Regional CO₂ inversions with LUMIA, the Lund University Modular Inversion Algorithm, v1.0

Atmospheric inversions are used to derive constraints on the net sources and sinks of CO2 and other stable atmospheric tracers from their observed concentrations. The resolution and accuracy that the fluxes can be estimated with depends, among other factors, on the quality and density of the observational coverage, on the precision and accuracy of the transport model used by the inversion to relate fluxes to observations, and on the adaptation of the statistical approach to the problem studied. In recent years, there has been an increasing demand from stakeholders for inversions at higher spatial resolution (country scale), in particular in the framework of the Paris agreement. This step up in resolution is in theory enabled by the growing availability of observations from surface in situ networks (such as ICOS in Europe) and from remote sensing products (OCO-2, GOSAT-2). The increase in the resolution of inversions is also a necessary step to provide efficient feedback to the bottom-up modeling community (vegetation models, fossil fuel emission inventories, etc.). However, it calls for new developments in the inverse models: diversification of the inversion approaches, shift from global to regional inversions, and improvement in the computational efficiency. In this context, we developed LUMIA, the Lund University Modular Inversion Algorithm. LUMIA is a Python library for inverse modeling built around the central idea of modularity: it aims to be a platform that enables users to construct and experiment with new inverse modeling setups while remaining easy to use and maintain. It is in particular designed to be transport-model-agnostic, which should facilitate isolating the transport model errors from those introduced by the inversion setup itself. We have constructed a first regional inversion setup using the LUMIA framework to conduct regional CO2 inversions in Europe using in situ data from surface and tall-tower observation sites. The inversions rely on a new offline coupling between the regional high-resolution FLEXPART Lagrangian particle dispersion model and the global coarse-resolution TM5 transport model. This test setup is intended both as a demonstration and as a reference for comparison with future LUMIA developments. The aims of this paper are to present the LUMIA framework (motivations for building it, development principles and future prospects) and to describe and test this first implementation of regional CO2 inversions in LUMIA.

Regional CO₂ inversions with LUMIA, the Lund University Modular Inversion Algorithm, v1.0

Atmospheric inversions are commonly used for estimating large-scale (continental to regional) net sources and sinks of CO2 and other stable atmospheric tracers from their observed concentrations. Recently, there has been an increasing demand from stakeholders for robust estimates of greenhouse gases at country-scale (or higher) resolution, in particular in the framework of the Paris agreement. This increase in resolution is in theory enabled by the growing availability of observations from surface in-situ networks (such as ICOS in Europe) and from remote sensing products (OCO-2, GOSAT-2). The increase in the resolution of inversions is also a necessary step to provide efficient feedback to the process-based (bottom-up) modelling community (vegetation models, fossil fuel emission inventories). This, however, calls for new developments in the inverse modelling systems, mainly in terms of diversification of the inversion approaches, shift from global to regional inversions, and improvement in the computational efficiency, We have developed the Lund University Modular Inversion Algorithm (LUMIA) as a tool to address some of these new developments. LUMIA is meant to be a platform for inverse modelling developments at Lund University. It aims at being a flexible, yet simple and easy to maintain set of tools that modellers can combine to build inverse modelling experiments. It is in particular designed to be transport model agnostic, which should facilitate isolating the transport model errors from those introduced by the inversion setup itself. Here, we briefly describe the motivations for developing LUMIA as well as the underlying development principles, current status and future prospects. We present a first LUMIA inversion setup for a regional CO2 inversions over Europe, based on a new coupling between the Lagrangian FLEXPART (high resolution foreground transport) and the global coarse resolution TM5 transport models, using in-situ data from surface and tall tower observation sites.

An Efficient Hardware Implementation of Finite Field Inversion for Elliptic Curve Cryptography

The modular inversion operation is an essential hardware design for computing speed when we use it in cryptography applications. Through this work, we present a FSM based design methodology to achieve speed, area and high-performance modular binary inversion algorithm over 256-bit prime field. The proposed architecture implemented using Xilinx Virtex-7 FPGA device, it achieves 37% reduction in area-delay product and 15% and 16% of improvement in speed and throughput respectively, when compared with existing designs. Also, ASIC based implementation is done using TSMC 65nm CMOS technology, the synthesis results achieved the maximum operating clock frequency is 833 MHz and throughput of 626Mbps, which makes it suitable for speed-critical cryptoapplications.

Fast constant-time gcd computation and modular inversion

This paper introduces streamlined constant-time variants of Euclid’s algorithm, both for polynomial inputs and for integer inputs. As concrete applications, this paper saves time in (1) modular inversion for Curve25519, which was previously believed to be handled much more efficiently by Fermat’s method, and (2) key generation for the ntruhrss701 and sntrup4591761 lattice-based cryptosystems.

Parity and the modular bootstrap

We consider unitary, modular invariant, two-dimensional CFTs which are invariant under the parity transformation PP. Combining PP with modular inversion SS leads to a continuous family of fixed points of the SPSP transformation. A particular subset of this locus of fixed points exists along the line of positive left- and right-moving temperatures satisfying \beta_L \beta_R = 4\pi^2βLβR=4π2. We use this fixed locus to prove a conjecture of Hartman, Keller, and Stoica that the free energy of a large-cc CFT_22 with a suitably sparse low-lying spectrum matches that of AdS_33 gravity at all temperatures and all angular potentials. We also use the fixed locus to generalize the modular bootstrap equations, obtaining novel constraints on the operator spectrum and providing a new proof of the statement that the twist gap is smaller than (c-1)/12(c−1)/12 when c>1c>1. At large cc we show that the operator dimension of the first excited primary lies in a region in the (h,\overline{h})(h,h¯)-plane that is significantly smaller than h+\overline{h}<c/6h+h¯>c/6. Our results for the free energy and constraints on the operator spectrum extend to theories without parity symmetry through the construction of an auxiliary parity-invariant partition function.