17,257 research outputs found

    Self-Supervised Learning to Prove Equivalence Between Straight-Line Programs via Rewrite Rules

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    We target the problem of automatically synthesizing proofs of semantic equivalence between two programs made of sequences of statements. We represent programs using abstract syntax trees (AST), where a given set of semantics-preserving rewrite rules can be applied on a specific AST pattern to generate a transformed and semantically equivalent program. In our system, two programs are equivalent if there exists a sequence of application of these rewrite rules that leads to rewriting one program into the other. We propose a neural network architecture based on a transformer model to generate proofs of equivalence between program pairs. The system outputs a sequence of rewrites, and the validity of the sequence is simply checked by verifying it can be applied. If no valid sequence is produced by the neural network, the system reports the programs as non-equivalent, ensuring by design no programs may be incorrectly reported as equivalent. Our system is fully implemented for a given grammar which can represent straight-line programs with function calls and multiple types. To efficiently train the system to generate such sequences, we develop an original incremental training technique, named self-supervised sample selection. We extensively study the effectiveness of this novel training approach on proofs of increasing complexity and length. Our system, S4Eq, achieves 97% proof success on a curated dataset of 10,000 pairs of equivalent programsComment: 30 pages including appendi

    Countermeasures for the majority attack in blockchain distributed systems

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    La tecnología Blockchain es considerada como uno de los paradigmas informáticos más importantes posterior al Internet; en función a sus características únicas que la hacen ideal para registrar, verificar y administrar información de diferentes transacciones. A pesar de esto, Blockchain se enfrenta a diferentes problemas de seguridad, siendo el ataque del 51% o ataque mayoritario uno de los más importantes. Este consiste en que uno o más mineros tomen el control de al menos el 51% del Hash extraído o del cómputo en una red; de modo que un minero puede manipular y modificar arbitrariamente la información registrada en esta tecnología. Este trabajo se enfocó en diseñar e implementar estrategias de detección y mitigación de ataques mayoritarios (51% de ataque) en un sistema distribuido Blockchain, a partir de la caracterización del comportamiento de los mineros. Para lograr esto, se analizó y evaluó el Hash Rate / Share de los mineros de Bitcoin y Crypto Ethereum, seguido del diseño e implementación de un protocolo de consenso para controlar el poder de cómputo de los mineros. Posteriormente, se realizó la exploración y evaluación de modelos de Machine Learning para detectar software malicioso de tipo Cryptojacking.DoctoradoDoctor en Ingeniería de Sistemas y Computació

    Fair Assortment Planning

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    Many online platforms, ranging from online retail stores to social media platforms, employ algorithms to optimize their offered assortment of items (e.g., products and contents). These algorithms tend to prioritize the platforms' short-term goals by solely featuring items with the highest popularity or revenue. However, this practice can then lead to undesirable outcomes for the rest of the items, making them leave the platform, and in turn hurting the platform's long-term goals. Motivated by that, we introduce and study a fair assortment planning problem, which requires any two items with similar quality/merits to be offered similar outcomes. We show that the problem can be formulated as a linear program (LP), called (FAIR), that optimizes over the distribution of all feasible assortments. To find a near-optimal solution to (FAIR), we propose a framework based on the Ellipsoid method, which requires a polynomial-time separation oracle to the dual of the LP. We show that finding an optimal separation oracle to the dual problem is an NP-complete problem, and hence we propose a series of approximate separation oracles, which then result in a 1/21/2-approx. algorithm and a PTAS for the original Problem (FAIR). The approximate separation oracles are designed by (i) showing the separation oracle to the dual of the LP is equivalent to solving an infinite series of parameterized knapsack problems, and (ii) taking advantage of the structure of the parameterized knapsack problems. Finally, we conduct a case study using the MovieLens dataset, which demonstrates the efficacy of our algorithms and further sheds light on the price of fairness.Comment: 86 pages, 7 figure

