Rough Version Research Articles

A novel bi-level temporally-distributed MPC approach: An application to green urban mobility

Model predictive control (MPC) has been widely used for traffic management, such as for minimizing the total time spent or the total emissions of vehicles. When long-term green urban mobility is considered including e.g. a constraint on the total yearly emissions, the optimization horizon of the MPC problem is significantly larger than the control sampling time, and thus the number of the variables that should be optimized per control time step becomes very large. For systems with dynamics that involve nonlinear, non-convex, and non-smooth functions, including urban traffic networks, this results in optimization problems that are computationally intractable in real time. In this paper, we propose a novel bi-level temporal distribution of such complex MPC optimization problems, and we develop two mathematically linked short-term and long-term MPC formulations with small and large control sampling times that will be solved together instead of the original complex optimization problem. The resulting bi-level control architecture is used to solve the two MPC formulations online for real-time control of urban traffic networks with the objective of long-term green mobility. In order to assess the performance of the bi-level control architecture, we perform a case study where a rough version of the model of the urban traffic flow, S-model, is used by the long-term MPC level to estimate the states of the urban traffic networks, and a detailed version of the model is used by the short-term MPC level. The results of the simulations prove the effectiveness (with respect to the objective of control, as well as computational efficiency) of the proposed bi-level MPC approach, compared to state-of-the-art control approaches.

Rough Entanglement: Not Enough Fourier

AbstractThis work presents a new form of entanglement known as rough entanglement. It is based on the quantum Fourier transform (QFT) and is an alternative to those used in quantum information processing for generating maximally and nonmaximally entangled states. The roughly entangled pairs are used in the quantum teleportation protocol, where, the performance achieved in the reconstruction of the teleported state is evaluated. The aforementioned teleportation is implemented on a simulator and a 5‐qubit physical machine from the IBM Q Experience inventory. Emphasis is placed on the teleportation of computational basis states (CBS) commonly used in quantum key distribution protocols. Finally, in previous works, it is shown that to generate Bell states the intervention of two QFT blocks is required, while the rough version requires only one. The lack of a second layer or QFT block in its constitution gives the name to this new type of entanglement.

A lightweight convolutional neural network as an alternative to DIC to measure in-plane displacement fields

Convolutional Neural Networks (CNNs) are now commonly used in the computer vision community, in particular for optical flow estimation. Some attempts to use such tools to measure displacement and strain fields from pairs of reference/deformed speckle images (like Digital Image Correlation) have been recently reported in the literature. The aim of this work is twofold. The first one is to customize a state-of-the-art CNN dedicated to optical flow estimation to reach better performance when processing speckle images. This is mainly obtained by removing the deepest levels. The second one is to further simplify the CNN by reducing as much as possible the number of filters in the remaining levels while keeping equivalent metrological performance to the original version, in order to accelerate image processing on a power-efficient compact Graphics Processing Unit (GPU).Synthetic images deformed through a suitable displacement field are used to assess the metrological performance of the different versions of the CNN tested in this study. We focus the sub-pixel part of the displacement is considered for this first attempt, this part being much more challenging to determine than integer displacements obtained at the pixel scale. The latter can be found by cross-correlation or with a rough version of DIC. Real images are tested with the simplest version of the CNN and obtained results are compared with those provided by classic subset-based Digital Image Correlation. The two main conclusions are i- that the customization procedure improves the metrological performance of the original version, and that ii- the metrological performance of the ultimate simplified version of the CNN is globally equivalent to the one of the initial version despite the drastic simplification obtained at the end of the procedure. This performance lies between that of DIC used with first- and second-order subset shape functions.

