1,289 research outputs found
Opening the system to the environment: new theories and tools in classical and quantum settings
The thesis is organized as follows. Section 2 is a first, unconventional, approach to the topic of EPs. Having grown interest in the topic of combinatorics and graph theory, I wanted to exploit its very abstract and mathematical tools to reinterpret something very physical, that is, the EPs in wave scattering. To do this, I build the interpretation of scattering events from a graph theory perspective and show how EPs can be understood within this interpretation. In Section 3, I move from a completely classical treatment to a purely quantum one. In this section, I consider two quantum resonators coupled to two baths and study their dynamics with local and global master equations. Here, the EPs are the key physical features used as a witness of validity of the master equation. Choosing the wrong master equation in the regime of interest can indeed mask physical and fundamental features of the system. In Section 4, there are no EPs. However I transition towards a classical/quantum framework via the topic of open systems. My main contribution in this work is the classical stochastic treatment and simulation of a spin coupled to a bath. In this work, I show how a natural quantum--to--classical transition occurs at all coupling strengths when certain limits of spin length are taken. As a key result, I also show how the coupling to the environment in this stochastic framework induces a classical counterpart to quantum coherences in equilibrium. After this last topic, in Section 5, I briefly present the key features of the code I built (and later extended) for the latter project. This, in the form of a Julia registry package named SpiDy.jl, has seen further applications in branching projects and allows for further exploration of the theoretical framework. Finally, I conclude with a discussion section (see Sec. 5) where I recap the different conclusions gathered in the previous sections and propose several possible directions.Engineering and Physical Sciences Research Council (EPSRC
The Local Structure of Injective LOT-Complexes
Labeled oriented trees, LOT's, encode spines of ribbon discs in the 4-ball
and ribbon 2-knots in the 4-sphere. The unresolved asphericity question for
these spines is a major test case for Whitehead's asphericity conjecture. In
this paper we give a complete description of the link of a reduced injective
LOT complex. An important case is the following: If is a reduced
injective LOT that does not contain boundary reduced sub-LOTs, then
is a bi-forest. As a consequence is aspherical, in
fact DR, and its fundamental group is locally indicable. We also show that a
general injective LOT complex is aspherical. Some of our results have already
appeared in print over the last two decades and are collected here
Engineering a Preprocessor for Symmetry Detection
State-of-the-art solvers for symmetry detection in combinatorial objects are becoming increasingly sophisticated software libraries. Most of the solvers were initially designed with inputs from combinatorics in mind (nauty, bliss, Traces, dejavu). They excel at dealing with a complicated core of the input. Others focus on practical instances that exhibit sparsity. They excel at dealing with comparatively easy but extremely large substructures of the input (saucy). In practice, these differences manifest in significantly diverging performances on different types of graph classes.
We engineer a preprocessor for symmetry detection. The result is a tool designed to shrink sparse, large substructures of the input graph. On most of the practical instances, the preprocessor improves the overall running time significantly for many of the state-of-the-art solvers. At the same time, our benchmarks show that the additional overhead is negligible.
Overall we obtain single algorithms with competitive performance across all benchmark graphs. As such, the preprocessor bridges the disparity between solvers that focus on combinatorial graphs and large practical graphs. In fact, on most of the practical instances the combined setup significantly outperforms previous state-of-the-art
On cocliques in commutative Schurian association schemes of the symmetric group
Given the symmetric group and a multiplicity-free
subgroup , the orbitals of the action of on by left
multiplication induce a commutative association scheme. The irreducible
constituents of the permutation character of acting on are indexed by
partitions of and if is the second largest partition in
dominance ordering among these, then the Young subgroup
admits two orbits in its action on , which
are and its complement.
In their monograph [Erd\H{o}s-Ko-Rado theorems: Algebraic Approaches. {\it
Cambridge University Press}, 2016] (Problem~16.13.1), Godsil and Meagher asked
whether is a coclique of a graph in the commutative
association scheme arising from the action of on . If such a graph
exists, then they also asked whether its smallest eigenvalue is afforded by the
-module.
In this paper, we initiate the study of this question by taking .
