What's in a Prior? Learned Proximal Networks for Inverse Problems

Proximal operators are ubiquitous in inverse problems, commonly appearing as part of algorithmic strategies to regularize problems that are otherwise ill-posed. Modern deep learning models have been brought to bear for these tasks too, as in the framework of plug-and-play or deep unrolling, where they loosely resemble proximal operators. Yet, something essential is lost in employing these purely data-driven approaches: there is no guarantee that a general deep network represents the proximal operator of any function, nor is there any characterization of the function for which the network might provide some approximate proximal. This not only makes guaranteeing convergence of iterative schemes challenging but, more fundamentally, complicates the analysis of what has been learned by these networks about their training data. Herein we provide a framework to develop learned proximal networks (LPN), prove that they provide exact proximal operators for a data-driven nonconvex regularizer, and show how a new training strategy, dubbed proximal matching, provably promotes the recovery of the log-prior of the true data distribution. Such LPN provide general, unsupervised, expressive proximal operators that can be used for general inverse problems with convergence guarantees. We illustrate our results in a series of cases of increasing complexity, demonstrating that these models not only result in state-of-the-art performance, but provide a window into the resulting priors learned from data

Double Public Key Signing Function Oracle Attack on EdDSA Software Implementations

EdDSA is a standardised elliptic curve digital signature scheme introduced to overcome some of the issues prevalent in the more established ECDSA standard. Due to the EdDSA standard specifying that the EdDSA signature be deterministic, if the signing function were to be used as a public key signing oracle for the attacker, the unforgeability notion of security of the scheme can be broken. This paper describes an attack against some of the most popular EdDSA implementations, which results in an adversary recovering the private key used during signing. With this recovered secret key, an adversary can sign arbitrary messages that would be seen as valid by the EdDSA verification function. A list of libraries with vulnerable APIs at the time of publication is provided. Furthermore, this paper provides two suggestions for securing EdDSA signing APIs against this vulnerability while it additionally discusses failed attempts to solve the issue

Scalable Multi-domain Trust Infrastructures for Segmented Networks

Within a trust infrastructure, a private key is often used to digitally sign a transaction, which can be verified with an associated public key. Using PKI (Public Key Infrastructure), a trusted entity can produce a digital signature, verifying the authenticity of the public key. However, what happens when external entities are not trusted to verify the public key or in cases where there is no Internet connection within an isolated or autonomously acting collection of devices? For this, a trusted entity can be elected to generate a key pair and then split the private key amongst trusted devices. Each node can then sign part of the transaction using their split of the shared secret. The aggregated signature can then define agreement on a consensus within the infrastructure. Unfortunately, this process has two significant problems. The first is when no trusted node can act as a dealer of the shares. The second is the difficulty of scaling the digital signature scheme. This paper outlines a method of creating a leaderless approach to defining trust domains to overcome weaknesses in the scaling of the elliptic curve digital signature algorithm. Instead, it proposes the usage of the Edwards curve digital signature algorithm for the definition of multiple trust zones. The paper shows that the computational overhead of the distributed key generation phase increases with the number of nodes in the trust domain but that the distributed signing has a relatively constant computational overhead

Self-interest And Public Interest: The Motivations Of Political Actors

Self-Interest and Public Interest in Western Politics showed that the public, politicians, and bureaucrats are often public spirited. But this does not invalidate public-choice theory. Public-choice theory is an ideal type, not a claim that self-interest explains all political behavior. Instead, public-choice theory is useful in creating rules and institutions that guard against the worst case, which would be universal self-interestedness in politics. In contrast, the public-interest hypothesis is neither a comprehensive explanation of political behavior nor a sound basis for institutional design

White-Box Transformers via Sparse Rate Reduction

In this paper, we contend that the objective of representation learning is to compress and transform the distribution of the data, say sets of tokens, towards a mixture of low-dimensional Gaussian distributions supported on incoherent subspaces. The quality of the final representation can be measured by a unified objective function called sparse rate reduction. From this perspective, popular deep networks such as transformers can be naturally viewed as realizing iterative schemes to optimize this objective incrementally. Particularly, we show that the standard transformer block can be derived from alternating optimization on complementary parts of this objective: the multi-head self-attention operator can be viewed as a gradient descent step to compress the token sets by minimizing their lossy coding rate, and the subsequent multi-layer perceptron can be viewed as attempting to sparsify the representation of the tokens. This leads to a family of white-box transformer-like deep network architectures which are mathematically fully interpretable. Despite their simplicity, experiments show that these networks indeed learn to optimize the designed objective: they compress and sparsify representations of large-scale real-world vision datasets such as ImageNet, and achieve performance very close to thoroughly engineered transformers such as ViT. Code is at \url{https://github.com/Ma-Lab-Berkeley/CRATE}.Comment: 33 pages, 11 figure