비혼부의 직업 생활 경험에 대한 근거이론 연구

This study explores the working life experiences of unmarried fathers. The researchers adopted Glaser’s grounded theory research method and Clarke’s situational analysis for the study subjects. The purpose of this study was to analyze the social discourses that affects the contents, context, and structure of 14 unmarried fathers’ working life experiences and to examine their situational knowledge. The research results are as follows. First, the core category analyzed based on Glaser’s approach of the grounded theory is “The reward and hope in the labor for survival with the dream postponed. “ It was found that the core category was affected by the conditions of “Becoming a working machine “ and accidental “Burnout labor”. Here, ‘Lack of human capital investment’ and ‘No leisure time’ are the context that influences the cause and outcome, and this study suggests the structure in which the cause－“Delay in self-development”－leads to the outcome of “Labor without content” in the context. Second, based on the result of Clarke’s situational analysis, the study drew a rough version and an organized version a situational map, showing the work and life experiences of unmarried fathers, a relationship map of the unmarried fathers, and a social/world arena map representing work/regional community. Lastly, through a positional map, the level of interaction and discourse of unmarried fathers were analyzed. Based on the results of the study, the researchers provided suggestions at the social welfare level to support the creation of responsible subjects and the lives of unmarried fathers.

SPX Calibration of Option Approximations under Rough Heston Model

The volatility of stock return does not follow the classical Brownian motion, but instead it follows a form that is closely related to fractional Brownian motion. Taking advantage of this information, the rough version of classical Heston model also known as rough Heston model has been derived as the macroscopic level of microscopic Hawkes process where it acts as a high-frequency price process. Unlike the pricing of options under the classical Heston model, it is significantly harder to price options under rough Heston model due to the large computational cost needed. Previously, some studies have proposed a few approximation methods to speed up the option computation. In this study, we calibrate five different approximation methods for pricing options under rough Heston model to SPX options, namely a third-order Padé approximant, three variants of fourth-order Padé approximant, and an approximation formula made from decomposing the option price. The main purpose of this study is to fill in the gap on lack of numerical study on real market options. The numerical experiment includes calibration of the mentioned methods to SPX options before and after the Lehman Brothers collapse.

A rough super-Brownian motion

We study the scaling limit of a branching random walk in static random environment in dimension d=1,2 and show that it is given by a super-Brownian motion in a white noise potential. In dimension 1 we characterize the limit as the unique weak solution to the stochastic PDE ∂tμ=(Δ+ξ)μ+ 2νμξ˜ for independent space white noise ξ and space-time white noise ξ˜. In dimension 2 the study requires paracontrolled theory and the limit process is described via a martingale problem. In both dimensions we prove persistence of this rough version of the super-Brownian motion.

The Signature Kernel Is the Solution of a Goursat PDE

Recently, there has been an increased interest in the development of kernel methods for learning with sequential data. The signature kernel is a learning tool with potential to handle irregularly sampled, multivariate time series. In "Kernels for sequentially ordered data" the authors introduced a kernel trick for the truncated version of this kernel avoiding the exponential complexity that would have been involved in a direct computation. Here we show that for continuously differentiable paths, the signature kernel solves a hyperbolic PDE and recognize the connection with a well known class of differential equations known in the literature as Goursat problems. This Goursat PDE only depends on the increments of the input sequences, does not require the explicit computation of signatures and can be solved efficiently using state-of-the-arthyperbolic PDE numerical solvers, giving a kernel trick for the untruncated signature kernel, with the same raw complexity as the method from "Kernels for sequentially ordered data", but with the advantage that the PDE numerical scheme is well suited for GPU parallelization, which effectively reduces the complexity by a full order of magnitude in the length of the input sequences. In addition, we extend the previous analysis to the space of geometric rough paths and establish, using classical results from rough path theory, that the rough version of the signature kernel solves a rough integral equation analogous to the aforementioned Goursat PDE. Finally, we empirically demonstrate the effectiveness of our PDE kernel as a machine learning tool in various machine learning applications dealing with sequential data. We release the library sigkernel publicly available at https://github.com/crispitagorico/sigkernel.