    Constrained Assortment Optimization under the Cross-Nested Logit Model

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    We study the assortment optimization problem under general linear constraints, where the customer choice behavior is captured by the Cross-Nested Logit model. In this problem, there is a set of products organized into multiple subsets (or nests), where each product can belong to more than one nest. The aim is to find an assortment to offer to customers so that the expected revenue is maximized. We show that, under the Cross-Nested Logit model, the assortment problem is NP-hard, even without any constraints. To tackle the assortment optimization problem, we develop a new discretization mechanism to approximate the problem by a linear fractional program with a performance guarantee of 1ϵ1+ϵ\frac{1 - \epsilon}{1+\epsilon}, for any accuracy level ϵ>0\epsilon>0. We then show that optimal solutions to the approximate problem can be obtained by solving mixed-integer linear programs. We further show that our discretization approach can also be applied to solve a joint assortment optimization and pricing problem, as well as an assortment problem under a mixture of Cross-Nested Logit models to account for multiple classes of customers. Our empirical results on a large number of randomly generated test instances demonstrate that, under a performance guarantee of 90%, the percentage gaps between the objective values obtained from our approximation methods and the optimal expected revenues are no larger than 1.2%

    A novel graph-based method for clustering human activities

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    Limit theorems for non-Markovian and fractional processes

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    This thesis examines various non-Markovian and fractional processes---rough volatility models, stochastic Volterra equations, Wiener chaos expansions---through the prism of asymptotic analysis. Stochastic Volterra systems serve as a conducive framework encompassing most rough volatility models used in mathematical finance. In Chapter 2, we provide a unified treatment of pathwise large and moderate deviations principles for a general class of multidimensional stochastic Volterra equations with singular kernels, not necessarily of convolution form. Our methodology is based on the weak convergence approach by Budhiraja, Dupuis and Ellis. This powerful approach also enables us to investigate the pathwise large deviations of families of white noise functionals characterised by their Wiener chaos expansion as~Xε=n=0εnIn(fnε).X^\varepsilon = \sum_{n=0}^{\infty} \varepsilon^n I_n \big(f_n^{\varepsilon} \big). In Chapter 3, we provide sufficient conditions for the large deviations principle to hold in path space, thereby refreshing a problem left open By Pérez-Abreu (1993). Hinging on analysis on Wiener space, the proof involves describing, controlling and identifying the limit of perturbed multiple stochastic integrals. In Chapter 4, we come back to mathematical finance via the route of Malliavin calculus. We present explicit small-time formulae for the at-the-money implied volatility, skew and curvature in a large class of models, including rough volatility models and their multi-factor versions. Our general setup encompasses both European options on a stock and VIX options. In particular, we develop a detailed analysis of the two-factor rough Bergomi model. Finally, in Chapter 5, we consider the large-time behaviour of affine stochastic Volterra equations, an under-developed area in the absence of Markovianity. We leverage on a measure-valued Markovian lift introduced by Cuchiero and Teichmann and the associated notion of generalised Feller property. This setting allows us to prove the existence of an invariant measure for the lift and hence of a stationary distribution for the affine Volterra process, featuring in the rough Heston model.Open Acces

    Discovering the hidden structure of financial markets through bayesian modelling

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    Understanding what is driving the price of a financial asset is a question that is currently mostly unanswered. In this work we go beyond the classic one step ahead prediction and instead construct models that create new information on the behaviour of these time series. Our aim is to get a better understanding of the hidden structures that drive the moves of each financial time series and thus the market as a whole. We propose a tool to decompose multiple time series into economically-meaningful variables to explain the endogenous and exogenous factors driving their underlying variability. The methodology we introduce goes beyond the direct model forecast. Indeed, since our model continuously adapts its variables and coefficients, we can study the time series of coefficients and selected variables. We also present a model to construct the causal graph of relations between these time series and include them in the exogenous factors. Hence, we obtain a model able to explain what is driving the move of both each specific time series and the market as a whole. In addition, the obtained graph of the time series provides new information on the underlying risk structure of this environment. With this deeper understanding of the hidden structure we propose novel ways to detect and forecast risks in the market. We investigate our results with inferences up to one month into the future using stocks, FX futures and ETF futures, demonstrating its superior performance according to accuracy of large moves, longer-term prediction and consistency over time. We also go in more details on the economic interpretation of the new variables and discuss the created graph structure of the market.Open Acces

