Sequential Information Flow and Real-Time Diagnosis of Swiss Inflation: Intra-Monthly DCF Estimates for a Low-Inflation Environment

The timely release of macroeconomic data imposes a distinct structure on the panel: the clustering and sequential ordering of real and nominal variables. We call this orderly release of economic data sequential information flow. The ordered panel generates a new class of restrictions that are helpful in interpreting the real-time estimates of monthly core inflation through the identification of turning points and structural shocks. After establishing the sought-after properties (of smoothness, stability, and forecasting) for core inflation, we turn to the discussion of real-time diagnosis for a low inflation environment. This is done in the context of weekly estimates of Swiss inflation. The intra-monthly estimates for core inflation find that it is worthwhile to update this measure at least twice a month.

Stone-Type Dualities for Separation Logics

Stone-type duality theorems, which relate algebraic and relational/topological models, are important tools in logic because -- in addition to elegant abstraction -- they strengthen soundness and completeness to a categorical equivalence, yielding a framework through which both algebraic and topological methods can be brought to bear on a logic. We give a systematic treatment of Stone-type duality for the structures that interpret bunched logics, starting with the weakest systems, recovering the familiar BI and Boolean BI (BBI), and extending to both classical and intuitionistic Separation Logic. We demonstrate the uniformity and modularity of this analysis by additionally capturing the bunched logics obtained by extending BI and BBI with modalities and multiplicative connectives corresponding to disjunction, negation and falsum. This includes the logic of separating modalities (LSM), De Morgan BI (DMBI), Classical BI (CBI), and the sub-classical family of logics extending Bi-intuitionistic (B)BI (Bi(B)BI). We additionally obtain as corollaries soundness and completeness theorems for the specific Kripke-style models of these logics as presented in the literature: for DMBI, the sub-classical logics extending BiBI and a new bunched logic, Concurrent Kleene BI (connecting our work to Concurrent Separation Logic), this is the first time soundness and completeness theorems have been proved. We thus obtain a comprehensive semantic account of the multiplicative variants of all standard propositional connectives in the bunched logic setting. This approach synthesises a variety of techniques from modal, substructural and categorical logic and contextualizes the "resource semantics" interpretation underpinning Separation Logic amongst them

How to use pen and paper tasks to aid tremor diagnosis in the clinic

When a patient presents with tremor, it can be useful to perform a few simple pen and paper tests. In this article, we explain how to maximise the value of handwriting and of drawing Archimedes spirals and straight lines as clinical assessments. These tasks take a matter of seconds to complete but provide a wealth of information that supplements the standard physical examination. They aid the diagnosis of a tremor disorder and can contribute to its longitudinal monitoring. Watching the patient’s upper limb while they write and draw may reveal abnormalities such as bradykinesia, dystonic posturing and distractibility. The finished script and drawings can then be evaluated for frequency, amplitude, direction and symmetry of oscillatory pen movements and for overall scale of penmanship. Essential, dystonic, functional and parkinsonian tremor each has a characteristic pattern of abnormality on these pen and paper tests

Method for universal detection of two-photon polarization entanglement

Detecting and quantifying quantum entanglement of a given unknown state poses problems that are fundamentally important for quantum information processing. Surprisingly, no direct (i.e., without quantum tomography) universal experimental implementation of a necessary and sufficient test of entanglement has been designed even for a general two-qubit state. Here we propose an experimental method for detecting a collective universal witness, which is a necessary and sufficient test of two-photon polarization entanglement. It allows us to detect entanglement for any two-qubit mixed state and to establish tight upper and lower bounds on its amount. A different element of this method is the sequential character of its main components, which allows us to obtain relatively complicated information about quantum correlations with the help of simple linear-optical elements. As such, this proposal realizes a universal two-qubit entanglement test within the present state of the art of quantum optics. We show the optimality of our setup with respect to the minimal number of measured quantities.Comment: 7 pages, 5 figure

Cutoff for random to random card shuffle

In this paper, we use the eigenvalues of the random to random card shuffle to prove a sharp upper bound for the total variation mixing time. Combined with the lower bound due to Subag, we prove that this walk exhibits cutoff at $\frac{3}{4} n \log n - \frac{1}{4}n\log\log{n}$ with window of order $n$, answering a conjecture of Diaconis

A calculus and logic of bunched resources and processes

Mathematical modelling and simulation modelling are fundamental tools of engineering, science, and social sciences such as economics, and provide decision-support tools in management. Mathematical models are essentially deployed at all scales, all levels of complexity, and all levels of abstraction. Models are often required to be executable, as a simulation, on a computer. We present some contributions to the process-theoretic and logical foundations of discrete-event modelling with resources and processes. Building on previous work in resource semantics, process calculus, and modal logic, we describe a process calculus with an explicit representation of resources in which processes and resources co-evolve. The calculus is closely connected to a substructural modal logic that may be used as a specification language for properties of models. In contrast to earlier work, we formulate the resource semantics, and its relationship with process calculus, in such a way that we obtain soundness and completeness of bisimulation with respect to logical equivalence for the naturally full range of logical connectives and modalities. We give a range of examples of the use of the process combinators and logical structure to describe system structure and behaviour