Comparison between Tensor Networks and Variational Quantum Classifier

The primary objective of this paper is to conduct a comparative analysis between two Machine Learning approaches: Tensor Networks (TN) and Variational Quantum Classifiers (VQC). While both approaches share similarities in their representation of the Hilbert space using a logarithmic number of parameters, they diverge in the manifolds they cover. Thus, the aim is to evaluate and compare the expressibility and trainability of these approaches. By conducting this comparison, we can gain insights into potential areas where quantum advantage may be found. Our findings indicate that VQC exhibits advantages in terms of speed and accuracy when dealing with data, characterized by a small number of features. However, for high-dimensional data, TN surpasses VQC in overall classification accuracy. We believe that this disparity is primarily attributed to challenges encountered during the training of quantum circuits. We want to stress that in this article, we focus on only one particular task and do not conduct thorough averaging of the results. Consequently, we recommend considering the results of this article as a unique case without excessive generalization

Vector bundles on the projective line and finite domination of chain complexes

Finitely dominated chain complexes over a Laurent polynomial ring in one indeterminate are characterised by vanishing of their Novikov homology. We present an algebro-geometric approach to this result, based on extension of chain complexes to sheaves on the projective line. We also discuss the K-theoretical obstruction to extension.Comment: v1: 11 page

An evaluation of NEXRAD precipitation estimates in complex terrain

This is the published version. Copyright 1999 American Geophysical UnionNext Generation Weather Radar (NEXRAD) precipitation estimates are used for hydrological, meteorological, and climatological studies at a wide range of spatial and temporal scales. The utility of radar-based precipitation estimates in such applications hinges on an understanding of the sources and magnitude of estimation error. This study examines precipitation estimation in the complex mountainous terrain of the northern Appalachian Mountains. Hourly digital precipitation (HDP) products for two WSR-88D radars in New York state are evaluated for a 2-year period. This analysis includes evaluation of range dependence and spatial distribution of estimates, radar intercomparisons for the overlap region, and radar-gage comparisons. The results indicate that there are unique challenges for radar-rainfall estimation in mountainous terrain. Beam blockage is a serious problem that is not corrected by existing NEXRAD algorithms. Underestimation and nondetection of precipitation are also significant concerns. Improved algorithms are needed for merging estimates from multiple radars with spatially variable biases

Mutator Dynamics on a Smooth Evolutionary Landscape

We investigate a model of evolutionary dynamics on a smooth landscape which features a ``mutator'' allele whose effect is to increase the mutation rate. We show that the expected proportion of mutators far from equilibrium, when the fitness is steadily increasing in time, is governed solely by the transition rates into and out of the mutator state. This results is a much faster rate of fitness increase than would be the case without the mutator allele. Near the fitness equilibrium, however, the mutators are severely suppressed, due to the detrimental effects of a large mutation rate near the fitness maximum. We discuss the results of a recent experiment on natural selection of E. coli in the light of our model.Comment: 4 pages, 3 figure

Critical Innovations in the UK Peer-to-Peer (P2P) and Equity Alternative Finance Markets for Small Firm Growth

© The Author(s) 2016. The final, definitive version of this paper has been published in The International Journal of Entrepreneurship and Innovation by Sage Publications Ltd. All rights reserved. It is available at: https://doi.org/10.1177/1465750316655906This paper examines the disruptive nature of financial innovations available to small firms by the growing range of online platforms that have emerged in the UK since the financial crisis. It is unveiled that finance provided to small firms via such mechanisms is not identical to more traditional sources and its adoption therefore cannot be said to be simply a question of direct substitution based, for example, on a price comparison. These offer a series of important advantages over more traditional sources of early-stage capital for entrepreneurs seeking funding. Service innovations around security, flexibility of terms, speed of access and transparency of pricing are as important as price considerations for many users, as are innovations made possible by the way these online markets are structured and in particular in the way these innovative structures allow important types of risk to be dispersed and mitigated.Peer reviewedFinal Accepted Versio

Influence of Hybridization on the Properties of the Spinless Falicov-Kimball Model

