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We present electrical and thermal transport measurements in single crystals of the metallic oxide RuO$_2$. The resistivity and Seebeck coefficient measured up to 970K confirm the metallic nature of transport. Magnetoresistance and Hall effect measurements as a function of orientation can be most easily described by a multiband transport model. We find that the ordinary Hall effect dominates any anomalous Hall signal in single crystals.

We study non-terminating graph rewriting models, whose local rules are applied non-deterministically -- and yet enjoy a strong form of determinism, namely space-time determinism. Of course in the case of terminating computation it is well-known that the mess introduced by asynchronous rule applications may not matter to the end result, as confluence conspires to produce a unique normal form. In the context of non-terminating computation however, confluence is a very weak property, and (almost) synchronous rule applications is always preferred e.g. when it comes to simulating dynamical systems. Here we provide sufficient conditions so that asynchronous local rule applications conspire to produce well-determined events in the space-time unfolding of the graph, regardless of their application orders. Our first example is an asynchronous simulation of a dynamical system. Our second example features time dilation, in the spirit of general relativity.

On the one side, the formalism of Global Transformations comes with the claim of capturing any transformation of space that is local, synchronous and deterministic.The claim has been proven for different classes of models such as mesh refinements from computer graphics, Lindenmayer systems from morphogenesis modeling and cellular automata from biological, physical and parallel computation modeling.The Global Transformation formalism achieves this by using category theory for its genericity, and more precisely the notion of Kan extension to determine the global behaviors based on the local ones.On the other side, Causal Graph Dynamics describe the transformation of port graphs in a synchronous and deterministic way and has not yet being tackled.In this paper, we show the precise sense in which the claim of Global Transformations holds for them as well.This is done by showing different ways in which they can be expressed as Kan extensions, each of them highlighting different features of Causal Graph Dynamics.Along the way, this work uncovers the interesting class of Monotonic Causal Graph Dynamics and their universality among General Causal Graph Dynamics.

We present new two-party protocols for the Unbalanced Private Set Union (UPSU) problem.Here, the Sender holds a set of data points, and the Receiver holds another (possibly much larger) set, and they would like for the Receiver to learn the union of the two sets and nothing else. Furthermore, the Sender's computational cost, along with the communication complexity, should be smaller when the Sender has a smaller set.While the UPSU problem has numerous applications and has seen considerable recent attention in the literature, our protocols are the first where the Sender's computational cost and communication volume are linear in the size of the Sender's set only, and do not depend on the size of the Receiver's set.Our constructions combine linearly homomorphic encryption (LHE) withfully homomorphic encryption (FHE). The first construction uses multi-point polynomial evaluation (MEv) on FHE, and achieves optimal linear cost for the Sender, but has higher quadratic computational cost for the Receiver. In the second construction we explore another trade-off: the Receiver computes fast polynomial Euclidean remainder in FHE while the Sender computes a fast MEv, in LHE only. This reduces the Receiver's cost to quasi-linear, with a modest increase in the computational cost for the Sender.Preliminary experimental results using HElib indicate that, for example, a Sender holding 1000 elements can complete our first protocol using less than 2s of computation time and less than 10MB of communication volume, independently of the Receiver's set size.

The layered delafossite metal PdCrO$_2$ is a natural heterostructure of highly conductive Pd layers Kondo coupled to localized spins in the adjacent Mott insulating CrO$_2$ layers. At high temperatures $T$ it has a $T$-linear resistivity which is not seen in the isostructural but non-magnetic PdCoO$_2$. The strength of the Kondo coupling is known, as-grown crystals are extremely high purity and the Fermi surface is both very simple and experimentally known. It is therefore an ideal material platform in which to investigate 'Planckian metal' physics. We do this by means of controlled introduction of point disorder, measurement of the thermal conductivity and Lorenz ratio and studying the sources of its high temperature entropy. The $T$-linear resistivity is seen to be due mainly to elastic scattering and to arise from a sum of several scattering mechanisms. Remarkably, this sum leads to a scattering rate within 10$\%$ of the Planckian value of $k_BT/$$\hbar$.

Graph-Rewriting Automata (GRA) are an extension of Cellular Automata to a dynamic structure using local graph-rewriting rules. This work introduces linear algebra based tools that allow for a practical investigation of their behavior in deeply extended time scales. A natural subset of GRA is explored in different ways thereby demonstrating the benefits of this method. Some elements of the subset were discovered to create chaotic patterns of growth and others to generate organic-looking graph structures. These phenomena suggest a strong relevance of GRA in the modeling natural complex systems. The approach presented here can be easily adapted to a wide range of GRA beyond the chosen subset.

