KV
K. Veerkamp
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1
In his paper "Group C*-algebras without the completely bounded approximation property", Haagerup proves several important results about the weak amenability of locally compact groups. Among these, is the result that a lattice in a second-countable, unimodular, locally compact group is weakly amenable if and only if the surrounding group itself is weakly amenable. A key ingredient in his proof is a method of using (linear) completely bounded Fourier multipliers on the lattice to construct (linear) completely bounded Fourier multipliers on the surrounding group. We use a similar approach to construct multilinear completely bounded Fourier multipliers on the group from multilinear completely bounded Fourier multipliers on the lattice. Our construction is both bounded in the norm of completely bounded Fourier multipliers and preserves uniform convergence on compact sets for bounded nets. We also prove an equivalent characterization of weak amenability where the Fourier algebra is replaced by the space of continuous and compactly supported $n$-linear Fourier multiplier symbols.
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In his paper "Group C*-algebras without the completely bounded approximation property", Haagerup proves several important results about the weak amenability of locally compact groups. Among these, is the result that a lattice in a second-countable, unimodular, locally compact group is weakly amenable if and only if the surrounding group itself is weakly amenable. A key ingredient in his proof is a method of using (linear) completely bounded Fourier multipliers on the lattice to construct (linear) completely bounded Fourier multipliers on the surrounding group. We use a similar approach to construct multilinear completely bounded Fourier multipliers on the group from multilinear completely bounded Fourier multipliers on the lattice. Our construction is both bounded in the norm of completely bounded Fourier multipliers and preserves uniform convergence on compact sets for bounded nets. We also prove an equivalent characterization of weak amenability where the Fourier algebra is replaced by the space of continuous and compactly supported $n$-linear Fourier multiplier symbols.
Student report
(2023)
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R.S. Raghav Shankar, M.M. Glaser, K. Veerkamp, L.C. Ottevanger, Amir Niknam, B.J.E. de Bruin
Currently, there is not a clear and well-defined metric available that can be used to measure safety and in turn justify resource allocation within the police Department. This metric will help decision-makers understand the situation better prior to taking major decisions. The large amount of data available to the police is not yet used to its full potential when making these critical decisions. This project aims to translate and quantify the qualitative concept of safety by relying on measurable values found in the Netherlands. The creation of this metric will successfully allow the police to compare, over time, how police resource allocation and intervention tactics lead to a safer society in the Netherlands. The proposed final equation is put together, combining Crime-Harm Index, Utility, and Effectiveness factor of the police. Each of these individual components of the equation were studied individually and the final equation has been explained and validated with hypothetical values. This leads to a composite safety factor, which is bounded from 0 to 1. The safety factor can be
later visualised, essentially displaying a hot-spot map that updates frequently. This will help the police in determining the effectiveness of their decisions and measure the impact of their interventions to a certain extent. Moving forward, we believe the Dutch National Police should take such a form of measurement into serious consideration, as this equation explores a more holistic representation of safety in Dutch society through various factors ...
later visualised, essentially displaying a hot-spot map that updates frequently. This will help the police in determining the effectiveness of their decisions and measure the impact of their interventions to a certain extent. Moving forward, we believe the Dutch National Police should take such a form of measurement into serious consideration, as this equation explores a more holistic representation of safety in Dutch society through various factors ...
Currently, there is not a clear and well-defined metric available that can be used to measure safety and in turn justify resource allocation within the police Department. This metric will help decision-makers understand the situation better prior to taking major decisions. The large amount of data available to the police is not yet used to its full potential when making these critical decisions. This project aims to translate and quantify the qualitative concept of safety by relying on measurable values found in the Netherlands. The creation of this metric will successfully allow the police to compare, over time, how police resource allocation and intervention tactics lead to a safer society in the Netherlands. The proposed final equation is put together, combining Crime-Harm Index, Utility, and Effectiveness factor of the police. Each of these individual components of the equation were studied individually and the final equation has been explained and validated with hypothetical values. This leads to a composite safety factor, which is bounded from 0 to 1. The safety factor can be
later visualised, essentially displaying a hot-spot map that updates frequently. This will help the police in determining the effectiveness of their decisions and measure the impact of their interventions to a certain extent. Moving forward, we believe the Dutch National Police should take such a form of measurement into serious consideration, as this equation explores a more holistic representation of safety in Dutch society through various factors
later visualised, essentially displaying a hot-spot map that updates frequently. This will help the police in determining the effectiveness of their decisions and measure the impact of their interventions to a certain extent. Moving forward, we believe the Dutch National Police should take such a form of measurement into serious consideration, as this equation explores a more holistic representation of safety in Dutch society through various factors
Bachelor thesis
(2020)
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K. Veerkamp, M.P.T. Caspers, D. Elkouss Coronas, D.C. Gijswijt, B.M. Terhal
Bell inequalities are certain probabilistic inequalities that should hold in the context of quantum measurement under assumption of a local hidden variable model. These inequalities can be violated according to the theory of quantum mechanics and have also been violated experimentally. Bell inequalities were therefore historically used to disprove local hidden variable models as an interpretation of quantum mechanics. An interesting question is to what degree Bell inequalities can be violated according to the theory of quantum mechanics. The degree to which a particular Bell inequality can be violated is quantified by the largest violation of the Bell inequality. A central question we address in this thesis is how large the largest violation can become when considering all possible Bell inequalities. In particular the CHSH-inequality, a well-known Bell inequality, has a largest violation equal to the square root of 2 and we want to find a Bell inequality with largest violation exceeding the square root of 2. This thesis consists of two main parts. In the first part we formally define Bell inequalities and the largest violation and prove several theorems about Bell inequalities. In the second part we search for Bell inequalities with largest violation exceeding the square root of 2. We do this by first approximating the largest violation of a given Bell inequality using numerical optimization. Next, using this approximation, we use numerical optimization to maximize the largest violation. Due to run-time restrictions we were only able to consider Bell inequalities with a relatively small number of terms and were unable to find any among them with largest violation exceeding the square root of 2.
...
Bell inequalities are certain probabilistic inequalities that should hold in the context of quantum measurement under assumption of a local hidden variable model. These inequalities can be violated according to the theory of quantum mechanics and have also been violated experimentally. Bell inequalities were therefore historically used to disprove local hidden variable models as an interpretation of quantum mechanics. An interesting question is to what degree Bell inequalities can be violated according to the theory of quantum mechanics. The degree to which a particular Bell inequality can be violated is quantified by the largest violation of the Bell inequality. A central question we address in this thesis is how large the largest violation can become when considering all possible Bell inequalities. In particular the CHSH-inequality, a well-known Bell inequality, has a largest violation equal to the square root of 2 and we want to find a Bell inequality with largest violation exceeding the square root of 2. This thesis consists of two main parts. In the first part we formally define Bell inequalities and the largest violation and prove several theorems about Bell inequalities. In the second part we search for Bell inequalities with largest violation exceeding the square root of 2. We do this by first approximating the largest violation of a given Bell inequality using numerical optimization. Next, using this approximation, we use numerical optimization to maximize the largest violation. Due to run-time restrictions we were only able to consider Bell inequalities with a relatively small number of terms and were unable to find any among them with largest violation exceeding the square root of 2.