How do you Develop a Data Standard? Wikibase might be the Solution…

Data standards allow us to aggregate, compare, compute and communicate data from a wide variety of origins. However, for historical reasons, data are most likely to be stored in many different formats and conform to different models. Every data set might contain a huge amount of information, but it becomes tremendously difficult to compare them without a common way to represent the data. That is when standards development jumps in. Developing a standard is a formidable process, often involving many stakeholders. Typically the initial blueprint of a standard is created by a limited number of people who have a clear view of their use cases. However, as development continues, additional stakeholders participate in the process. As a result, conflicting opinions and interests will influence the development of the standard. Compromises need to be made and the standard might look very different from the initial concept. In order to address the needs of the community, a high level of engagement in the development process is encouraged. However, this does not necessarily increase the usability of the standard. To mitigate this, there is a need to test the standard during the early stages of development. In order to facilitate this, we explored the use of Wikibase to create an initial implementation of the standard. Wikibase is the underlying technology that drives Wikidata. The software is open-source and can be customized for creating collaborative knowledge bases. In addition to containing an RDF (Resource Description Framework) triple store under the hood, it provides users with an easy-to-use graphical user interface (see Fig. 1). This facilitates the use of an implementation of a standard by non-technical users. The Wikibase remains fully flexible in the way data are represented and no data model is enforced. This allows users to map their data onto the standard without any restrictions. Retrieving information from RDF data can be done through the SPARQL query language (W3C 2020). The software package has also a built-in SPARQL endpoint, allowing users to extract the relevant information: Does the standard cover all use cases envisioned? Are parts of the standard underdeveloped? Are the controlled vocabularies sufficient to describe the data? Does the standard cover all use cases envisioned? Are parts of the standard underdeveloped? Are the controlled vocabularies sufficient to describe the data? This strategy was applied during the development of the TDWG Collection Description standard. After completing a rough version of the standard, the different terms that were defined in the first version were transferred to a Wikibase instance running on WBStack (Addshore 2020). Initially, collection data were entered manually, which revealed several issues. The Wikibase allowed us to easily define controlled vocabularies and expand them as needed. The feedback reported from users then flowed back to the further development of the standard. Currently we envisage creating automated scripts that will import data en masse from collections. Using the SPARQL query interface, it will then be straightforward to ensure that data can be extracted from the Wikibase to support the envisaged use cases.

Three sphere inequality for second order elliptic equations with coefficients with jump discontinuity

This is a short note to complete the paper appeared in Francini et al. (2016) [4], where a rough version of the classical well known Hadamard three-circle theorem for solution of an elliptic PDE in divergence form has been proved. Precisely, instead of circles, the authors obtain a similar inequality in a more complicated geometry. In this paper we clean the geometry and obtain a generalized version of the three-circle inequality for elliptic equation with coefficients with discontinuity of jump type.

Rough differential equations with power type nonlinearities

In this note we consider differential equations driven by a signal x which is γ-Hölder with γ>13, and is assumed to possess a lift as a rough path. Our main point is to obtain existence of solutions when the coefficients of the equation behave like power functions of the form |ξ|κ with κ∈(0,1). Two different methods are used in order to construct solutions: (i) In a 1-d setting, we resort to a rough version of Lamperti’s transform. (ii) For multidimensional situations, we quantify some improved regularity estimates when the solution approaches the origin.

Schizosaccharomyces japonicus: A Distinct Dimorphic Yeast among the Fission Yeasts.

Genomic sequencing data and morphological properties demonstrate evolutionary relationships among groups of the fission yeast, Schizosaccharomyces Phylogenetically, S. japonicus is the furthest removed from other species of fission yeast. The basic characteristics of cell proliferation are shared among all fission yeast, including the process of binary fission during vegetative growth, conjugation and karyogamy with horsetail movement, mating-type switching, and sporulation. However, S. japonicus also exhibits characteristics that are unique to filamentous fungi. S. japonicus is a nonpathogenic yeast that exhibits dimorphism. Depending on the environmental conditions, S. japonicus transforms from yeast cells into filamentous cells (hyphae), and blue light triggers synchronous septation of hyphal cells. A rough version of the whole-genome sequence is now available, facilitating genetic manipulation of S. japonicus. Furthermore, the extensive genetic knowledge available for S. pombe is aiding the development of genetic tools for analyzing S. japonicus. S. japonicus will help shed light on the evolutionary relationships among the fission yeast.