Without a hybridization between the localized f- and the conduction (c-) electron states the spinless Falicov-Kimball model (FKM) is exactly solvable in the limit of high spatial dimension, as first shown by Brandt and Mielsch. Here I show that at least for sufficiently small c-f-interaction this exact inhomogeneous ground state is also obtained in Hartree-Fock approximation. With hybridization the model is no longer exactly solvable, but the approximation yields that the inhomogeneous charge-density wave (CDW) ground state remains stable also for finite hybridization V smaller than a critical hybridization V_c, above which no inhomogeneous CDW solution but only a homogeneous solution is obtained. The spinless FKM does not allow for a ''ferroelectric'' ground state with a spontaneous polarization, i.e. there is no nonvanishing $$-expectation value in the limit of vanishing hybridization.Comment: 7 pages, 6 figure

Towards better utilization of NEXRAD data in hydrology: An overview of hydro-NEXRAD

With a very modest investment in computer hardware and the open-source local data manger (LDM) software from UCAR\u27s Unidata Program Center, an individual researcher can receive a variety of NEXRAD Level III gridded rainfall products, and the unprocessed Level II data in real-time from most NEXRAD radars. Additionally, the National Climatic Data Center has vast archives of these products and Level II data. Still, significant obstacles remain in order to unlock the full potential of the data. One set of obstacles is related to effective management of multi-terabyte data sets: storing, compressing, and backing up. A second set of obstacles, for hydrologists and hydrometeorologists in particular, is that the NEXRAD Level III products are not well suited for application in hydrology. There is a strong need for the generation of high-quality products directly from the Level II data with well-documented steps that include quality control, removal of false echoes, rainfall estimation algorithms with variety of corrections, coordinate conversion and georeferencing, conversion to a convenient data format(s), and integration with GIS. For hydrologists it is imperative that these procedures are basin-centered as opposed to radar-centered. Thirdly, the amount of data present in a multi-year, multi-radar dataset is such that simple cataloging and indexing of the data is not sufficient. Rather, sophisticated metadata extraction and management techniques are required. The authors describe and discuss the Hydro-NEXRAD software system that addresses the above three challenges. With support from the National Science Foundation through its ITR program, the authors are developing a basin-centered framework for addressing all these issues in a comprehensive manner, tailored specifically for use of NEXRAD data in hydrology and hydrometeorology. Through a flexible web interface users can search a large metadata database base, managed by a relational database, for subsets of interest. Well-chosen and documented defaults are provided for the flow from unprocessed NEXRAD data to basin-centered rainfall estimates at a desired space-time resolution. In addition to the web interface, there are web services that provide access to scripts and compiled programs. © 2007 ASCE

EGIA–evolutionary optimisation of gene regulatory networks, an integrative approach

Quantitative modelling of gene regulatory networks (GRNs) is still limited by data issues such as noise and the restricted length of available time series, creating an under-determination problem. However, large amounts of other types of biological data and knowledge are available, such as knockout experiments, annotations and so on, and it has been postulated that integration of these can improve model quality. However, integration has not been fully explored, to date. Here, we present a novel integrative framework for different types of data that aims to enhance model inference. This is based on evolutionary computation and uses different types of knowledge to introduce a novel customised initialisation and mutation operator and complex evaluation criteria, used to distinguish between candidate models. Specifically, the algorithm uses information from (i) knockout experiments, (ii) annotations of transcription factors, (iii) binding site motifs (expressed as position weight matrices) and (iv) DNA sequence of gene promoters, to drive the algorithm towards more plausible network structures. Further, the evaluation basis is also extended to include structure information included in these additional data. This framework is applied to both synthetic and real gene expression data. Models obtained by data integration display both quantitative and qualitative improvement

Pedestrian, Crowd, and Evacuation Dynamics

This contribution describes efforts to model the behavior of individual pedestrians and their interactions in crowds, which generate certain kinds of self-organized patterns of motion. Moreover, this article focusses on the dynamics of crowds in panic or evacuation situations, methods to optimize building designs for egress, and factors potentially causing the breakdown of orderly motion.Comment: This is a review paper. For related work see http://www.soms.ethz.c

Technical Design Report for the PANDA Solenoid and Dipole Spectrometer Magnets

This document is the Technical Design Report covering the two large spectrometer magnets of the PANDA detector set-up. It shows the conceptual design of the magnets and their anticipated performance. It precedes the tender and procurement of the magnets and, hence, is subject to possible modifications arising during this process.Comment: 10 pages, 14MB, accepted by FAIR STI in May 2009, editors: Inti Lehmann (chair), Andrea Bersani, Yuri Lobanov, Jost Luehning, Jerzy Smyrski, Technical Coordiantor: Lars Schmitt, Bernd Lewandowski (deputy), Spokespersons: Ulrich Wiedner, Paola Gianotti (deputy