We show that the answer to this question is affirmative for the pair of
groups , where and , or and is one of , or . For the pair , we also prove that the answer to this question
of Godsil and Meagher is negative
On a Vehicle Routing Problem with Customer Costs and Multi Depots
The Vehicle Routing Problem with Customer Costs (short VRPCC) was developed for railway maintenance scheduling. In detail, corrective maintenance jobs for unexpected occurring failures are planned to a short time horizon. These jobs are geographically distributed in the railway net. Furthermore, dependent on the severity of the failure, it can be necessary to reduce the top speed on the track section in order to avoid safety risks or a too fast deterioration. For fatal failures, it can even be necessary to close the track section. The resulting limitations on railway service lead to penalty costs for the maintenance operator. These must be paid until the track is repaired and the restrictions are removed. By scheduling the maintenance tasks, these penalty costs can be reduced by proceeding corresponding maintenance tasks earlier. However, this may in return lead to increased costs for moving the maintenance machines and crews.
For this scheduling problem, the VRPCC was developed. With it, for each maintenance vehicle and crew, a route is defined that describes the order to proceed maintenance tasks. Two kinds of costs are considered: Firstly, travel costs for machinery and crew; and secondly, penalty costs for an unsafe track condition that have to be paid for each day from failure detection to maintenance completion. To model the penalties, the novel customer costs are defined. In detail, for each maintenance activity a customer cost coefficient is given which incur for each day between failure detection and failure repair. The objective function of this problem is defined by the sum of travel costs and time-dependent customer costs. With it, the priority of customers can be taken into account without losing the sight on travel costs.
This new vehicle routing problem was introduced in this thesis by a non-linear partition and permutation model. In this model, a feasible solution is defined by a partition of the job set into subsets that represent the allocation of jobs to vehicles and a permutation for each subset that represent the order of processing the jobs. Then, the start times of the jobs were calculated based on the order given by the permutations. It was taken into account that work can only be done in eight hour shifts during the night. Based on the start times, the customer cost value of each job is computed which equals to the paid penalty costs. Then, the costs of a schedule are calculated via the sum of travel costs and customer costs.
To solve the VRPCC by a commercial linear programming solver, different formulations of the VRPCC as mixed-integer linear program were developed. In doing so, the start times became decision variables. It turned out that including customer costs led to problems harder to solve than vehicle routing problems where only travel costs are minimized.
Further, in the thesis several construction heuristics for the VRPCC were designed and investigated. Also two local search algorithms, first and best improvement, were applied. The computational experiments showed that the solutions generated by the local search algorithm were much better than the solutions of the construction heuristics.
The main part of this thesis was to design a Branch-and-Bound algorithm for the VRPCC. For this purpose, new lower bounds for the customer cost part of the objective function were formulated. The computational experiments showed that a lower bound computed from the LP relaxation of a specific bin packing problem had the best trade-off between computational effort and bound quality. For the travel cost part of the objective function, several known lower bounds from the TSP were compared.
To design a Branch-and-Bound algorithm, beside efficient lower bound, also suitable branching strategies are necessary to split the problem space into smaller subspaces. In this thesis two branching strategies were developed which are based on the non-linear partition and permutation model to take advantage from the problem structure. To be more precise, new branches are generated by appending or including a job to an uncompleted schedule. Consequently, the start times can be computed directly from the so far planned jobs and more tight lower bounds can be computed for the so far unplanned jobs.
By means of computational experiments, the developed Branch-and-Bound algorithms were compared with the classical approach, which means solving a mixed-integer linear program of the VRPCC by a commercial solver. The results showed that both Branch-and-Bound algorithms solved the small instances faster than the classical approach
Algorithms Transcending the SAT-Symmetry Interface
Dedicated treatment of symmetries in satisfiability problems (SAT) is
indispensable for solving various classes of instances arising in practice.
However, the exploitation of symmetries usually takes a black box approach.
Typically, off-the-shelf external, general-purpose symmetry detection tools are
invoked to compute symmetry groups of a formula. The groups thus generated are
a set of permutations passed to a separate tool to perform further analyzes to
understand the structure of the groups. The result of this second computation
is in turn used for tasks such as static symmetry breaking or dynamic pruning
of the search space. Within this pipeline of tools, the detection and analysis
of symmetries typically incurs the majority of the time overhead for symmetry
exploitation.
In this paper we advocate for a more holistic view of what we call the
SAT-symmetry interface. We formulate a computational setting, centered around a
new concept of joint graph/group pairs, to analyze and improve the detection
and analysis of symmetries. Using our methods, no information is lost
performing computational tasks lying on the SAT-symmetry interface. Having
access to the entire input allows for simpler, yet efficient algorithms.
