Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

Convex bodies: the brunn–minkowski theory

Cyber-physical systems are ubiquitous in power systems, transportation networks, industrial control processes, and critical infrastructures. These systems need to operate reliably in the face of unforeseen failures and external malicious attacks. In this paper: (i) we propose a mathematical framework for cyber-physical systems, attacks, and monitors; (ii) we characterize fundamental monitoring limitations from system-theoretic and graph-theoretic perspectives; and (ii) we design centralized and distributed attack detection and identification monitors. Finally, we validate our findings through compelling examples.

/pdf/attack-detection-and-identification-in-cyber-physical-3fy6vyw4zt.pdf

Attack Detection and Identification in Cyber-Physical Systems

With rapid progress and significant successes in a wide spectrum of applications, deep learning is being applied in many safety-critical environments. However, deep neural networks (DNNs) have been recently found vulnerable to well-designed input samples called adversarial examples . Adversarial perturbations are imperceptible to human but can easily fool DNNs in the testing/deploying stage. The vulnerability to adversarial examples becomes one of the major risks for applying DNNs in safety-critical environments. Therefore, attacks and defenses on adversarial examples draw great attention. In this paper, we review recent findings on adversarial examples for DNNs, summarize the methods for generating adversarial examples, and propose a taxonomy of these methods. Under the taxonomy, applications for adversarial examples are investigated. We further elaborate on countermeasures for adversarial examples. In addition, three major challenges in adversarial examples and the potential solutions are discussed.

Adversarial Examples: Attacks and Defenses for Deep Learning

We present a systematic study of the geometric Renyi divergence (GRD), also known as the maximal Renyi divergence, from the point of view of quantum information theory. We show that this divergence, together with its extension to channels, has many appealing structural properties. For example we prove a chain rule inequality that immediately implies the "amortization collapse" for the geometric Renyi divergence, addressing an open question by Berta et al. [arXiv:1808.01498, Equation (55)] in the area of quantum channel discrimination. As applications, we explore various channel capacity problems and construct new channel information measures based on the geometric Renyi divergence, sharpening the previously best-known bounds based on the max-relative entropy while still keeping the new bounds single-letter efficiently computable. A plethora of examples are investigated and the improvements are evident for almost all cases.

Geometric R\'{e}nyi Divergence and its Applications in Quantum Channel Capacities

We introduce a new quantum Renyi divergence $D^{\#}_{\alpha}$ for $\alpha \in (1,\infty)$ defined in terms of a convex optimization program. This divergence has several desirable computational and operational properties such as an efficient semidefinite programming representation for states and channels, and a chain rule property. An important property of this new divergence is that its regularization is equal to the sandwiched (also known as the minimal) quantum Renyi divergence. This allows us to prove several results. First, we use it to get a converging hierarchy of upper bounds on the regularized sandwiched $\alpha$-Renyi divergence between quantum channels for $\alpha > 1$. Second it allows us to prove a chain rule property for the sandwiched $\alpha$-Renyi divergence for $\alpha > 1$ which we use to characterize the strong converse exponent for channel discrimination. Finally it allows us to get improved bounds on quantum channel capacities.

/pdf/defining-quantum-divergences-via-convex-optimization-bxi5ojg9ar.pdf

Defining quantum divergences via convex optimization

Sums-of-squares techniques have played an important role in optimization and control. One question that has attracted a lot of attention is to exploit sparsity in order to reduce the size of sum-of-squares programs. In this paper we consider the problem of finding sparse sum-of-squares certificates for functions defined on a finite abelian group G. In this setting the natural basis over which to measure sparsity is the Fourier basis of G (also called the basis of characters of G). We establish combinatorial conditions on subsets S and τ of Fourier basis elements under which nonnegative functions with Fourier support S are sums of squares of functions with Fourier support τ. Our combinatorial condition involves constructing a chordal cover of a graph related to G and S with maximal cliques related to τ. These techniques allow us to show that any nonnegative quadratic function in binary variables is a sum of squares of functions of degree at most ⌈n/2⌉, resolving a conjecture of Laurent [11]. They also allow us to show that any nonnegative function of degree d on G = ℤN has a sum-of-squares certificate supported on at most 3d log(N/d) Fourier basis elements. By duality this construction yields the first explicit family of polytopes in increasing dimensions that have a semidefinite programming description that is vanishingly smaller than any linear programming description.

Sparse sum-of-squares certificates on finite abelian groups

The nonnegative rank of a matrix A is the smallest integer r such that A can be written as the sum of r rank-one nonnegative matrices. The nonnegative rank has received a lot of attention recently due to its application in optimization, probability and communication complexity. In this paper we study a class of atomic rank functions defined on a convex cone which generalize several notions of "positive" ranks such as nonnegative rank or cp-rank (for completely positive matrices). The main contribution of the paper is a new method to obtain lower bounds for such ranks which improve on previously known bounds. Additionally the bounds we propose can be computed by semidefinite programming. The idea of the lower bound relies on an atomic norm approach where the atoms are self-scaled according to the vector (or matrix, in the case of nonnegative rank) of interest. This results in a lower bound that is invariant under scaling and that is at least as good as other existing norm-based bounds. 
We mainly focus our attention on the two important cases of nonnegative rank and cp-rank where our bounds satisfying interesting properties: For the nonnegative rank we show that our lower bound can be interpreted as a non-combinatorial version of the fractional rectangle cover number, while the sum-of-squares relaxation is closely related to the Lov\'asz theta number of the rectangle graph of the matrix. We also prove that the lower bound inherits many of the structural properties satisfied by the nonnegative rank such as invariance under diagonal scaling, subadditivity, etc. We also apply our method to obtain lower bounds on the cp-rank for completely positive matrices. In this case we prove that our lower bound is always greater than or equal the plain rank lower bound, and we show that it has interesting connections with combinatorial lower bounds based on edge-clique cover number.

Self-scaled bounds for atomic cone ranks: applications to nonnegative rank and cp-rank

The nonnegative rank of an entrywise nonnegative matrix $$A \in \mathbb {R}^{m \times n}_+$$A?R+m×n is the smallest integer $$r$$r such that $$A$$A can be written as $$A=UV$$A=UV where $$U \in \mathbb {R}^{m \times r}_+$$U?R+m×r and $$V \in \mathbb {R}^{r \times n}_+$$V?R+r×n are both nonnegative. The nonnegative rank arises in different areas such as combinatorial optimization and communication complexity. Computing this quantity is NP-hard in general and it is thus important to find efficient bounding techniques especially in the context of the aforementioned applications. In this paper we propose a new lower bound on the nonnegative rank which, unlike most existing lower bounds, does not solely rely on the matrix sparsity pattern and applies to nonnegative matrices with arbitrary support. The idea involves computing a certain nuclear norm with nonnegativity constraints which allows to lower bound the nonnegative rank, in the same way the standard nuclear norm gives lower bounds on the standard rank. Our lower bound is expressed as the solution of a copositive programming problem and can be relaxed to obtain polynomial-time computable lower bounds using semidefinite programming. We compare our lower bound with existing ones, and we show examples of matrices where our lower bound performs better than currently known ones.

/pdf/lower-bounds-on-nonnegative-rank-via-nonnegative-nuclear-15ndhxghag.pdf

Hamza Fawzi

Papers

Geometric R\'{e}nyi Divergence and its Applications in Quantum Channel Capacities

Defining quantum divergences via convex optimization

Sparse sum-of-squares certificates on finite abelian groups

Self-scaled bounds for atomic cone ranks: applications to nonnegative rank and cp-rank

Lower bounds on nonnegative rank via nonnegative nuclear norms