The current state-of-the-art thermoelectric materials are generally composed of expensive, scarce, and toxic elements. In this respect, copper-based sulfide compounds have emerged as viable alternatives. Herein, we report for the first time the successful synthesis of single-phase cubic isocubanite CuFe2S3 using mechanical-alloying combined with microwave-assisted synthesis. The isocubanite phase synthesized via this ultra-fast out-of-equilibrium process exhibits a maximum thermoelectric figure of merit, zTmax ~ 0.14 at 673 K. Besides the thermoelectric properties, insights about the structure of isocubanite, based on the refinement of X-ray diffraction data and first principles calculations, are also investigated in detail. It confirms that the Cu-Fe cations in synthetic isocubanite overwhelmingly occupy the 4d sites of the cubic structure in an inherently disordered fashion., Comment: 18 pages, 7 figures

Proofs of Retrievability are protocols which allow a Client to store data remotely and to efficiently ensure, via audits, that the entirety of that data is still intact. Dynamic Proofs of Retrievability (DPoR) also support efficient retrieval and update of any small portion of the data.We propose a novel protocol for arbitrary outsourced data storage that achieves both low remote storage size and audit complexity.A key ingredient, that can be also of intrinsic interest, reduces to efficiently evaluating a secret polynomial at given public points, when the (encrypted) polynomial is stored on an untrusted Server.The Server performs the evaluations and also returns associated certificates. A Client can check that the evaluations are correct using the certificates and some pre-computed keys, more efficiently than re-evaluating the polynomial.Our protocols support two important features: the polynomial itself can be encrypted on the Server, and it can be dynamically updated by changing individual coefficients cheaply without redoing the entire setup.Our methods rely on linearly homomorphic encryption and pairings, and our implementation shows good performance for polynomial evaluations with millions of coefficients, and efficient DPoR with terabytes of data.For instance, for a 1TB database, compared to the state of art, we can reduce the Client storage by 5000x, communication size by 20x, and client-side audit time by 2x, at the cost of one order of magnitude increase in server-side audit time.

Global transformations form a categorical framework adapting graph transformations to describe fully synchronous rule systems on a given data structure.In this work we focus on data structures that can be captured as presheaves and study the computational aspects of such synchronous rule systems.To obtain an online algorithm, a complete study of the sub-steps within each synchronous step is done at the semantic level.This leads to the definition of accretive rule systems and a local criterion to characterize these systems.Finally an online computation algorithm for theses systems is given.

In this paper, we come back on the notion of local simulation allowing to transform a cellular automaton into a closely related one with different local encoding of information. In a previous paper, we applied it to the Firing Squad Synchronization Problem. In this paper, we show that the approach is not tied to this problem by applying it to the class of Real-Time Sequence Generation problems. We improve in particular on the generation of n 3 sequence by using local mappings to obtain millions of 5state solution, one of them using 58 transitions. It is based on the solution of Kamikawa and Umeo that uses 6 states and 74 transitions. Then, we explain in which sense even bigger classes of problems can be considered.

In this paper, we formalize precisely the sense in which the application of cellular automaton to partial configuration is a natural extension of its local transition function through the categorical notion of Kan extension. In fact, the two possible ways to do such an extension and the ingredients involved in their definition are related through Kan extensions in many ways. These relations provide additional links between computer science and category theory, and also give a new point of view on the famous Curtis-Hedlung theorem of cellular automata from the extended topological point of view provided by category theory. These relations provide additional links between computer science and category theory. No prior knowledge of category theory is assumed.

We want to replace categories, functors and natural transformations by categories, open functors and open natural transformations. In analogy with open dynamical systems, the adjective open is added here to mean that some external information is taken into account. For the particular use of the authors, such an open functor is described by two components: a presheaf representing the possible external influences for each input, and a classical functor from the category of elements of this presheaf to the category of results. Considering the appropriate notion of composition then leads to a bicategory. This report describes this bicategory with as little auxiliary constructions as possible and gives all the details of all the proofs needed to establish the bicategory, as explicitly as possible. Subsequent reports will give other presentations of this bicategory and compare it to other existing constructions, e.g. spans, fibrations, pseudoadjunctions, Kleisli bicategories of pseudo-monads, and profunctors (or distributors).

Proofs of Retrievability (PoRs) are protocols which allow a client to store data remotely and to efficiently ensure, via audits, that the entirety of that data is still intact. A dynamic PoR system also supports efficient retrieval and update of any small portion of the data. We propose new, simple protocols for dynamic PoR that are designed for practical efficiency, trading decreased persistent storage for increased server computation, and show in fact that this tradeoff is inherent via a lower bound proof of time-space for any PoR scheme. Notably, ours is the first dynamic PoR which does not require any special encoding of the data stored on the server, meaning it can be trivially composed with any database service or with existing techniques for encryption or redundancy. Our implementation and deployment on Google Cloud Platform demonstrates our solution is scalable: for example, auditing a 1TB file takes just less than 5 minutes and costs less than $0.08 USD. We also present several further enhancements, reducing the amount of client storage, or the communication bandwidth, or allowing public verifiability, wherein any untrusted third party may conduct an audit.

