in software engineering, as well as learning taxonomies used in education. Our approach extends traditional experimental design by providing a more comprehensive and efficient way of decomposing an experimental research project into manageable stages that are designed rather than improvised, leading to a well-structured way of assessing the knowledge gained. We provide an insight into our experiences with this approach in the context of experimental research in management of Alcatel Australia's new-generation Enriched Experience Network