Preface

This special issue is devoted to some aspects of the new ideas that recently arose from the work of Thomas Ehrhard on the models of linear logic (LL) and of the λ-calculus. In some sense, the very origin of these ideas dates back to the introduction of LL in the 80s by Jean-Yves Girard. An obvious remark is that LL yielded a first logical quantitative account of the use of resources: the logical distinction between linear and non-linear formulas through the introduction of the exponential connectives. As explicitly mentioned by Girard in his first paper on the subject, the quantitative approach, to which he refers as ‘quantitative semantics,’ had a crucial influence on the birth of LL. And even though, at that time, it was given up for lack of ‘any logical justification’ (quoting the author), it contained rough versions of many concepts that were better understood, precisely introduced and developed much later, like differentiation and Taylor expansion for proofs. Around 2003, and thanks to the developments of LL and of the whole research area between logic and theoretical computer science, Ehrhard could come back to these fundamental intuitions and introduce the structure of finiteness space, allowing to reformulate this quantitative approach in a standard algebraic setting. The interpretation of LL in the category Fin of finiteness spaces and finitary relations suggested to Ehrhard and Regnier the differential extensions of LL and of the simply typed λ-calculus: Differential Linear Logic (DiLL) and the differential λ-calculus. The theory of LL proof-nets could be straightforwardly extended to DiLL, and a very natural notion of Taylor expansion of a proof-net (and of a λ-term) was introduced: an element of the Taylor expansion of the proof-net/term α is itself a (differential) proof-net/term and an approximation of α.

Pictish symbol stones and early cross-slabs from Orkney

Orkney shared in the flowering of interest in stone carving that took place throughout Scotland from the 7th century ad onwards. The corpus illustrated here includes seven accomplished Pictish symbol-bearing stones, four small stones incised with rough versions of symbols, at least one relief-ornamented Pictish cross-slab, thirteen cross-slabs (including recumbent slabs), two portable cross-slabs and two pieces of church furniture in the form of an altar frontal and a portable altar slab. The art-historical context for this stone carving shows close links both with Shetland to the north and Caithness to the south, as well as more distant links with Iona and with the Pictish mainland south of the Moray Firth. The context and function of the stones are discussed and a case is made for the existence of an early monastery on the island of Flotta.

On the relational complexity of a finite permutation group

The relational complexity $$\rho (X,G)$$?(X,G) of a finite permutation group is the least k for which the group can be viewed as an automorphism group acting naturally on a homogeneous relational system whose relations are k-ary (an explicit permutation group theoretic version of this definition is also given). In the context of primitive permutation groups, the natural questions are (a) rough estimates, or (preferably) precise values for $$\rho $$? in natural cases; and (b) a rough determination of the primitive permutation groups with $$\rho $$? either very small (bounded) or very large (much larger than the logarithm of the degree). The rough version of (a) is relevant to (b). Our main result is an explicit characterization of the binary ($$\rho =2$$?=2) primitive affine permutation groups. We also compute the precise relational complexity of $${{\mathrm{Alt}}}_n$$Altn acting on k-sets, correcting (Cherlin in Sporadic homogeneous structures. In: The Gelfand Mathematical Seminars, 1996---1999, pp. 15---48, Birkhauser 2000, Example 5).

The heritability of cancer.

The heritability of cancer.

Rough ISODATA Algorithm

Cluster analysis is a branch of data mining, which plays a vital role in bringing out hidden information in databases. Clustering algorithms help medical researchers in identifying the presence of natural subgroups in a data set. Different types of clustering algorithms are available in the literature. The most popular among them is k-means clustering. Even though k-means clustering is a popular clustering method widely used, its application requires the knowledge of the number of clusters present in the given data set. Several solutions are available in literature to overcome this limitation. The k-means clustering method creates a disjoint and exhaustive partition of the data set. However, in some situations one can come across objects that belong to more than one cluster. In this paper, a clustering algorithm capable of producing rough clusters automatically without requiring the user to give as input the number of clusters to be produced. The efficiency of the algorithm in detecting the number of clusters present in the data set has been studied with the help of some real life data sets. Further, a nonparametric statistical analysis on the results of the experimental study has been carried out in order to analyze the efficiency of the proposed algorithm in automatic detection of the number of clusters in the data set with the help of rough version of Davies-Bouldin index.