Photosynthetic Adaptation to Length of Day Is Dependent on S-Sulfocysteine Synthase Activity in the Thylakoid Lumen

Abstract Arabidopsis (Arabidopsis thaliana) chloroplasts contain two O-acetyl-serine(thiol)lyase (OASTL) homologs, OAS-B, which is an authentic OASTL, and CS26, which has S-sulfocysteine synthase activity. In contrast with OAS-B, the loss of CS26 function resulted in dramatic phenotypic changes, which were dependent on the light treatment. We have performed a detailed characterization of the photosynthetic and chlorophyll fluorescence parameters in cs26 plants compared with those of wild-type plants under short-day growth conditions (SD) and long-day growth conditions (LD). Under LD, the photosynthetic characterization, which was based on substomatal CO2 concentrations and CO2 concentration in the chloroplast curves, revealed significant reductions in most of the photosynthetic parameters for cs26, which were unchanged under SD. These parameters included net CO2 assimilation rate, mesophyll conductance, and mitochondrial respiration at darkness. The analysis also showed that cs26 under LD required more absorbed quanta per driven electron flux and fixed CO2. The nonphotochemical quenching values suggested that in cs26 plants, the excess electrons that are not used in photochemical reactions may form reactive oxygen species. A photoinhibitory effect was confirmed by the background fluorescence signal values under LD and SD, which were higher in young leaves compared with mature ones under SD. To hypothesize the role of CS26 in relation to the photosynthetic machinery, we addressed its location inside of the chloroplast. The activity determination and localization analyses that were performed using immunoblotting indicated the presence of an active CS26 enzyme exclusively in the thylakoid lumen. This finding was reinforced by the observation of marked alterations in many lumenal proteins in the cs26 mutant compared with the wild type.</jats:p

Nrf2 in early vascular ageing: calcification, senescence and therapy

Under normal physiological conditions, free radical generation and antioxidant defences are balanced, and reactive oxygen species (ROS) usually act as secondary messengers in a plethora of biological processes. However, when this balance is impaired, oxidative stress develops due to imbalanced redox homeostasis resulting in cellular damage. Oxidative stress is now recognized as a trigger of cellular senescence, which is associated with multiple chronic 'burden of lifestyle' diseases, including atherosclerosis, type-2 diabetes, chronic kidney disease and vascular calcification; all of which possess signs of early vascular ageing. Nuclear factor erythroid 2-related factor 2 (Nrf2), termed the master regulator of antioxidant responses, is a transcription factor found to be frequently dysregulated in conditions characterized by oxidative stress and inflammation. Recent evidence suggests that activation of Nrf2 may be beneficial in protecting against vascular senescence and calcification. Both natural and synthetic Nrf2 agonists have been introduced as promising drug classes in different phases of clinical trials. However, overexpression of the Nrf2 pathway has also been linked to tumorigenesis, which highlights the requirement for further understanding of pathways involving Nrf2 activity, especially in the context of cellular senescence and vascular calcification. Therefore, comprehensive translational pre-clinical and clinical studies addressing the targeting capabilities of Nrf2 agonists are urgently required. The present review discusses the impact of Nrf2 in senescence and calcification in early vascular ageing, with focus on the potential clinical implications of Nrf2 agonists and non-pharmacological Nrf2 therapeutics

Soliton pair dynamics in patterned ferromagnetic ellipses

Confinement alters the energy landscape of nanoscale magnets, leading to the appearance of unusual magnetic states, such as vortices, for example. Many basic questions concerning dynamical and interaction effects remain unanswered, and nanomagnets are convenient model systems for studying these fundamental physical phenomena. A single vortex in restricted geometry, also known as a non-localized soliton, possesses a characteristic translational excitation mode that corresponds to spiral-like motion of the vortex core around its equilibrium position. Here, we investigate, by a microwave reflection technique, the dynamics of magnetic soliton pairs confined in lithographically defined, ferromagnetic Permalloy ellipses. Through a comparison with micromagnetic simulations, the observed strong resonances in the subgigahertz frequency range can be assigned to the translational modes of vortex pairs with parallel or antiparallel core polarizations. Vortex polarizations play a negligible role in the static interaction between two vortices, but their effect dominates the dynamics.Comment: supplemental movies on http://www.nature.com/nphys/journal/v1/n3/suppinfo/nphys173_S1.htm