Specifically, we devise algorithms and heuristics for computing finest direct
disjoint decompositions, finding equivalent orbits, and finding natural
symmetric group actions. Our algorithms run in what we call
instance-quasi-linear time, i.e., almost linear time in terms of the input size
of the original formula and the description length of the symmetry group
returned by symmetry detection tools. Our algorithms improve over both
heuristics used in state-of-the-art symmetry exploitation tools, as well as
theoretical general-purpose algorithms
Estimates of the reproduction ratio from epidemic surveillance may be biased in spatially structured populations
An accurate and timely estimate of the reproduction ratio R of an infectious
disease epidemic is crucial to make projections on its evolution and set up the
appropriate public health response. Estimates of R routinely come from
statistical inference on timelines of cases or their proxies like symptomatic
cases, hospitalizatons, deaths. Here, however, we prove that these estimates of
R may not be accurate if the population is made up of spatially distinct
communities, as the interplay between space and mobility may hide the true
epidemic evolution from surveillance data. This means that surveillance may
underestimate R over long periods, to the point of mistaking a growing epidemic
for a subsiding one, misinforming public health response. To overcome this, we
propose a correction to be applied to surveillance data that removes this bias
and ensures an accurate estimate of R across all epidemic phases. We use
COVID-19 as case study; our results, however, apply to any epidemic where
mobility is a driver of circulation, including major challenges of the next
decades: respiratory infections (influenza, SARS-CoV-2, emerging pathogens),
vector-borne diseases (arboviruses). Our findings will help set up public
health response to these threats, by improving epidemic monitoring and
surveillance.Comment: 11 pages, 4 figures, plus Supplementary Informatio
One Drop of Non-Determinism in a Random Deterministic Automaton
Every language recognized by a non-deterministic finite automaton can be recognized by a deterministic automaton, at the cost of a potential increase of the number of states, which in the worst case can go from n states to 2? states. In this article, we investigate this classical result in a probabilistic setting where we take a deterministic automaton with n states uniformly at random and add just one random transition. These automata are almost deterministic in the sense that only one state has a non-deterministic choice when reading an input letter. In our model each state has a fixed probability to be final. We prove that for any d ? 1, with non-negligible probability the minimal (deterministic) automaton of the language recognized by such an automaton has more than n^d states; as a byproduct, the expected size of its minimal automaton grows faster than any polynomial. Our result also holds when each state is final with some probability that depends on n, as long as it is not too close to 0 and 1, at distance at least ?(1/?n) to be precise, therefore allowing models with a sublinear number of final states in expectation
Design of an E-learning system using semantic information and cloud computing technologies
Humanity is currently suffering from many difficult problems that threaten the life and survival of the human race. It is very easy for all mankind to be affected, directly or indirectly, by these problems. Education is a key solution for most of them. In our thesis we tried to make use of current technologies to enhance and ease the learning process.
We have designed an e-learning system based on semantic information and cloud computing, in addition to many other technologies that contribute to improving the educational process and raising the level of students. The design was built after much research on useful technology, its types, and examples of actual systems that were previously discussed by other researchers.
In addition to the proposed design, an algorithm was implemented to identify topics found in large textual educational resources. It was tested and proved to be efficient against other methods. The algorithm has the ability of extracting the main topics from textual learning resources, linking related resources and generating interactive dynamic knowledge graphs. This algorithm accurately and efficiently accomplishes those tasks even for bigger books. We used Wikipedia Miner, TextRank, and Gensim within our algorithm. Our algorithmâs accuracy was evaluated against Gensim, largely improving its accuracy.
Augmenting the system design with the implemented algorithm will produce many useful services for improving the learning process such as: identifying main topics of big textual learning resources automatically and connecting them to other well defined concepts from Wikipedia, enriching current learning resources with semantic information from external sources, providing student with browsable dynamic interactive knowledge graphs, and making use of learning groups to encourage students to share their learning experiences and feedback with other learners.Programa de Doctorado en IngenierĂa TelemĂĄtica por la Universidad Carlos III de MadridPresidente: Luis SĂĄnchez FernĂĄndez.- Secretario: Luis de la Fuente ValentĂn.- Vocal: Norberto FernĂĄndez GarcĂ
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