    Moduli Stabilisation and the Statistics of Low-Energy Physics in the String Landscape

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    In this thesis we present a detailed analysis of the statistical properties of the type IIB flux landscape of string theory. We focus primarily on models constructed via the Large Volume Scenario (LVS) and KKLT and study the distribution of various phenomenologically relevant quantities. First, we compare our considerations with previous results and point out the importance of Kähler moduli stabilisation, which has been neglected in this context so far. We perform different moduli stabilisation procedures and compare the resulting distributions. To this end, we derive the expressions for the gravitino mass, various quantities related to axion physics and other phenomenologically interesting quantities in terms of the fundamental flux dependent quantities gsg_s, W0W_0 and n\mathfrak{n}, the parameter which specifies the nature of the non-perturbative effects. Exploiting our knowledge of the distribution of these fundamental parameters, we can derive a distribution for all the quantities we are interested in. For models that are stabilised via LVS we find a logarithmic distribution, whereas for KKLT and perturbatively stabilised models we find a power-law distribution. We continue by investigating the statistical significance of a newly found class of KKLT vacua and present a search algorithm for such constructions. We conclude by presenting an application of our findings. Given the mild preference for higher scale supersymmetry breaking, we present a model of the early universe, which allows for additional periods of early matter domination and ultimately leads to rather sharp predictions for the dark matter mass in this model. We find the dark matter mass to be in the very heavy range mχ10101011 GeVm_{\chi}\sim 10^{10}-10^{11}\text{ GeV}

    Investigation of microparticle behavior in Newtonian, viscoelastic, and shear-thickening flows in straight microchannels

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    Sorting and separation of small substances such as cells, microorganisms, and micro- and nano-particles from a heterogeneous mixture is a common sample preparation step in many areas of biology, biotechnology, and medicine. Portability and inexpensive design of microfluidic-based sorting systems have benefited many of these biomedical applications. Accordingly, we have investigated microparticle hydrodynamics in fluids with various rheological behaviors (i.e., Newtonian, shear-thinning viscoelastic and shear-thickening non-Newtonian) flowing in straight microchannels. Numerical models were developed to simulate particles trajectories in Newtonian water and shear-thinning polyethylene oxide (PEO) solutions. The validated models were then used to perform numerical parametric studies and non-dimensional analysis on the Newtonian inertia-magnetic and shear-thinning elasto-inertal focusing regimes. Finally, the straight microfluidic device that was tested for Newtonian water and shear-thinning viscoelastic PEO solution, were adopted to experimentally study microparticle behavior in SiO2/Water shear-thickening nanofluid

    Simulation and Optimization of Scheduling Policies in Dynamic Stochastic Resource-Constrained Multi-Project Environments

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    The goal of the Project Management is to organise project schedules to complete projects before their completion dates, specified in their contract. When a project is beyond its completion date, organisations may lose the rewards from project completion as well as their organisational prestige. Project Management involves many uncertain factors such as unknown new project arrival dates and unreliable task duration predictions, which may affect project schedules that lead to delivery overruns. Successful Project Management could be done by considering these uncertainties. In this PhD study, we aim to create a more comprehensive model which considers a system where projects (of multiple types) arrive at random to the resource-constrained environment for which rewards for project delivery are impacted by fees for late project completion and tasks may complete sooner or later than expected task duration. In this thesis, we considered two extensions of the resource-constrained multi-project scheduling problem (RCMPSP) in dynamic environments. RCMPSP requires scheduling tasks of multiple projects simultaneously using a pool of limited renewable resources, and its goal usually is the shortest make-span or the highest profit. The first extension of RCMPSP is the dynamic resource-constrained multi-project scheduling problem. Dynamic in this problem refers that new projects arrive randomly during the ongoing project execution, which disturbs the existing project scheduling plan. The second extension of RCMPSP is the dynamic and stochastic resource-constrained multi-project scheduling problem. Dynamic and stochastic represent that both random new projects arrivals and stochastic task durations. In these problems, we assumed that projects generate rewards at their completion; completions later than a due date cause tardiness costs, and we seek to maximise average profits per unit time or the expected discounted long-run profit. We model these problems as infinite-horizon discrete-time Markov decision processes
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