Machine Learning-Based Feasibility Checks for Dynamic Time Slot Management

Online grocers typically let customers choose a delivery time slot to receive their goods. To ensure a reliable service, the retailer may want to close time slots as capacity fills up. The number of customers that can be served per slot largely depends on the specific order sizes and delivery locations. Conceptually, checking whether it is possible to serve a certain customer in a certain time slot given a set of already accepted customer orders involves solving a vehicle routing problem with time windows. This is challenging in practice as there is little time available and not all relevant information is known in advance. We explore the use of machine learning to support time slot decisions in this context. Our results on realistic instances using a commercial route solver suggest that machine learning can be a promising way to assess the feasibility of customer insertions. On large-scale routing problems it performs better than insertion heuristic

On the linear forms of the Schrodinger equation

Generalizing the linearisation procedure used by Dirac and later by L\'evy-Leblond, we derive the first-order non-relativistic wave equations for particles of spin 1 and spin 3/2 starting from the Schrodinger equation

Scaling anomaly in cosmic string background

We show that the classical scale symmetry of a particle moving in cosmic string background is broken upon inequivalent quantization of the classical system, leading to anomaly. The consequence of this anomaly is the formation of single bound state in the coupling interval \gamma\in(-1,1). The inequivalent quantization is characterized by a 1-parameter family of self-adjoint extension parameter \omega. It has been conjectured that the formation of loosely bound state in cosmic string background may lead to the so called anomalous scattering cross section for the particles, which is usually seen in molecular physics.Comment: 4 pages,1 figur

The nuclear energy density functional formalism

The present document focuses on the theoretical foundations of the nuclear energy density functional (EDF) method. As such, it does not aim at reviewing the status of the field, at covering all possible ramifications of the approach or at presenting recent achievements and applications. The objective is to provide a modern account of the nuclear EDF formalism that is at variance with traditional presentations that rely, at one point or another, on a {\it Hamiltonian-based} picture. The latter is not general enough to encompass what the nuclear EDF method represents as of today. Specifically, the traditional Hamiltonian-based picture does not allow one to grasp the difficulties associated with the fact that currently available parametrizations of the energy kernel $E[g',g]$ at play in the method do not derive from a genuine Hamilton operator, would the latter be effective. The method is formulated from the outset through the most general multi-reference, i.e. beyond mean-field, implementation such that the single-reference, i.e. "mean-field", derives as a particular case. As such, a key point of the presentation provided here is to demonstrate that the multi-reference EDF method can indeed be formulated in a {\it mathematically} meaningful fashion even if $E[g',g]$ does {\it not} derive from a genuine Hamilton operator. In particular, the restoration of symmetries can be entirely formulated without making {\it any} reference to a projected state, i.e. within a genuine EDF framework. However, and as is illustrated in the present document, a mathematically meaningful formulation does not guarantee that the formalism is sound from a {\it physical} standpoint. The price at which the latter can be enforced as well in the future is eventually alluded to.Comment: 64 pages, 8 figures, submitted to Euroschool Lecture Notes in Physics Vol.IV, Christoph Scheidenberger and Marek Pfutzner editor

Hamilton's Formalism for Systems with Constraints

The main goal of these lectures is to introduce and review the Hamiltonian formalism for classical constrained systems and in particular gauge theories. Emphasis is put on the relation between local symmetries and constraints and on the relation between Lagrangean and Hamiltonian symmetries.Comment: 52 pages, revised LATEX version, ETH-TH/93-48, Lectures given at the Seminar "The Canonical Formalism in Classical and Quantum General Relativity", Bad Honnef, September 9

In-plane Hall effect in c-axis-oriented MgB2 thin films

We have measured the longitudinal resistivity and the Hall resistivity in the ab-plane of highly c-axis-oriented MgB2 thin films. In the normal state, the Hall coefficient (R_H) behaves as R_H ~ T with increasing temperature (T) up to 130 K and then deviates from that linear T-dependence at higher temperatures. The T^2 dependence of the cotangent of the Hall angle is only observed above 130 K. The mixed-state Hall effect reveals no sign anomaly over a wide range of current densities from 10^2 to 10^4 A/cm^2 and for magnetic fields up to 5 T.Comment: 5 pages including 5 figure

SciPy 1.0: fundamental algorithms for scientific computing in Python.

SciPy is an open-source scientific computing library for the Python programming language. Since its initial release in 2001, SciPy has become a de facto standard for leveraging scientific algorithms in Python, with over 600 unique code contributors, thousands of dependent packages, over 100,000 dependent repositories and millions of downloads per year. In this work, we provide an overview of the capabilities and development practices of SciPy 1.0 and highlight some recent technical developments