In this paper, we come back on the notion of local simulation allowing to transform a cellular automaton into a closely related one with different local encoding of information. This notion is used to explore solutions of the Firing Squad Synchronization Problem that are minimal both in time (2n -- 2 for n cells) and, up to current knowledge, also in states (6 states). While only one such solution was proposed by Mazoyer since 1987, 718 new solutions have been generated by Clergue, Verel and Formenti in 2018 with a cluster of machines. We show here that, starting from existing solutions, it is possible to generate millions of such solutions using local simulations using a single common personal computer.

The one-dimensional cobaltate Ca3Co2O6 is an intriguing material having an unconventional magnetic structure, displaying quantum tunneling phenomena in its magnetization. Using a newly developed experimental method, s-core-level non-resonant inelastic x-ray scattering (s-NIXS), we were able to image the atomic Co 3d orbital that is responsible for the Ising magnetism in this system. We show that we can directly observe that it is the complex d2 orbital occupied by the sixth electron at the high-spin Co-trig{3+} (d6) sites that generates this behavior. This is extremely rare in the research field of transition metal compounds, and is only made possible by the delicately balanced prismatic trigonal coordination. The ability to directly relate the orbital occupation with the local crystal structure is essential to model the magnetic properties of this system.

Replacing lithium ions with sodium ions as the charge carriers in rechargeable batteries can induce noticeable differences in the electrochemical storage mechanisms of electrode materials. Many material parameters, such as particle size, morphology, and the presence of defects, are known to further affect the storage mechanism. Here, we report an investigation of how the introduction of titanium vacancies into anatase TiO2 affects the sodium storage mechanism. From pair distribution function analysis, we observe that sodium ions are inserted into titanium vacancies at the early stage of the discharge process. This is supported by density functional theory calculations, which predict that sodium insertion is more favourable at vacancies than at interstitial sites. Our calculations also show that the intercalation voltage is sensitive to the anion coordination environment of the vacancy. Sodiation to higher concentrations induces a phase transition toward a disordered rhombohedral structure, similar to that observed in defect-free TiO2. Finally, we find that the X-ray diffraction pattern of the rhombohedral phase drastically changes depending on the composition and degree of disorder, providing further comprehension on the sodium storage mechanism of anatase.

We have studied the electronic structure of BaCoO$_3$ using soft x-ray absorption spectroscopy at the Co-$L_{2,3}$ and O-$K$ edges, magnetic circular dichroism at the Co-$L_{2,3}$ edges, as well as valence band hard x-ray photoelectron spectroscopy. The quantitative analysis of the spectra established that the Co ions are in the formal low-spin tetravalent 3$d^5$ state and that the system is a negative charge transfer Mott insulator. The spin-orbit coupling plays also an important role for the magnetism of the system. At the same time, a trigonal crystal field is present with sufficient strength to bring the 3$d^5$ ion away from the $J_{eff} = 1/2$ state. The sign of this crystal field is such that the $a_{1g}$ orbital is doubly occupied, explaining the absence of a Peierl's transition in this system which consists of chains of face-sharing CoO$_6$ octahedra. Moreover, with one hole residing in the $e_g^{\pi}$, the presence of an orbital moment and strong magneto-crystalline anisotropy can be understood. Yet, we also infer that crystal fields with lower symmetry must be present to reproduce the measured orbital moment quantitatively, thereby suggesting the possibility for orbital ordering to occur in BaCoO$_3$.

We present a study of the of thermal transport in thin single crystals of iron-intercalated titanium disulphide, Fe$_{x}$TiS$_2$ for $0\leq x \leq 0.20$. We determine the distribution of intercalants using high-resolution crystallographic and magnetic measurements, confirming the insertion of Fe without long-range ordering. We find that iron intercalation perturbs the lattice very little, and suppresses the tendency of TiS$_2$ to self-intercalate with excess Ti. We observe trends in the thermal conductivity that are compatible with our ab initio calculations of thermal transport in perfectly stoichiometric TiS$_2$.

The electronic transport properties of the delafossite oxides ABO$_2$ are usually understood in terms of two well separated entities, namely, the triangular A$^+$ and (BO$_2$)$^-$ layers. Here we review several cases among this extensive family of materials where the transport depends on the interlayer coupling and displays unconventional properties. We review the doped thermoelectrics based on CuRhO$_2$ and CuCrO$_2$, which show a high-temperature recovery of Fermi-liquid transport exponents, as well as the highly anisotropic metals PdCoO$_2$, PtCoO$_2$ and PdCrO$_2$ where the sheer simplicity of the Fermi surface leads to unconventional transport. We present some of the theoretical tools that have been used to investigate these transport properties and review what can and cannot be learned from the extensive set of electronic structure calculations that have been performed., Comment: 35 pages, 19 figures