The Return of John Moffat

The Return of John Moffat

Collapsing manifolds with boundary

This paper studies manifolds-with-boundary collapsing in the Gromov– Hausdorff topology. The main aim is an understanding of the relationship of the topology and geometry of a limiting sequence of manifolds-with-boundary to that of a limit space, which is presumed to be without geodesic terminals. The first group of results provide a fiber bundle structure to the manifolds-with-boundary. One of the main theorems establishes a disc bundle structure for any manifold-with-boundary having two-sided bounds on sectional curvature and second fundamental form, and a lower bound on intrinsic injectivity radius, which is sufficiently close in the Gromov–Hausdorff topology to a closed manifold. Another result is a rough version of Toponogov’s Splitting Theorem. The second group of results identify Gromov–Hausdorff limits of certain sequences of manifolds with non-convex boundaries as Alexandrov spaces of curvature bounded below.

Similarity retrieval of shape images based on database classification

Shape is a key visual feature used to describe image content. This paper develops a novel shape-based similarity retrieval system based on database classification which exploits the contour and interior region of a shape efficiently. In this system, the database of shape images is categorized automatically into 11 classes by a simple contour feature. In query, the contour feature of the input image is used to decide which class the query image belongs to. Then, the possible classes are selected dynamically from the database and to form candidate sets with different priority orders. Then, ART region feature is employed to compare the query with the candidate sets according to the priority order. Instead of using the original contour of a shape image directly, we employ a rough version of the original contour for the classification of shapes. The similarity test results indicate that the proposed method improves retrieval accuracy and speed significantly, as compared to ART.

Central Bank Structure, Policy Efficiency, and Macroeconomic Performance: Exploring Empirical Relationships

A ll economists agree that more information is better than less. When people are better informed, they make better decisions, enhancing the efficiency of the economy in allocating resources and improving overall welfare. It would be difficult to find an area of economic life where this line of argument has carried more weight than it has in central banking circles in recent years. The job of central bankers is to conduct monetary policy in order to promote price stability, sustainable growth, and a stable financial system. They do this in an environment fraught with unavoidable uncertainties. But in conducting policy, there is one uncertainty that policymakers can reduce: the uncertainty they themselves create. Everyone agrees that monetary policymakers should do their best to minimize the noise their actions add to the environment. The essence of good, transparent policy is that the economy and the markets respond to the data, not to the policymakers. The result of this agreement is that today we have the nearly universal and immediate public broadcast of all interest rate changes. As everyone in financial markets around the world knows, the Federal Reserve’s Federal Open Market Committee (FOMC) makes a public statement at 2:15 p.m. EST following each meeting. But the first public announcement of a move in the federal funds rate target was made on February 4, 1994, and the regular issuance of a statement became an official feature of the FOMC’s procedures only on January 19, 2000. Before that, it was customary for FOMC policy changes to be communicated to market participants through actions rather than words. There are still people who argue for the efficacy of central bank secrecy in various forms, claiming that surprises are more effective and that even accurate information can be misinterpreted, resulting in undesirable financial market volatility. We think that it is fair to say that these arguments have not been persuasive and that the advocates of policy transparency have won the day. We have been reduced to arguments about the mechanics and exact timing of the release of information. Should the minutes of a meeting be released as soon as physically possible following the meeting, as done by the Bank of England’s Monetary Policy Committee; or should there be a modest delay until just after the following meeting, which is the FOMC’s practice; or is it acceptable to wait for years, as the European Central Bank is planning to do? Is it necessary or advisable for the head of the interest rate–setting body to hold regularly scheduled news conferences? Should the policymakers be required to appear before legislative bodies to provide descriptions of their decisionmaking processes and justifications for their actions? How public should the inputs— forecasts, models, and anecdotes—into interest rate decisions be? All of these questions concern minor issues about the availability of information. As for general principles, we have now progressed to the point where on September 26, 1999, the Interim Committee of the Board of Governors of the International Monetary Fund issued the Code of Good Practices on Transparency in Monetary and Financial Policies: Declaration and Principles (which we will refer to as the IMF Code). As in the case of other standards and codes promulgated under the auspices of the IMF,1 the expectation is that they will be adhered to by all of the countries in the world. We take the statements in the IMF Code to represent a rough version of the consensus on the value of monetary policy transparency. Paragraph 4 of the IMF Code states: